Recent zbMATH articles in MSC 94 https://www.zbmath.org/atom/cc/94 2022-05-16T20:40:13.078697Z Unknown author Werkzeug One hundred prisoners and a lightbulb https://www.zbmath.org/1483.00005 2022-05-16T20:40:13.078697Z "Dehaye, Paul-Olivier" https://www.zbmath.org/authors/?q=ai:dehaye.paul-olivier "Ford, Daniel" https://www.zbmath.org/authors/?q=ai:ford.daniel-j|ford.daniel-k|ford.daniel-a "Segerman, Henry" https://www.zbmath.org/authors/?q=ai:segerman.henry Summary: This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Guarding a subgraph as a tool in pursuit-evasion games https://www.zbmath.org/1483.05101 2022-05-16T20:40:13.078697Z "Bokal, Drago" https://www.zbmath.org/authors/?q=ai:bokal.drago "Jerebic, Janja" https://www.zbmath.org/authors/?q=ai:jerebic.janja Pursuit-evasion games on a reflexive graph $$G$$ are games in which several cops search a graph for a robber. Both characters move along the edges of $$G$$ and the robber is captured if a cop steps on the vertex the intruder is on. This paper studies the idea of guarding a subgraph in a pursuit-evasion game. Guarding a subgraph $$H$$ of $$G$$ is defined as setting up $$H$$ such that if the robber enters $$H$$, he can be instantly captured. In this case, the cop can be thought of as a guard and the robber as an intruder. This paper formally introduces this strategy as an algorithm, proves a characterization of games when a single guard can win against several intruders, and most importantly, it introduces the idea of a robber shadow. This is defined as the maximal set of vertices from which the cop parries the protected subgraph'. This paper shows that this shadow, and thus algorithms for a successful guard and for a successful intruder (if they exist), can be computed in polynomial time. Additionally, it is shown that the shadow functions generalize graph retractions. Reviewer: Solden Stoll (Seattle) On local super antimagic total face coloring and the application in developing a cipher block chaining key https://www.zbmath.org/1483.05140 2022-05-16T20:40:13.078697Z "Dafik" https://www.zbmath.org/authors/?q=ai:dafik.d "Nisviasari, R." https://www.zbmath.org/authors/?q=ai:nisviasari.r "Maryati, T. K." https://www.zbmath.org/authors/?q=ai:maryati.tita-khalis "Agustin, I. H." https://www.zbmath.org/authors/?q=ai:agustin.ika-hesti "Venkatachalam, M." https://www.zbmath.org/authors/?q=ai:venkatachalam.mathiyazhagan Summary: There is a specific complexity in the use of IOT, especially in maintaining a secure data transaction. We need a good cryptosystem, since the best encryption key relays on the management cryptosystem. The biggest problem, then, is how to encrypt the plaintext into a ciphertext as hard as possible. We attempt to use the local super antimagic total face coloring of graph in developing a cipher block chaining key. By a local super antimagic total face coloring, we mean a bijection from the set of vertices, edges, and faces to $$\{1, 2, 3, \dots, |V(G)|+|E(G)|+|F(G)|\}$$ such that any adjacent two faces $$f_1$$ and $$f_2$$ will receive a different weights $$w(f_1) \neq w(f_2)$$ for $$f_1, f_2 \in F(G)$$. If we use the weights as the color of all faces, the local super antimagic total face labeling is said to be a local super antimagic total face coloring. The minimum number possible to color all faces is called the local antimagic total face chromatic number, denoted by $$\gamma latf (G)$$. Once, this resulting coloring in hand, we can develop a cipher block chaining key. Penalising transmission to hubs in scale-free spatial random graphs https://www.zbmath.org/1483.05161 2022-05-16T20:40:13.078697Z "Komjáthy, Júlia" https://www.zbmath.org/authors/?q=ai:komjathy.julia "Lapinskas, John" https://www.zbmath.org/authors/?q=ai:lapinskas.john "Lengler, Johannes" https://www.zbmath.org/authors/?q=ai:lengler.johannes Summary: We study the spread of information in finite and infinite inhomogeneous spatial random graphs. We assume that each edge has a transmission cost that is a product of an i.i.d. random variable $$L$$ and a penalty factor: edges between vertices of expected degrees $$w_1$$ and $$w_2$$ are penalised by a factor of $$(w_1w_2)^{\mu}$$ for all $$\mu > 0$$. We study this process for scale-free percolation, for (finite and infinite) Geometric Inhomogeneous Random Graphs, and for Hyperbolic Random Graphs, all with power law degree distributions with exponent $$\tau > 1$$. For $$\tau < 3$$, we find a threshold behaviour, depending on how fast the cumulative distribution function of $$L$$ decays at zero. If it decays at most polynomially with exponent smaller than $$(3-\tau)/(2\mu)$$ then explosion happens, i.e., with positive probability we can reach infinitely many vertices with finite cost (for the infinite models), or reach a linear fraction of all vertices with bounded costs (for the finite models). On the other hand, if the cdf of $$L$$ decays at zero at least polynomially with exponent larger than $$(3-\tau)/(2\mu)$$, then no explosion happens. This behaviour is arguably a better representation of information spreading processes in social networks than the case without penalising factor, in which explosion always happens unless the cdf of $$L$$ is doubly exponentially flat around zero. Finally, we extend the results to other penalty functions, including arbitrary polynomials in $$w_1$$ and $$w_2$$. In some cases the interesting phenomenon occurs that the model changes behaviour (from explosive to conservative and vice versa) when we reverse the role of $$w_1$$ and $$w_2$$. Intuitively, this could corresponds to reversing the flow of information: gathering information might take much longer than sending it out. Two-point AG codes from the Beelen-Montanucci maximal curve https://www.zbmath.org/1483.11126 2022-05-16T20:40:13.078697Z "Landi, Leonardo" https://www.zbmath.org/authors/?q=ai:landi.leonardo "Vicino, Lara" https://www.zbmath.org/authors/?q=ai:vicino.lara Summary: In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a lower bound on the minimum distance of such codes. AG codes with better parameters with respect to comparable two-point codes from the Garcia-Güneri-Stichtenoth (GGS) curve are discovered. Rotated $$D_n$$-lattices in dimensions power of 3 https://www.zbmath.org/1483.11135 2022-05-16T20:40:13.078697Z "Ferrari, Agnaldo J." https://www.zbmath.org/authors/?q=ai:ferrari.agnaldo-jose "Jorge, Grasiele C." https://www.zbmath.org/authors/?q=ai:jorge.grasiele-cristiane "de Andrade, Antonio A." https://www.zbmath.org/authors/?q=ai:de-andrade.antonio-aparecido Summary: In this work, we present constructions of families of rotated $$D_n$$-lattices which may be good for signal transmission over both Gaussian and Rayleigh fading channels. The lattices are obtained as sublattices of a family of rotated $$\mathbb{Z} \oplus \mathcal{A}_2^k$$ lattices, where $$\mathcal{A}_2^k$$ is a direct sum of $$k=\frac{3^{r-1}-1}{2}$$ copies of the $$A_2$$-lattice, using free $$\mathbb{Z}$$-modules in $$\mathbb{Z}[\zeta_{3^r}+\zeta_{3^r}^{-1}]$$. New results on quasi-subfield polynomials https://www.zbmath.org/1483.11258 2022-05-16T20:40:13.078697Z "Euler, Marie" https://www.zbmath.org/authors/?q=ai:euler.marie "Petit, Christophe" https://www.zbmath.org/authors/?q=ai:petit.christophe.1 Quasi-subfield polynomials have been introduced recently in the context of the discrete logarithm problem for elliptic curves over an extension field~$$\mathbb F_{q^n}$$. They generalize subfield polynomials $$X^{q^m} \!-\! X$$, whose roots form the subfield~$$\mathbb F_{q^m}$$ if $$m \mid n$$, to polynomials of the form $$X^{q^m} \!-\! \lambda$$ with~$$\lambda$$ a polynomial of low degree, such that it splits (almost) completely over~$$\mathbb F_{q^n}$$ even if $$m \nmid n$$. The zero set of such a polynomial has been proposed for an index calculus factor base, as an alternative to a subfield or a vector space as in previous algorithms. The paper at hand investigates properties and constructions of quasi-subfield polynomials further. For~$$p$$ a prime, it is shown that for any polynomial $$X^{p^m} \!-\! \lambda$$ that completely splits over~$$\mathbb F_{p^n}$$ and has a linearized polynomial~$$\lambda$$, there holds $$\beta \mathrel {\mathop :} = \frac {\ell n} {m^2} \ge \frac 3 4$$ where $$\ell \mathrel {\mathop :} = \log_p \deg \lambda$$, a bound that is matched e.g.\ by $$X\smash{^{p^2}} \!+\! X^p \!+\! X$$ over~$$\mathbb F_{p^3}$$. The proof proceeds by examining (conjugated) powers of certain companion matrices. Furthermore, new families of quasi-subfield polynomials are constructed whose roots form either an additive or a multiplicative subgroup. Finally, the impact of quasi-subfield polynomials with parameter~$$\beta$$ on the elliptic curve discrete logarithm problem is discussed. The analysis suggests that, unless algorithmic improvements for solving sparse polynomial systems occur, the proposed approach beats generic algorithms only if $$\beta < 0.103$$, which is out of reach by current construction methods. Reviewer: Jens Zumbrägel (Passau) Further factorization of $$x^n-1$$ over a finite field. II https://www.zbmath.org/1483.11259 2022-05-16T20:40:13.078697Z "Wu, Yansheng" https://www.zbmath.org/authors/?q=ai:wu.yansheng "Yue, Qin" https://www.zbmath.org/authors/?q=ai:yue.qin On the infiniteness of a family of APN functions https://www.zbmath.org/1483.11261 2022-05-16T20:40:13.078697Z "Bartoli, Daniele" https://www.zbmath.org/authors/?q=ai:bartoli.daniele "Calderini, Marco" https://www.zbmath.org/authors/?q=ai:calderini.marco "Polverino, Olga" https://www.zbmath.org/authors/?q=ai:polverino.olga "Zullo, Ferdinando" https://www.zbmath.org/authors/?q=ai:zullo.ferdinando Summary: APN functions play a fundamental role in cryptography against attacks on block ciphers. Several families of quadratic APN functions have been proposed in the recent years, whose construction relies on the existence of specific families of polynomials. A key question connected with such constructions is to determine whether such APN functions exist for infinitely many dimensions or do not. In this paper we consider a family of functions recently introduced by \textit{K. Li} et al. [Two new infinite classes of APN functions'', Preprint, \url{arXiv:2105.08464}] showing that for any dimension $$m \geq 3$$ there exists an APN function belonging to such a family. Our main result is proved by a combination of different techniques arising from both algebraic varieties over finite fields connected with linearized permutation rational functions and partial vector space partitions, together with investigations on the kernels of linearized polynomials. New P$$c$$N and AP$$c$$N functions over finite fields https://www.zbmath.org/1483.11263 2022-05-16T20:40:13.078697Z "Wu, Yanan" https://www.zbmath.org/authors/?q=ai:wu.yanan "Li, Nian" https://www.zbmath.org/authors/?q=ai:li.nian "Zeng, Xiangyong" https://www.zbmath.org/authors/?q=ai:zeng.xiangyong Functions with low differential uniformity over finite fields have been widely investigated because of their applications in cryptography. Classically, the differential uniformity of $$f:\mathbb{F}_{p^n}\rightarrow \mathbb{F}_{p^n}$$ is defined as the maximum of the quantities $\#\{x \in \mathbb{F}_{p^n}\,:\, f(x+a)-f(x)=b \},$ with $$a,b$$ ranging in $$\mathbb{F}_{p^n}.$$ Recently, inspired from the development of a new differential attack, Ellingsen et al. proposed a new type of differential uniformity (the so called c-differential uniformity), replacing the above mentioned quantity with $\#\{ x \in \mathbb{F}_{p^n}\,:\, f(x+a)-cf(x)=b \},$ where $$c\in \mathbb{F}_{p^n}$$. In this paper, the authors propose two classes of functions with $$c$$-differential uniformity 1 and three classes of functions with $$c$$-differential uniformity 2. The main tools are the AGW criterion, the cyclotomic technique and the switching method. Reviewer: Marco Timpanella (Perugia) Faster cofactorization with ECM using mixed representations https://www.zbmath.org/1483.11264 2022-05-16T20:40:13.078697Z "Bouvier, Cyril" https://www.zbmath.org/authors/?q=ai:bouvier.cyril "Imbert, Laurent" https://www.zbmath.org/authors/?q=ai:imbert.laurent Summary: This paper introduces a novel implementation of the elliptic curve factoring method specifically designed for medium-size integers such as those arising by billions in the cofactorization step of the Number Field Sieve. In this context, our algorithm requires fewer modular multiplications than any other publicly available implementation. The main ingredients are: the use of batches of primes, fast point tripling, optimal double-base decompositions and Lucas chains, and a good mix of Edwards and Montgomery representations. For the entire collection see [Zbl 1481.94004]. The hulls of matrix-product codes over commutative rings and applications https://www.zbmath.org/1483.14047 2022-05-16T20:40:13.078697Z "Deajim, Abdulaziz" https://www.zbmath.org/authors/?q=ai:deajim.abdulaziz "Bouye, Mohamed" https://www.zbmath.org/authors/?q=ai:bouye.mohamed "Guenda, Kenza" https://www.zbmath.org/authors/?q=ai:guenda.kenza This paper explores the hull of the matrix product codes over a commutative ring. For a matrix product code $$[\mathcal{C}_1, \cdots, \mathcal{C}_s]A$$ where $$\mathcal{C}_{1}, \cdots, \mathcal{C}_s$$ and linear codes of the same length and A a given matrix, some connections between the hull of $$[\mathcal{C}_{1}, \cdots, \mathcal{C}_s]A$$ and the hull of $$\mathcal{C}_{1}, \cdots, \mathcal{C}_s$$ are provided. This allowed to give some necessary and sufficient conditions for a matrix-product codes to be LCD. Under some assumptions, LCD matrix product codes over the residue field of a finite chain are provided by using torsion codes and the existence of asymptotically good sequences of LCD matrix product codes over finite chain ring is proved. Reviewer: Joël Kabore (Ouagadougou) Enumeration of some matrices and free linear codes over commutative finite local rings https://www.zbmath.org/1483.15024 2022-05-16T20:40:13.078697Z "Sirisuk, Siripong" https://www.zbmath.org/authors/?q=ai:sirisuk.siripong This work generalizes results of \textit{K. Abdel-Ghaffar} [Linear Algebra Appl. 436, No. 7, 2665--2669 (2012; Zbl 1236.15043)], who enumerated $$m\times n$$ matrices of rank $$r$$ over finite fields having a given number of rows of single unit. A vector of single unit is a vector with exactly one entry equal to a unit and all other entires equal to $$0$$. In this article, the setting is generalized to finite commutative local rings $$R$$. Such rings have the advantage that one can work in the residue field and lift the enumeration results back to $$R$$ with some modifications. The author enumerates the number of $$m\times n$$ matrices of McCoy rank $$r$$ (see [\textit{N. H. McCoy} [Rings and ideals. La Salle, IL: Open Court Publishing (1948; Zbl 0041.36406)]) over $$R$$ with exactly $$k$$ rows of unit weight and, furthermore, counts the number of free linear codes of $$R^n$$ of rank $$r$$ containing exactly $$k$$ standard basis vectors. Free linear codes of $$R^n$$ are free submodules of $$R^n$$. The formulae for these two enumeration problems closely resemble their finite field counterparts. Reviewer: Joshua Maglione (Bielefeld) The projective symmetry group of a finite frame https://www.zbmath.org/1483.20026 2022-05-16T20:40:13.078697Z "Chien, Tuan-Yow" https://www.zbmath.org/authors/?q=ai:chien.tuan-yow "Waldron, Shayne" https://www.zbmath.org/authors/?q=ai:waldron.shayne-f-d Summary: We define the \textit{projective symmetry group} of a finite sequence of vectors (a frame) in a natural way as a group of permutations on the vectors (or their indices). This definition ensures that the projective symmetry group is the same for a frame and its complement. We give an algorithm for computing the projective symmetry group from a small set of projective invariants when the underlying field is a subfield of $$\mathbb{C}$$ which is closed under conjugation. This algorithm is applied in a number of examples including equiangular lines (in particular SICs), MUBs, and harmonic frames. A new refinement of Jensen's inequality with applications in information theory https://www.zbmath.org/1483.26020 2022-05-16T20:40:13.078697Z "Xiao, Lei" https://www.zbmath.org/authors/?q=ai:xiao.lei "Lu, Guoxiang" https://www.zbmath.org/authors/?q=ai:lu.guoxiang Summary: In this paper, we present a new refinement of Jensen's inequality with applications in information theory. The refinement of Jensen's inequality is obtained based on the general functional in the work of Popescu et al. As the applications in information theory, we provide new tighter bounds for Shannon's entropy and some $$f$$-divergences. Existence and uniqueness of an entropy solution for a nonlinear reaction-diffusion system applied to texture analysis https://www.zbmath.org/1483.35114 2022-05-16T20:40:13.078697Z "Zirhem, Mariam" https://www.zbmath.org/authors/?q=ai:zirhem.mariam "Alaa, Nour Eddine" https://www.zbmath.org/authors/?q=ai:eddine-alaa.nour|alaa.noureddine Summary: Texture analysis is one of the most important tasks in image processing that refers to a class of mathematical models, which characterize the spatial variations of an image. In order to extract features of interest, we propose a new coupled reaction-diffusion system that results from a non linear minimization problem. New techniques and approaches are used to establish existence and uniqueness of an entropy solution of the proposed system. Parameter-free quantification of stochastic and chaotic signals https://www.zbmath.org/1483.37097 2022-05-16T20:40:13.078697Z "Lopes, S. R." https://www.zbmath.org/authors/?q=ai:lopes.sergio-roberto "Prado, T. L." https://www.zbmath.org/authors/?q=ai:prado.t-l "Corso, G." https://www.zbmath.org/authors/?q=ai:corso.gilberto "dos S. Lima, G. Z." https://www.zbmath.org/authors/?q=ai:dos-s-lima.g-z "Kurths, J." https://www.zbmath.org/authors/?q=ai:kurths.jurgen Summary: Recurrence entropy $$(\mathcal{S})$$ is a novel time series quantifier based on recurrence microstates. Here we show for the first time that $$\max(\mathcal{S})$$ can be used as a \textit{parameter-free} quantifier of short and long-term memories (time-correlations) of stochastic and chaotic signals. $$\max(\mathcal{S})$$ can also evaluate properties of the distribution function of the data set that are not related to time correlation. To illustrate this fact, we show that even shuffled versions of distinct time correlated stochastic signals lead to different, but coherently varying, values of $$\max(\mathcal{S})$$. Such a property of $$\max(\mathcal{S})$$ is associated to its ability to quantify in how many ways distinct short recurrence sequences can be found in time series. Applied to a deterministic dissipative system, the method brings evidence about the attractor properties and the degree of chaoticity. We conclude that the development of a new parameter-free quantifier of stochastic and chaotic time series can open new perspectives to stochastic data and deterministic time series analyses and may find applications in many areas of science. D'oh! Fourier. Theory, applications, and derivatives https://www.zbmath.org/1483.42001 2022-05-16T20:40:13.078697Z "Nixon, Mark" https://www.zbmath.org/authors/?q=ai:nixon.mark-r|nixon.mark-s Publisher's description: D'oh! Fourier introduces the Fourier transform and is aimed at undergraduates in Computer Science, Mathematics, and Applied Sciences, as well as for those wishing to extend their education. Formulated around ten key points, this accessible book is light-hearted and illustrative, with many applications. The basis and deployment of the Fourier transform are covered applying real-world examples throughout inductively rather than the theoretical approach deductively. The key components of the textbook are continuous signals analysis, discrete signals analysis, image processing, applications of Fourier analysis, together with the origin and nature of the transform itself. D'oh! Fourier is reproducible via MATLAB/Octave and is supported by a comprehensive website which provides the code contained within the book. Signal analysis using Born-Jordan-type distributions https://www.zbmath.org/1483.42004 2022-05-16T20:40:13.078697Z "Cordero, Elena" https://www.zbmath.org/authors/?q=ai:cordero.elena "de Gosson, Maurice" https://www.zbmath.org/authors/?q=ai:de-gosson.maurice-a "Dörfler, Monika" https://www.zbmath.org/authors/?q=ai:dorfler.monika "Nicola, Fabio" https://www.zbmath.org/authors/?q=ai:nicola.fabio The Chapter contains results concerning recent advances in signal theory using time-frequency distributions. The authors demonstrate that some new members of the Cohen class that generalize the Wigner distribution are useful in damping artefacts in certain signals. Main properties as well as drawbacks are presented. Last but not least, several open problems are also discussed. For the entire collection see [Zbl 1470.42002]. Reviewer: Liviu Goraş (Iaşi) An epigraphical approach to the representer theorem https://www.zbmath.org/1483.52007 2022-05-16T20:40:13.078697Z "Duval, Vincent" https://www.zbmath.org/authors/?q=ai:duval.vincent A new principle meant to describe solutions to convex variational problems involving finitely many measurements is proposed by means of an epigraphical approach to the celebrated representer theorem. The optimality of the new method is analyzed on several problems concerning the recovery of Radon measures. An appendix with several additional results closes the paper. Reviewer: Sorin-Mihai Grad (Paris) Application of Kähler manifold to signal processing and Bayesian inference https://www.zbmath.org/1483.53121 2022-05-16T20:40:13.078697Z "Choi, Jaehyung" https://www.zbmath.org/authors/?q=ai:choi.jaehyung "Mullhaupt, Andrew P." https://www.zbmath.org/authors/?q=ai:mullhaupt.andrew-p Summary: We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such as $$\alpha$$-divergence, information distance and the dual $$\alpha$$-connection structure. The Kähler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the $$\alpha$$-generalization of the geometric objects. The Laplace-Beltrami operator is also simplified in the Kähler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the Kähler structure. For the entire collection see [Zbl 1470.00021]. Universality of approximate message passing algorithms https://www.zbmath.org/1483.60007 2022-05-16T20:40:13.078697Z "Chen, Wei-Kuo" https://www.zbmath.org/authors/?q=ai:chen.wei-kuo "Lam, Wai-Kit" https://www.zbmath.org/authors/?q=ai:lam.wai-kit Summary: We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an $$n\times n$$ random symmetric matrix $$A$$. We establish universality in noise for this AMP in the $$n$$-limit and validate this behavior in a number of AMPs popularly adapted in compressed sensing, statistical inferences, and optimizations in spin glasses. Debruijn identities: from Shannon, Kullback-Leibler and Fisher to generalized $$\phi$$-entropies, $$\phi$$-divergences and $$\phi$$-Fisher informations https://www.zbmath.org/1483.62008 2022-05-16T20:40:13.078697Z "Zozor, Steeve" https://www.zbmath.org/authors/?q=ai:zozor.steeve "Brossier, Jean-Marc" https://www.zbmath.org/authors/?q=ai:brossier.jean-marc Summary: In this paper we propose a generalization of the usual deBruijn identity that links the Shannon differential entropy (or the Kullback-Leibler divergence) and the Fisher information (or the Fisher divergence) of the output of a Gaussian channel. The generalization makes use of $$\phi$$-entropies on the one hand, and of $$\phi$$-divergences (of the Csiza'r class) on the other hand, as generalizations of the Shannon entropy and of the Kullback-Leibler divergence respectively. The generalized deBruijn identities induce the definition of generalized Fisher informations and generalized Fisher divergences; some of such generalizations exist in the literature. Moreover, we provide results that go beyond the Gaussian channel: we are then able to characterize a noisy channel using general measures of mutual information, both for Gaussian and non-Gaussian channels. For the entire collection see [Zbl 1470.00021]. Bayesian or Laplacien inference, entropy and information theory and information geometry in data and signal processing https://www.zbmath.org/1483.62011 2022-05-16T20:40:13.078697Z "Mohammad-Djafari, Ali" https://www.zbmath.org/authors/?q=ai:mohammad-djafari.ali Summary: The main object of this tutorial article is first to review the main inference tools using Bayesian approach, Entropy, Information theory and their corresponding geometries. This review is focused mainly on the ways these tools have been used in data, signal and image processing. After a short introduction of the different quantities related to the Bayes rule, the entropy and the Maximum Entropy Principle (MEP), relative entropy and the Kullback-Leibler divergence, Fisher information, we will study their use in different fields of data and signal processing such as: entropy in source separation, Fisher information in model order selection, different Maximum Entropy based methods in time series spectral estimation and finally, general linear inverse problems. For the entire collection see [Zbl 1470.00021]. Shannon's formula and Hartley's rule: a mathematical coincidence? https://www.zbmath.org/1483.62065 2022-05-16T20:40:13.078697Z "Rioul, Olivier" https://www.zbmath.org/authors/?q=ai:rioul.olivier "Magossi, José Carlos" https://www.zbmath.org/authors/?q=ai:magossi.jose-carlos Summary: \textit{Shannon's formula} $$C = \frac{1}{2} \log(1+P/N)$$ is the emblematic expression for the information capacity of a communication channel. Hartley's name is often associated with it, owing to \textit{Hartley's rule:} counting the highest possible number of distinguishable values for a given amplitude $$A$$ and precision $$\pm \Delta$$ yields a similar expression $$C' = \log(1+A/\Delta)$$. In the information theory community, the following historical'' statements are generally well accepted: (1) Hartley put forth his rule twenty years before Shannon; (2) Shannon's formula as a fundamental tradeoff between transmission rate, bandwidth, and signal-to-noise ratio came unexpected in 1948; (3) Hartley's rule is an imprecise relation while Shannon's formula is exact; (4) Hartley's expression is not an appropriate formula for the capacity of a communication channel. We show that all these four statements are questionable, if not wrong. For the entire collection see [Zbl 1470.00021]. What is resolution? A statistical minimax testing perspective on superresolution microscopy https://www.zbmath.org/1483.62117 2022-05-16T20:40:13.078697Z "Kulaitis, Gytis" https://www.zbmath.org/authors/?q=ai:kulaitis.gytis "Munk, Axel" https://www.zbmath.org/authors/?q=ai:munk.axel "Werner, Frank" https://www.zbmath.org/authors/?q=ai:werner.frank.1 The authors suggest a statistical description, which allows one to understand both the effect of the experimental setup and the random nature of photon counts on the resulting resolution. On the one hand, for Poisson measurements, they get linear dependence of the (minimax) detection boundary on the full width at half maximum (FWHM) and on the other hand, for a homogeneous Gaussian model the dependence of resolution is nonlinear. They conclude that at small physical scales modeling by homogeneous Gaussians is inadequate. In comparison to the Poisson model, that seems to provide a statistically sound description of resolution at the nanoscale. Their theory seems to be also applicable to other imaging setups. Reviewer: Makrina Agaoglou (Bristol) Novel mathematics inspired by industrial challenges https://www.zbmath.org/1483.65008 2022-05-16T20:40:13.078697Z Publisher's description: This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics. The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields. The articles of this volume will be reviewed individually. Interpolation and sampling with exponential splines of real order https://www.zbmath.org/1483.65025 2022-05-16T20:40:13.078697Z "Massopust, Peter" https://www.zbmath.org/authors/?q=ai:massopust.peter-r Summary: The existence of fundamental cardinal exponential B-splines of positive real order $$\sigma$$ is established subject to two conditions on $$\sigma$$ and their construction is implemented. A sampling result for these fundamental cardinal exponential B-splines is also presented. The gap between theory and practice in function approximation with deep neural networks https://www.zbmath.org/1483.65028 2022-05-16T20:40:13.078697Z "Adcock, Ben" https://www.zbmath.org/authors/?q=ai:adcock.ben "Dexter, Nick" https://www.zbmath.org/authors/?q=ai:dexter.nick-c Reversible interpolation of vectorial images by an anisotropic diffusion-projection PDE https://www.zbmath.org/1483.65034 2022-05-16T20:40:13.078697Z "Roussos, Anastasios" https://www.zbmath.org/authors/?q=ai:roussos.anastasios "Maragos, Petros" https://www.zbmath.org/authors/?q=ai:maragos.petros Summary: In this paper, a nonlinear model for the interpolation of vector-valued images is proposed. This model is based on an anisotropic diffusion PDE and performs an interpolation that is reversible. The interpolation solution is restricted to the subspace of functions that can recover the discrete input image, after an appropriate smoothing and sampling. The proposed nonlinear diffusion flow lies on this subspace while its strength and anisotropy adapt to the local variations and geometry of image structures. The derived method effectively reconstructs the real image structures and yields a satisfactory interpolation result. Compared to classic and other existing PDE-based interpolation methods, our proposed method seems to increase the accuracy of the result and to reduce the undesirable artifacts, such as blurring, ringing, block effects and edge distortion. We present extensive experimental results that demonstrate the potential of the method as applied to graylevel and color images. PRP-like algorithm for monotone operator equations https://www.zbmath.org/1483.65090 2022-05-16T20:40:13.078697Z "Abubakar, Auwal Bala" https://www.zbmath.org/authors/?q=ai:bala-abubakar.auwal "Kumam, Poom" https://www.zbmath.org/authors/?q=ai:kumam.poom "Mohammad, Hassan" https://www.zbmath.org/authors/?q=ai:mohammad.hassan "Ibrahim, Abdulkarim Hassan" https://www.zbmath.org/authors/?q=ai:ibrahim.abdulkarim-hassan Summary: Many studies have been devoted to develop and improve the iterative methods for solving convex constraint nonlinear equations problem (CCP). Based on the projection technique, we introduce a derivative-free method for approximating the solution of CCP. The proposed method is suitable for solving large-scale nonlinear equations due to its lower storage requirements. The directions generated by the proposed method at every iteration are bounded. Under some mild conditions, we establish the global convergence result of the proposed method. Numerical experiments are provided to show the efficiency of the method in solving CCP. Moreover, we tested the capability of the method in solving the monotone nonlinear operator equation equivalent to the $$\ell_1$$-norm regularized minimization problem. An accelerated smoothing gradient method for nonconvex nonsmooth minimization in image processing https://www.zbmath.org/1483.65102 2022-05-16T20:40:13.078697Z "Wang, Weina" https://www.zbmath.org/authors/?q=ai:wang.weina "Chen, Yunmei" https://www.zbmath.org/authors/?q=ai:chen.yunmei Summary: In this paper, we propose a fast and provably convergent smoothing gradient descent type algorithm with extrapolation for solving a general class of nonsmooth and nonconvex inverse problems arising from image processing. Our algorithm has a localizer selective policy to switch between gradient descent scheme with or without extrapolation to possibly speed up the decreasing of the smoothed objective function and ensure the convergence. Moreover, the algorithm adaptively reduces the smoothing factor to guarantee that any accumulation point of the generated sequence is an (affine-scaled) Clarke stationary point of the original nonsmooth and nonconvex problem. Extensive numerical experiments and comparisons indicate the effectiveness of the proposed algorithm in natural image deblurring, CT and MRI reconstruction. A joint reconstruction and lambda tomography regularization technique for energy-resolved x-ray imaging https://www.zbmath.org/1483.65236 2022-05-16T20:40:13.078697Z "Webber, James W." https://www.zbmath.org/authors/?q=ai:webber.james-w "Quinto, Eric Todd" https://www.zbmath.org/authors/?q=ai:quinto.eric-todd "Miller, Eric L." https://www.zbmath.org/authors/?q=ai:miller.eric-l Uniform error estimates for nonequispaced fast Fourier transforms https://www.zbmath.org/1483.65242 2022-05-16T20:40:13.078697Z "Potts, Daniel" https://www.zbmath.org/authors/?q=ai:potts.daniel "Tasche, Manfred" https://www.zbmath.org/authors/?q=ai:tasche.manfred Summary: In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. So far, various window functions have been used and new window functions have recently been proposed. We present novel error estimates for NFFT with compactly supported, continuous window functions and derive rules for convenient choice from the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter. Comments on: A secure anti-collusion data sharing scheme for dynamic groups in the cloud'' https://www.zbmath.org/1483.68023 2022-05-16T20:40:13.078697Z "Wang, Qiang" https://www.zbmath.org/authors/?q=ai:wang.qiang.1 "Zhang, Hao" https://www.zbmath.org/authors/?q=ai:zhang.hao.3|zhang.hao|zhang.hao.2|zhang.hao.4|zhang.hao.1 "Sun, Jianfei" https://www.zbmath.org/authors/?q=ai:sun.jianfei "Xiong, Hu" https://www.zbmath.org/authors/?q=ai:xiong.hu "Qin, Zhiguang" https://www.zbmath.org/authors/?q=ai:qin.zhiguang Summary: Very recently, \textit{Z. Zhu} and \textit{R. Jiang} [A secure anti-collusion data sharing scheme for dynamic groups in the cloud'', IEEE Trans. Parallel Distrib. Syst. 27, No. 1, 40--50 (2016; \url{doi:10.1109/TPDS.2015.2388446})] suggested a secure anti-collusion data sharing scheme for dynamic groups in the cloud. In this letter, we found that Zhu-Jiang's scheme is insecure against forgery attack in registration phase for existing users. Our proposed attack demonstrates that any outside adversary can masquerade as the group manager to issue invalid or expired secret keys to the existing group users. After that, we present our suggestion to tackle the problem without sacrificing any original characters (such as high efficiency and group-dynamicity) of the scheme. The consensus number of a cryptocurrency https://www.zbmath.org/1483.68027 2022-05-16T20:40:13.078697Z "Guerraoui, Rachid" https://www.zbmath.org/authors/?q=ai:guerraoui.rachid "Kuznetsov, Petr" https://www.zbmath.org/authors/?q=ai:kuznetsov.petr "Monti, Matteo" https://www.zbmath.org/authors/?q=ai:monti.matteo "Pavlovic, Matej" https://www.zbmath.org/authors/?q=ai:pavlovic.matej "Seredinschi, Dragos-Adrian" https://www.zbmath.org/authors/?q=ai:seredinschi.dragos-adrian Summary: Many blockchain-based algorithms, such as Bitcoin, implement a decentralized asset transfer system, often referred to as a cryptocurrency. As stated in the original paper by Nakamoto, at the heart of these systems lies the problem of preventing double-spending; this is usually solved by achieving consensus on the order of transfers among the participants. In this paper, we treat the asset transfer problem as a concurrent object and determine its consensus number, showing that consensus is, in fact, not necessary to prevent double-spending. We first consider the problem as defined by Nakamoto, where only a single process -- the account owner -- can withdraw from each account. Safety and liveness need to be ensured for correct account owners, whereas misbehaving account owners might be unable to perform transfers. We show that the consensus number of an asset transfer object is 1. We then consider a more general $$k$$-shared asset transfer object where up to $$k$$ processes can atomically withdraw from the same account, and show that this object has consensus number $$k$$. We establish our results in the context of shared memory with benign faults, allowing us to properly understand the level of difficulty of the asset transfer problem. We also translate these results in the message passing setting with Byzantine players, a model that is more relevant in practice. In this model, we describe an asynchronous Byzantine fault-tolerant asset transfer implementation that is both simpler and more efficient than state-of-the-art consensus-based solutions. Our results are applicable to both the permissioned (private) and permissionless (public) setting, as normally their differentiation is hidden by the abstractions on top of which our algorithms are based. Correction to: The consensus number of a cryptocurrency'' https://www.zbmath.org/1483.68028 2022-05-16T20:40:13.078697Z "Guerraoui, Rachid" https://www.zbmath.org/authors/?q=ai:guerraoui.rachid "Kuznetsov, Petr" https://www.zbmath.org/authors/?q=ai:kuznetsov.petr "Monti, Matteo" https://www.zbmath.org/authors/?q=ai:monti.matteo "Pavlovic, Matej" https://www.zbmath.org/authors/?q=ai:pavlovic.matej "Seredinschi, Dragos-Adrian" https://www.zbmath.org/authors/?q=ai:seredinschi.dragos-adrian From the text: In the original publication of the article [the authors, ibid. 35, No. 1, 1--15 (2022; Zbl 1483.68027)], the title of the article was incorrectly published as The consensus number of a cryptocurrency (extended version)''. The corrected version is The consensus number of a cryptocurrency''. This erratum corrects the same. Equal to the task? https://www.zbmath.org/1483.68043 2022-05-16T20:40:13.078697Z "Heather, James" https://www.zbmath.org/authors/?q=ai:heather.james "Schneider, Steve" https://www.zbmath.org/authors/?q=ai:schneider.steve-a Summary: Many methods of analysing security protocols have been proposed, but most such methods rely on analysing a protocol running only a finite network. Some, however -- notably, data independence, the strand spaces model, and the rank functions model -- can be used to prove correctness of a protocol running on an unbounded network. \textit{A. W. Roscoe} and \textit{P. J. Broadfoot} in [Proving security protocols with model checkers by data independence techniques'', J. Comput. Secur. 7, No. 2--3, 147--190 (1999; \url{doi:10.3233/JCS-1999-72-303})] show how data independence techniques may be used to verify a security protocol running on an unbounded network. They also consider a weakness inherent in the RSA algorithm, discovered by \textit{M. Franklin} and \textit{M. Reiter} [A linear protocol failure for RSA with exponent three'', presented at the Rump Session of Crypto'95, Santa Barbara, CA (1995)], and show that their data independence approach cannot deal with an intruder endowed with the ability to exploit this weakness. In this paper, we show that neither can the use of honest ideals in the strand spaces model or the use of rank functions in the CSP model be easily adapted to cover such an intruder. In each case, the inequality tests required to model the new intruder cause problems when attempting to extend analysis of a finite network to cover an unbounded network. The results suggest that more work is needed on adapting the intruder model to allow for cryptographic attacks. For the entire collection see [Zbl 1014.68936]. A message authentication code based on the composition of universal hash families https://www.zbmath.org/1483.68045 2022-05-16T20:40:13.078697Z "Li, Xue Yuan" https://www.zbmath.org/authors/?q=ai:li.xue-yuan "Wang, Xin Mei" https://www.zbmath.org/authors/?q=ai:wang.xinmei (no abstract) tPAKE: typo-tolerant password-authenticated key exchange https://www.zbmath.org/1483.68048 2022-05-16T20:40:13.078697Z "Pongmorrakot, Thitikorn" https://www.zbmath.org/authors/?q=ai:pongmorrakot.thitikorn "Chatterjee, Rahul" https://www.zbmath.org/authors/?q=ai:chatterjee.rahul Summary: Password-authenticated key exchange (PAKE) enables a user to authenticate to a server by proving the knowledge of the password without actually revealing their password to the server. PAKE protects user passwords from being revealed to an adversary who compromises the server (or a disgruntled employee). Existing PAKE protocols, however, do not allow even a small typographical mistake in the submitted password, such as accidentally adding a character at the beginning or at the end of the password. Logins are rejected for such password submissions; the user has to retype their password and reengage in the PAKE protocol with the server. Prior works have shown that users often make typographical mistakes while typing their passwords. Allowing users to log in with small typographical mistakes would improve the usability of passwords and help users log in faster. Towards this, we introduce tPAKE: a typo-tolerant PAKE, that allows users to authenticate (or exchange high-entropy keys) using a password while tolerating small typographical mistakes. tPAKEallows edit-distance-based errors, but only those that are frequently made by users. This benefits security, while still improving usability. We discuss the security considerations and challenges in designing tPAKE. We implement tPAKE and show that it is computationally feasible to be used in place of traditional PAKEs while providing improved usability. We also provide an extension to tPAKE, called adaptive-tPAKE, that will enable the server to allow a user to log in with their frequent mistakes (without ever learning those mistakes). For the entire collection see [Zbl 1475.68018]. SPEC: an equivalence checker for security protocols https://www.zbmath.org/1483.68050 2022-05-16T20:40:13.078697Z "Tiu, Alwen" https://www.zbmath.org/authors/?q=ai:tiu.alwen-fernanto "Nguyen, Nam" https://www.zbmath.org/authors/?q=ai:nguyen.nam-hoai|nguyen.nam-tuan|nguyen.nam-phuong|nguyen.nam-hai|nguyen.nam-trung|nguyen.nam-ky|nguyen.nam-anh|nguyen.nam-v "Horne, Ross" https://www.zbmath.org/authors/?q=ai:horne.ross Summary: SPEC is an automated equivalence checker for security protocols specified in the spi-calculus, an extension of the pi-calculus with cryptographic primitives. The notion of equivalence considered is a variant of bisimulation, called open bisimulation, that identifies processes indistinguishable when executed in any context. SPEC produces compact and independently checkable bisimulations that are useful for automating the process of producing proof-certificates for security protocols. This paper gives an overview of SPEC and discusses techniques to reduce the size of bisimulations, utilising up-to techniques developed for the spi-calculus. SPEC is implemented in the Bedwyr logic programming language that we demonstrate can be adapted to tackle further protocol analysis problems not limited to bisimulation checking. For the entire collection see [Zbl 1347.68009]. Shorter circuit obfuscation in challenging security models https://www.zbmath.org/1483.68071 2022-05-16T20:40:13.078697Z "Brakerski, Zvika" https://www.zbmath.org/authors/?q=ai:brakerski.zvika "Dagmi, Or" https://www.zbmath.org/authors/?q=ai:dagmi.or Summary: The study of program obfuscation is seeing great progress in recent years, which is crucially attributed to the introduction of graded encoding schemes by \textit{S. Garg} et al. [Lect. Notes Comput. Sci. 7881, 1--17 (2013; Zbl 1300.94055)]. In such schemes, elements of a ring can be encoded such that the content of the encoding is hidden, but restricted algebraic manipulations, followed by zero-testing, can be performed publicly. This primitive currently underlies all known constructions of general-purpose obfuscators. However, the security properties of the current candidate graded encoding schemes are not well understood, and new attacks frequently introduced. It is therefore important to assume as little as possible about the security of the graded encoding scheme, and use as conservative security models as possible. This often comes at a cost of reducing the efficiency or the functionality of the obfuscator. In this work, we present a candidate obfuscator, based on composite-order graded encoding schemes, which obfuscates circuits directly a la [\textit{J. Zimmerman}, Lect. Notes Comput. Sci. 9057, 439--467 (2015; Zbl 1371.68054); \textit{B. Applebaum} and \textit{Z. Brakerski}, Lect. Notes Comput. Sci. 9015, 528--556 (2015; Zbl 1382.94049); J. Cryptology 34, No. 2, Paper No. 14, 41 p. (2021; Zbl 1467.94025)]. Our construction requires a graded encoding scheme with only 3 plaintext slots'' (= sub-rings of the underlying ring), which is directly related to the size and complexity of the obfuscated program. We prove that our obfuscator is superior to previous works in two different security models. \begin{itemize} \item[1.]We prove that our obfuscator is indistinguishability-secure (iO) in the unique representation generic graded encoding model. Previous works either required a composite-order scheme with polynomially many slots, or were provable in a milder security model. This immediately translates to a polynomial improvement in efficiency, and shows that improved security does not come at the cost of efficiency in this case. \item [2.]Following [\textit{S. Badrinarayanan} et al., Lect. Notes Comput. Sci. 9666, 764--791 (2016; Zbl 1371.94622)], we consider a model where finding any non-trivial'' encoding of zero breaks the security of the encoding scheme. We show that, perhaps surprisingly, secure obfuscation is possible in this model even for some classes of non-evasive functions (for example, any class of conjunctions). We define the property required of the function class, formulate an appropriate (generic) security model, and prove that our aforementioned obfuscator is virtual-black-box (VBB) secure in this model. \end{itemize} For the entire collection see [Zbl 1344.94004]. The privacy blanket of the shuffle model https://www.zbmath.org/1483.68100 2022-05-16T20:40:13.078697Z "Balle, Borja" https://www.zbmath.org/authors/?q=ai:balle.borja "Bell, James" https://www.zbmath.org/authors/?q=ai:bell.james-j|bell.james-r|bell.james-f|bell.james-h.1 "Gascón, Adrià" https://www.zbmath.org/authors/?q=ai:gascon.adria "Nissim, Kobbi" https://www.zbmath.org/authors/?q=ai:nissim.kobbi Summary: This work studies differential privacy in the context of the recently proposed shuffle model. Unlike in the local model, where the server collecting privatized data from users can track back an input to a specific user, in the shuffle model users submit their privatized inputs to a server anonymously. This setup yields a trust model which sits in between the classical curator and local models for differential privacy. The shuffle model is the core idea in the encode, shuffle, analyze (ESA) model introduced by \textit{A. Bittau} et al. [Prochlo: strong privacy for analytics in the crowd'', in: Proceedings of the 26th symposium on operating systems principles, SOPS'17. New York, NY: Association for Computing Machinery (ACM). 441--459 (2017; \url{doi:10.1145/3132747.3132769})]. Recent work by \textit{A. Cheu} et al. [Lect. Notes Comput. Sci. 11476, 375--403 (2019; Zbl 1470.94081)] analyzes the differential privacy properties of the shuffle model and shows that in some cases shuffled protocols provide strictly better accuracy than local protocols. Additionally, \textit{Ú. Erlingsson} et al. [in: Proceedings of the 30th annual ACM-SIAM symposium on discrete algorithms, SODA'19. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); New York, NY: Association for Computing Machinery (ACM). 2468--2479 (2019; Zbl 1432.68133)] provide a privacy amplification bound quantifying the level of curator differential privacy achieved by the shuffle model in terms of the local differential privacy of the randomizer used by each user. In this context, we make three contributions. First, we provide an optimal single message protocol for summation of real numbers in the shuffle model. Our protocol is very simple and has better accuracy and communication than the protocols for this same problem proposed by Cheu et al. [loc. cit.]. Optimality of this protocol follows from our second contribution, a new lower bound for the accuracy of private protocols for summation of real numbers in the shuffle model. The third contribution is a new amplification bound for analyzing the privacy of protocols in the shuffle model in terms of the privacy provided by the corresponding local randomizer. Our amplification bound generalizes the results by Erlingsson et al. [loc. cit.] to a wider range of parameters, and provides a whole family of methods to analyze privacy amplification in the shuffle model. For the entire collection see [Zbl 1428.94005]. Output compression, MPC, and iO for Turing machines https://www.zbmath.org/1483.68103 2022-05-16T20:40:13.078697Z "Badrinarayanan, Saikrishna" https://www.zbmath.org/authors/?q=ai:badrinarayanan.saikrishna "Fernando, Rex" https://www.zbmath.org/authors/?q=ai:fernando.rex "Koppula, Venkata" https://www.zbmath.org/authors/?q=ai:koppula.venkata "Sahai, Amit" https://www.zbmath.org/authors/?q=ai:sahai.amit "Waters, Brent" https://www.zbmath.org/authors/?q=ai:waters.brent Summary: In this work, we study the fascinating notion of output-compressing randomized encodings for Turing machines, in a shared randomness model. In this model, the encoder and decoder have access to a shared random string, and the efficiency requirement is, the size of the encoding must be independent of the running time and output length of the Turing machine on the given input, while the length of the shared random string is allowed to grow with the length of the output. We show how to construct output-compressing randomized encodings for Turing machines in the shared randomness model, assuming iO for circuits and any assumption in the set \{LWE, DDH, $$\mathrm{N}^\mathrm{th}$$ Residuosity\}. We then show interesting implications of the above result to basic feasibility questions in the areas of secure multiparty computation (MPC) and indistinguishability obfuscation (iO): \par 1.) Compact MPC for Turing machines in the random oracle model. In the context of MPC, we consider the following basic feasibility question: does there exist a malicious-secure MPC protocol for Turing machines whose communication complexity is independent of the running time and output length of the Turing machine when executed on the combined inputs of all parties? We call such a protocol as a compact MPC protocol. \textit{P. Hubáček} and \textit{D. Wichs} [in: Proceedings of the 6th conference on innovations in theoretical computer science, ITCS'15. New York, NY: Association for Computing Machinery (ACM). 163--172 (2015; Zbl 1364.68201)] showed via an incompressibility argument, that, even for the restricted setting of circuits, it is impossible to construct a malicious secure two party computation protocol in the plain model where the communication complexity is independent of the output length. In this work, we show how to evade this impossibility by compiling any (noncompact) MPC protocol in the plain model to a compact MPC protocol for Turing machines in the random oracle model, assuming output-compressing randomized encodings in the shared randomness model. \par 2.) Succinct iO for Turing machines in the shared randomness model. In all existing constructions of iO for Turing machines, the size of the obfuscated program grows with a bound on the input length. In this work, we show how to construct an iO scheme for Turing machines in the shared randomness model where the size of the obfuscated program is independent of a bound on the input length, assuming iO for circuits and any assumption in the set \{LWE, DDH, $$\mathrm{N}^\mathrm{th}$$ Residuosity\}. For the entire collection see [Zbl 1428.94008]. A view of P systems from information theory https://www.zbmath.org/1483.68128 2022-05-16T20:40:13.078697Z "Sempere, José M." https://www.zbmath.org/authors/?q=ai:sempere.jose-m Summary: In this work we propose new view of P systems by using the framework of information theory. Given a cell-like P system with communication and evolution rules, we analyze the amount of information that it holds as the result of symbol movements across the membranes. Under this approach, we propose new definitions and results related to the information of P systems and their entropy. In addition, we propose a new working manner for P systems based only in the entropy evolution during the computation time. For the entire collection see [Zbl 1358.68015]. How to implement a non-uniform or non-closed shuffle https://www.zbmath.org/1483.68132 2022-05-16T20:40:13.078697Z "Saito, Takahiro" https://www.zbmath.org/authors/?q=ai:saito.takahiro "Miyahara, Daiki" https://www.zbmath.org/authors/?q=ai:miyahara.daiki "Abe, Yuta" https://www.zbmath.org/authors/?q=ai:abe.yuta "Mizuki, Takaaki" https://www.zbmath.org/authors/?q=ai:mizuki.takaaki "Shizuya, Hiroki" https://www.zbmath.org/authors/?q=ai:shizuya.hiroki Summary: Card-based protocols allow to perform secure multiparty computations using a deck of physical cards, and rely on shuffle actions such as the (normal) shuffle, the random cut, and the random bisection cut. A shuffle action is mathematically defined by a pair of a permutation set (which is a subset of the symmetric group) and a probability distribution on it; while one can theoretically consider any shuffle action in mind, he or she may be unable to determine whether it can be easily implemented by human hands. As one of the most general results, Koch and Walzer showed that any uniform closed shuffle (meaning that its permutation set is a subgroup and its distribution is uniform) can be implemented by human hands with the help of additional cards. However, there are several existing protocols which use non-uniform and/or non-closed shuffles. To implement these specific shuffles, Nishimura et al. proposed an idea of using (special) physical cases that can store piles of cards as well as Koch and Walzer proposed an implementation of a specific non-closed shuffle with additional cards. Because their implementations handle a limited class of non-uniform and/or non-closed shuffles, it is still open to find a general method for implementing any shuffle. In this paper, we solve the above problem; we implement any'' shuffle with only additional cards, provided that every probability of its distribution is a rational number. Therefore, our implementation works for any non-closed or non-uniform shuffle (if the distribution is rational as above). For the entire collection see [Zbl 1464.68016]. Adaptively secure MPC with sublinear communication complexity https://www.zbmath.org/1483.68134 2022-05-16T20:40:13.078697Z "Cohen, Ran" https://www.zbmath.org/authors/?q=ai:cohen.ran "Shelat, Abhi" https://www.zbmath.org/authors/?q=ai:shelat.abhi "Wichs, Daniel" https://www.zbmath.org/authors/?q=ai:wichs.daniel Summary: A central challenge in the study of MPC is to balance between security guarantees, hardness assumptions, and resources required for the protocol. In this work, we study the cost of tolerating adaptive corruptions in MPC protocols under various corruption thresholds. In the strongest setting, we consider adaptive corruptions of an arbitrary number of parties (potentially all) and achieve the following results: \begin{itemize} \item [--] A two-round secure function evaluation (SFE) protocol in the CRS model, assuming LWE and indistinguishability obfuscation (iO). The communication, the CRS size, and the online-computation are sublinear in the size of the function. The iO assumption can be replaced by secure erasures. Previous results required either the communication or the CRS size to be polynomial in the function size. \item [--] Under the same assumptions, we construct a Bob-optimized'' 2PC (where Alice talks first, Bob second, and Alice learns the output). That is, the communication complexity and total computation of Bob are sublinear in the function size and in Alice's input size. We prove impossibility of Alice-optimized'' protocols. \item [--] Assuming LWE, we bootstrap adaptively secure NIZK arguments to achieve proof size sublinear in the circuit size of the NP-relation. \end{itemize} On a technical level, our results are based on laconic function evaluation (LFE) [\textit{W. Quach} et al., Laconic function evaluation and applications'', in: Proceedings of the 59th annual IEEE symposium on foundations of computer science, FOCS'18. Los Alamitos, CA: IEEE Computer Society. 859--870 (2018; \url{doi:10.1109/FOCS.2018.00086})] and shed light on an interesting duality between LFE and FHE. Next, we analyze adaptive corruptions of all-but-one of the parties and show a two-round SFE protocol in the threshold PKI model (where keys of a threshold FHE scheme are pre-shared among the parties) with communication complexity sublinear in the circuit size, assuming LWE and NIZK. Finally, we consider the honest-majority setting, and show a two-round SFE protocol with guaranteed output delivery under the same constraints. For the entire collection see [Zbl 1428.94005]. Quantum algorithm for Boolean equation solving and quantum algebraic attack on cryptosystems https://www.zbmath.org/1483.68137 2022-05-16T20:40:13.078697Z "Chen, Yu-Ao" https://www.zbmath.org/authors/?q=ai:chen.yu-ao "Gao, Xiao-Shan" https://www.zbmath.org/authors/?q=ai:gao.xiaoshan Summary: This paper presents a quantum algorithm to decide whether a Boolean equation system $$\mathcal{F}$$ has a solution and to compute one if $$\mathcal{F}$$ does have solutions with any given success probability. The runtime complexity of the algorithm is polynomial in the size of $$\mathcal{F}$$ and the condition number of certain Macaulay matrix associated with $$\mathcal{F}$$. As a consequence, the authors give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are polynomial in the size of $$\mathcal{F}$$. The authors apply the proposed quantum algorithm to the cryptanalysis of several important cryptosystems: The stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the corresponding condition numbers are large. This leads to a new criterion for designing such cryptosystems which are safe against the attack of quantum computers: The corresponding condition number. Model counting with error-correcting codes https://www.zbmath.org/1483.68242 2022-05-16T20:40:13.078697Z "Achlioptas, Dimitris" https://www.zbmath.org/authors/?q=ai:achlioptas.dimitris "Theodoropoulos, Panos" https://www.zbmath.org/authors/?q=ai:theodoropoulos.panos Summary: The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani showing that NP is as easy as detecting unique solutions. While theoretically sound, the random parity constraints used in that construction suffer from the following drawback: each constraint, on average, involves half of all variables. As a result, the branching factor associated with searching for models that also satisfy the parity constraints quickly gets out of hand. In this work we prove that one can work with much shorter parity constraints and still get rigorous mathematical guarantees, especially when the number of models is large so that many constraints need to be added. Our work is motivated by the realization that the essential feature for a system of parity constraints to be useful in probabilistic model counting is that its set of solutions resembles an error-correcting code. Entropy and monotonicity in artificial intelligence https://www.zbmath.org/1483.68272 2022-05-16T20:40:13.078697Z "Bouchon-Meunier, Bernadette" https://www.zbmath.org/authors/?q=ai:bouchon-meunier.bernadette "Marsala, Christophe" https://www.zbmath.org/authors/?q=ai:marsala.christophe Summary: Entropies and measures of information are extensively used in several domains and applications in Artificial Intelligence. Among the original quantities from Information theory and Probability theory, a lot of extensions have been introduced to take into account fuzzy sets, intuitionistic fuzzy sets and other representation models of uncertainty and imprecision. In this paper, we propose a study of the common property of monotonicity of such measures with regard to a refinement of information, showing that the main differences between these quantities come from the diversity of orders defining such a refinement. Our aim is to propose a clarification of the concept of refinement of information and the underlying monotonicity, and to illustrate this paradigm by the utilisation of such measures in Artificial Intelligence. A two-stage method for spectral-spatial classification of hyperspectral images https://www.zbmath.org/1483.68282 2022-05-16T20:40:13.078697Z "Chan, Raymond H." https://www.zbmath.org/authors/?q=ai:chan.raymond-hon-fu "Kan, Kelvin K." https://www.zbmath.org/authors/?q=ai:kan.kelvin-k "Nikolova, Mila" https://www.zbmath.org/authors/?q=ai:nikolova.mila "Plemmons, Robert J." https://www.zbmath.org/authors/?q=ai:plemmons.robert-james Summary: We propose a novel two-stage method for the classification of hyperspectral images. Pixel-wise classifiers, such as the classical support vector machine (SVM), consider spectral information only. As spatial information is not utilized, the classification results are not optimal and the classified image may appear noisy. Many existing methods, such as morphological profiles, superpixel segmentation, and composite kernels, exploit the spatial information. In this paper, we propose a two-stage approach inspired by image denoising and segmentation to incorporate the spatial information. In the first stage, SVMs are used to estimate the class probability for each pixel. In the second stage, a convex variant of the Mumford-Shah model is applied to each probability map to denoise and segment the image into different classes. Our proposed method effectively utilizes both spectral and spatial information of the data sets and is fast as only convex minimization is needed in addition to the SVMs. Experimental results on three widely utilized real hyperspectral data sets indicate that our method is very competitive in accuracy, timing, and the number of parameters when compared with current state-of-the-art methods, especially when the inter-class spectra are similar or the percentage of training pixels is reasonably high. Group invariance, stability to deformations, and complexity of deep convolutional representations https://www.zbmath.org/1483.68335 2022-05-16T20:40:13.078697Z "Bietti, Alberto" https://www.zbmath.org/authors/?q=ai:bietti.alberto "Mairal, Julien" https://www.zbmath.org/authors/?q=ai:mairal.julien Summary: The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional representations of signals; we study their invariance to translations and to more general groups of transformations, their stability to the action of diffeomorphisms, and their ability to preserve signal information. This analysis is carried by introducing a multilayer kernel based on convolutional kernel networks and by studying the geometry induced by the kernel mapping. We then characterize the corresponding reproducing kernel Hilbert space (RKHS), showing that it contains a large class of convolutional neural networks with homogeneous activation functions. This analysis allows us to separate data representation from learning, and to provide a canonical measure of model complexity, the RKHS norm, which controls both stability and generalization of any learned model. In addition to models in the constructed RKHS, our stability analysis also applies to convolutional networks with generic activations such as rectified linear units, and we discuss its relationship with recent generalization bounds based on spectral norms. A robust generative classifier against transfer attacks based on variational auto-encoders https://www.zbmath.org/1483.68349 2022-05-16T20:40:13.078697Z "Zhang, Chen" https://www.zbmath.org/authors/?q=ai:zhang.chen "Tang, Zhuo" https://www.zbmath.org/authors/?q=ai:tang.zhuo "Zuo, Youfei" https://www.zbmath.org/authors/?q=ai:zuo.youfei "Li, Kenli" https://www.zbmath.org/authors/?q=ai:li.kenli "Li, Keqin" https://www.zbmath.org/authors/?q=ai:li.keqin Summary: Deep neural networks (DNNs) are vulnerable to adversarial examples. Even under black-box setting that is without access to the target model, transfer-based attacks can easily fool the DNNs. To alleviate this problem, we propose a robust classification model against transfer attacks based on the framework of variational Auto-Encoders (VAEs) which are probabilistic generative models and have been successfully used to a large mount of tasks. Specifically, our model simulates the data generative process with several multivariate Gaussian distributions and DNNs: (1) We assume that the latent embedding generated by an \textit{encoder} (a DNN) of each category corresponds to a multivariate Gaussian distribution. (2) A \textit{decoder} (a DNN) is proposed to decodes the latent embedding into an observable. (3) Theoretical analysis illustrates that our model can predict data's labels by maximizing the lower bound on the log-likelihood for each category utilizing Bayes' theorem with excellent robustness against transfer attacks. Inference in our model is done in a variational way so the Stochastic Gradient Variational Bayes (SGVB) estimator and reparamerization trick can be utilized to optimize the evidence lower bound (ELBO). The experiments with quantitative comparisons show that our approach reaches state-of-the-art with significantly better robustness. A modified extended Kalman filter method for multi-layered neural network training https://www.zbmath.org/1483.68355 2022-05-16T20:40:13.078697Z "Kim, Kyungsup" https://www.zbmath.org/authors/?q=ai:kim.kyungsup "Won, Yoojae" https://www.zbmath.org/authors/?q=ai:won.yoojae Summary: This paper discusses extended Kalman filter method for solving learning problems of multilayered neural networks. A lot of learning algorithms for deep layered network are sincerely suffered from complex computation and slow convergence because of a very large number of free parameters. We consider an efficient learning algorithm for deep neural network. Extended Kalman filter method is applied to parameter estimation of neural network to improve convergence and computation complexity. We discuss how an efficient algorithm should be developed for neural network learning by using Extended Kalman filter. A decomposable Winograd method for N-D convolution acceleration in video analysis https://www.zbmath.org/1483.68431 2022-05-16T20:40:13.078697Z "Huang, Di" https://www.zbmath.org/authors/?q=ai:huang.di "Zhang, Rui" https://www.zbmath.org/authors/?q=ai:zhang.rui|zhang.rui.3|zhang.rui.4|zhang.rui.1|zhang.rui.5|zhang.rui.2 "Zhang, Xishan" https://www.zbmath.org/authors/?q=ai:zhang.xishan "Wu, Fan" https://www.zbmath.org/authors/?q=ai:wu.fan "Wang, Xianzhuo" https://www.zbmath.org/authors/?q=ai:wang.xianzhuo "Jin, Pengwei" https://www.zbmath.org/authors/?q=ai:jin.pengwei "Liu, Shaoli" https://www.zbmath.org/authors/?q=ai:liu.shaoli "Li, Ling" https://www.zbmath.org/authors/?q=ai:li.ling "Chen, Yunji" https://www.zbmath.org/authors/?q=ai:chen.yunji Summary: Winograd's minimal filtering algorithm has been widely used in 2-D Convolutional Neural Networks (CNNs) to reduce the number of multiplications for faster processing. However, it is only effective on convolutions with kernel size as $$3$$ and stride as 1, because it suffers from significantly increased FLOPs and numerical accuracy problems for kernel size larger than $$3$$ and fails on convolution with stride larger than 1. Worse, the extension to N-D convolution will intensify the numerical accuracy problem. These problems severely obstruct Winograd's minimal filtering algorithm's application to video analysis. In this paper, we propose a novel Decomposable Winograd Method (DWM) for the N-D convolution acceleration, which breaks through the limitation of original Winograd's minimal filtering algorithm to more general convolutions. DWM decomposes kernels with large size or stride>1 to several small kernels with stride as 1 for further applying Winograd algorithm, so that DWM can reduce the number of multiplications while keeping the numerical accuracy. It enables the fast exploration of larger kernel size, larger stride value, and higher dimensions in CNNs for high performance and accuracy and even the potential for new CNNs. Comparing against the original Winograd algorithm, the proposed DWM is able to support all kinds of N-D convolutions with a speedup of $$1.44\times -3.38\times$$, without affecting the numerical accuracy. New robust PCA for outliers and heavy sparse noises' detection via affine transformation, the $$L_{\ast, w}$$ and $$L_{2,1}$$ norms, and spatial weight matrix in high-dimensional images: from the perspective of signal processing https://www.zbmath.org/1483.68436 2022-05-16T20:40:13.078697Z "Liang, Peidong" https://www.zbmath.org/authors/?q=ai:liang.peidong "Likassa, Habte Tadesse" https://www.zbmath.org/authors/?q=ai:likassa.habte-tadesse "Zhang, Chentao" https://www.zbmath.org/authors/?q=ai:zhang.chentao "Guo, Jielong" https://www.zbmath.org/authors/?q=ai:guo.jielong Summary: In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, $$L_{\ast, w}$$, and the $$L_{2,1}$$ norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the $$L_{2,1}$$ norm to tackle the dilemma of extreme values in the high-dimensional images, and the $$L_{\ast, w}$$ norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases. Adaptive channel selection for robust visual object tracking with discriminative correlation filters https://www.zbmath.org/1483.68450 2022-05-16T20:40:13.078697Z "Xu, Tianyang" https://www.zbmath.org/authors/?q=ai:xu.tianyang "Feng, Zhenhua" https://www.zbmath.org/authors/?q=ai:feng.zhenhua "Wu, Xiao-Jun" https://www.zbmath.org/authors/?q=ai:wu.xiaojun.1 "Kittler, Josef" https://www.zbmath.org/authors/?q=ai:kittler.josef Summary: Discriminative Correlation Filters (DCF) have been shown to achieve impressive performance in visual object tracking. However, existing DCF-based trackers rely heavily on learning regularised appearance models from invariant image feature representations. To further improve the performance of DCF in accuracy and provide a parsimonious model from the attribute perspective, we propose to gauge the relevance of multi-channel features for the purpose of channel selection. This is achieved by assessing the information conveyed by the features of each channel as a group, using an adaptive group elastic net inducing independent sparsity and temporal smoothness on the DCF solution. The robustness and stability of the learned appearance model are significantly enhanced by the proposed method as the process of channel selection performs implicit spatial regularisation. We use the augmented Lagrangian method to optimise the discriminative filters efficiently. The experimental results obtained on a number of well-known benchmarking datasets demonstrate the effectiveness and stability of the proposed method. A superior performance over the state-of-the-art trackers is achieved using less than 10\% deep feature channels. Binary handwriting image enhancement by directional field-guided morphology https://www.zbmath.org/1483.68473 2022-05-16T20:40:13.078697Z "Adamski, Marcin" https://www.zbmath.org/authors/?q=ai:adamski.marcin "Sarnacki, Kacper" https://www.zbmath.org/authors/?q=ai:sarnacki.kacper "Saeed, Khalid" https://www.zbmath.org/authors/?q=ai:saeed.khalid Summary: This paper proposes a technique for processing handwriting images. The algorithm used in this study is an improvement to the binarisation process. The enhancement focuses on correcting damaged lines that usually arise during the binarisation process, particularly, spurious holes, discontinuities, and eroded boundaries. The presented method uses a morphogical dilation operation in which a structural element is locally adapted using the information from a directional field. The adaptation process involves a new criterion for selecting orientation and shape of a structural element that combines directional field, a coherence measure, and a circular histogram. The field was computed using gradient-based approach, and a method based on a Hessian matrix. During experiments, our method was applied to the output of selected binarisation algorithms. The experiments were conducted on grayscale signature images (from the CEDAR database) and handwriting images (from the DIBCO database). The results of the algorithm were compared to the results of standard morphological operations (dilation, erosion, opening, and closing) and median filtering. The experiments show that the proposed method achieves significant accuracy improvement (8\%--12\% for Acc, 15\%--32\% for Acc2 measures), reduces the number of unwanted artefacts, and produces images with less distortion compared to those from standard approaches. Evaluation metrics for conditional image generation https://www.zbmath.org/1483.68474 2022-05-16T20:40:13.078697Z "Benny, Yaniv" https://www.zbmath.org/authors/?q=ai:benny.yaniv "Galanti, Tomer" https://www.zbmath.org/authors/?q=ai:galanti.tomer "Benaim, Sagie" https://www.zbmath.org/authors/?q=ai:benaim.sagie "Wolf, Lior" https://www.zbmath.org/authors/?q=ai:wolf.lior Summary: We present two new metrics for evaluating generative models in the class-conditional image generation setting. These metrics are obtained by generalizing the two most popular unconditional metrics: the Inception Score (IS) and the Fréchet Inception Distance (FID). A theoretical analysis shows the motivation behind each proposed metric and links the novel metrics to their unconditional counterparts. The link takes the form of a product in the case of IS or an upper bound in the FID case. We provide an extensive empirical evaluation, comparing the metrics to their unconditional variants and to other metrics, and utilize them to analyze existing generative models, thus providing additional insights about their performance, from unlearned classes to mode collapse. How to simulate it in Isabelle: towards formal proof for secure multi-party computation https://www.zbmath.org/1483.68486 2022-05-16T20:40:13.078697Z "Butler, David" https://www.zbmath.org/authors/?q=ai:butler.david-k|butler.david-j|butler.david-g|butler.david-a|butler.david-c|butler.david-lee|butler.david-e "Aspinall, David" https://www.zbmath.org/authors/?q=ai:aspinall.david "Gascón, Adrià" https://www.zbmath.org/authors/?q=ai:gascon.adria Summary: In cryptography, secure multi-party computation (MPC) protocols allow participants to compute a function jointly while keeping their inputs private. Recent breakthroughs are bringing MPC into practice, solving fundamental challenges for secure distributed computation. Just as with classic protocols for encryption and key exchange, precise guarantees are needed for MPC designs and implementations; any flaw will give attackers a chance to break privacy or correctness. In this paper we present the first (as far as we know) formalisation of some MPC security proofs. These proofs provide probabilistic guarantees in the computational model of security, but have a different character to machine proofs and proof tools implemented so far -- MPC proofs use a simulation approach, in which security is established by showing indistinguishability between execution traces in the actual protocol execution and an ideal world where security is guaranteed by definition. We show that existing machinery for reasoning about probabilistic programs can be adapted to this setting, paving the way to precisely check a new class of cryptography arguments. We implement our proofs using the CryptHOL framework inside Isabelle/HOL. For the entire collection see [Zbl 1369.68009]. QBism and relational quantum mechanics compared https://www.zbmath.org/1483.81009 2022-05-16T20:40:13.078697Z "Pienaar, Jacques" https://www.zbmath.org/authors/?q=ai:pienaar.jacques Summary: The subjective Bayesian interpretation of quantum mechanics (QBism) and Rovelli's relational interpretation of quantum mechanics (RQM) are both notable for embracing the radical idea that measurement outcomes correspond to events whose occurrence (or not) is relative to an observer. Here we provide a detailed study of their similarities and especially their differences. A quintet of quandaries: five No-Go theorems for relational quantum mechanics https://www.zbmath.org/1483.81010 2022-05-16T20:40:13.078697Z "Pienaar, Jacques" https://www.zbmath.org/authors/?q=ai:pienaar.jacques Summary: Relational quantum mechanics (RQM) proposes an ontology of relations between physical systems, where any system can serve as an observer' and any physical interaction between systems counts as a measurement'. Quantities take unique values spontaneously in these interactions, and the occurrence of such quantum events' is strictly relative to the observing system, making them relative facts'. The quantum state represents the objective information that one system has about another by virtue of correlations between their physical variables. The ontology of RQM thereby strives to uphold the universality and completeness of quantum theory, while at the same time maintaining that the actualization of each unique quantum event is a fundamental physical event. Can RQM sustain this precarious balancing act? Here we present five no-go theorems that imply it cannot; something has to give way. Mirror entanglement measure of multipartite quantum states with respect to $$k$$-partitions https://www.zbmath.org/1483.81032 2022-05-16T20:40:13.078697Z "Wang, Yinzhu" https://www.zbmath.org/authors/?q=ai:wang.yinzhu "Liu, Yaxue" https://www.zbmath.org/authors/?q=ai:liu.yaxue "Zhou, Fangyu" https://www.zbmath.org/authors/?q=ai:zhou.fangyu "Yang, Lili" https://www.zbmath.org/authors/?q=ai:yang.lili "Yan, Donghua" https://www.zbmath.org/authors/?q=ai:yan.donghua Summary: In \textit{A. Monras} et al. [Phys. Rev. A 84, No. 1, Article ID 012301. 11 p. ( 2011; \url{doi:10.1103/PhysRevA.84.012301})], the authors presented an entanglement measure for bipartite pure states based on local unitary operations. In this paper, motivated by this idea, we obtained an entanglement measure for multipartite quantum states with respect to $$k$$-partitions, which is called mirror entanglement measure for multipartite $$k$$-nonseparable states, it is simply denoted by $$k$$-MEM. We show that this measure is well-defined, i.e., it satisfies some necessary conditions of entanglement measure including vanishes iff the multipartite quantum states are $$k$$-separable, invariance under local unitary operation and monotonicity under local quantum operation and classical communication. Multiparty quantum rotation operation sharing https://www.zbmath.org/1483.81035 2022-05-16T20:40:13.078697Z "Peng, Jia-Yin" https://www.zbmath.org/authors/?q=ai:peng.jiayin "Xiang, Yi" https://www.zbmath.org/authors/?q=ai:xiang.yi Summary: Combining the ideas of quantum state sharing and multi-party quantum remote control, a novel four-participant quantum rotation operation sharing protocol was proposed, which utilizes pre-shared entanglement and local operations. Concretely, using 4-qubit entanglement of Greenberger-Home-Zeilinger (GHZ) type state as quantum channel, the two senders of the protocol can remotely and independently implement various rotation operations on the target state of any site, which requires mutual cooperation between two agents. Moreover, by utilizing $$(M + N)$$-qubit GHZ type state as the entanglement channel, the above four-participant situation can be easily generalized to the scenario with $$M$$ senders and $$N$$ agents. Quantum image edge detection based on multi-directions gray-scale morphology https://www.zbmath.org/1483.81043 2022-05-16T20:40:13.078697Z "Li, Wan-Xiu" https://www.zbmath.org/authors/?q=ai:li.wan-xiu "Zhou, Ri-Gui" https://www.zbmath.org/authors/?q=ai:zhou.rigui "Yu, Han" https://www.zbmath.org/authors/?q=ai:yu.han Summary: Aiming at extending the classical strong mathematical morphology operations to quantum image processing field, in this paper, an quantum image edge detection method is designed based on the novel enhanced quantum representation of digital images (NEQR) and multi-directions Gray-scale morphology. Because NEQR is more convenient for gray operation of quantum image. In addition, based on multi-directional feature of image edges, the multi-directional structures are constructed by combining the mathematical morphology. Compared with the existing quantum image edge detection methods, this method can reach a better effect. Noisy Simon period finding https://www.zbmath.org/1483.81044 2022-05-16T20:40:13.078697Z "May, Alexander" https://www.zbmath.org/authors/?q=ai:may.alexander "Schlieper, Lars" https://www.zbmath.org/authors/?q=ai:schlieper.lars "Schwinger, Jonathan" https://www.zbmath.org/authors/?q=ai:schwinger.jonathan Summary: Let $$f: \mathbb{F}_2^n \rightarrow \mathbb{F}_2^n$$ be a Boolean function with period $$\mathbf{s}$$. It is well-known that Simon's algorithm finds $$\mathbf{s}$$ in time polynomial in $$n$$ on quantum devices that are capable of performing error-correction. However, today's quantum devices are inherently noisy, too limited for error correction, and Simon's algorithm is not error-tolerant. We show that even noisy quantum period finding computations may lead to speedups in comparison to purely classical computations. To this end, we implemented Simon's quantum period finding circuit on the 15-qubit quantum device IBM Q 16 Melbourne. Our experiments show that with a certain probability $$\tau (n)$$ we measure erroneous vectors that are not orthogonal to $$\mathbf{s}$$. We propose new, simple, but very effective smoothing techniques to classically mitigate physical noise effects such as e.g. IBM Q's bias towards the 0-qubit. After smoothing, our noisy quantum device provides us a statistical distribution that we can easily transform into an LPN instance with parameters $$n$$ and $$\tau (n)$$. Hence, in the noisy case we may not hope to find periods in time polynomial in $$n$$. However, we may still obtain a quantum advantage if the error $$\tau (n)$$ does not grow too large. This demonstrates that quantum devices may be useful for period finding, even before achieving the level of full error correction capability. For the entire collection see [Zbl 1476.94005]. Interpolation-based high capacity quantum image steganography https://www.zbmath.org/1483.81048 2022-05-16T20:40:13.078697Z "Zhao, Shan" https://www.zbmath.org/authors/?q=ai:zhao.shan "Yan, Fei" https://www.zbmath.org/authors/?q=ai:yan.fei "Chen, Kehan" https://www.zbmath.org/authors/?q=ai:chen.kehan "Yang, Huamin" https://www.zbmath.org/authors/?q=ai:yang.huamin Summary: Encryption and information hiding are widely used in security applications requiring copyright protection, over-communication, and tamper detection. Quantum steganography, using quantum images and audio as information carriers, is a fascinating hybrid of classical and quantum informatics. While existing steganography techniques offer high invisibility, current embedding capacities remain insufficient. As such, a high capacity quantum steganography algorithm, based on image interpolation, is proposed in this study. In this approach, quantum interpolation is conducted by maximizing difference values between neighboring pixels to generate a cover image. Secret message embedding and extraction steps are then developed for the resulting quantum images, in addition to corresponding quantum circuit networks. A series of simulation experiments were conducted to demonstrate the implementation and assess the performance of the proposed technique, the efficiency of which was evaluated using several performance metrics and the visual quality of the stego-images. The resulting information capacity was much higher than that of existing quantum steganography algorithms. This suggests the proposed strategy to be a promising trade-off between invisibility and capacity, providing new motivation to investigate image steganography using quantum computing resources. Verifiable quantum secret sharing scheme using $$d$$-dimensional GHZ state https://www.zbmath.org/1483.81049 2022-05-16T20:40:13.078697Z "Bai, Chen-Ming" https://www.zbmath.org/authors/?q=ai:bai.chenming "Zhang, Sujuan" https://www.zbmath.org/authors/?q=ai:zhang.sujuan "Liu, Lu" https://www.zbmath.org/authors/?q=ai:liu.lu Summary: In this paper we propose two verifiable threshold quantum secret sharing protocols with $$d$$-dimensional GHZ state. In the proposed protocol, the dealer Alice firstly divides all participants into two groups to achieve the two-line transmission. Then she randomly generates a three-qudit GHZ state, inserts the first two particles into two detecting photon sequences and sends them to participants in each group. In the distribution phase, each participant calculates and sends his commitment values to Alice by quantum secure direct communication. Furthermore, each participant performs a unitary operation on these received particles and sends them to the next participant using the decoy-photon technique. In the verification phase, Alice can perform two rounds of verification and test all participants' honesty. In addition, we demonstrate our protocol to be secure against both eavesdropping and dishonest participants and compare our scheme with the existing schemes. Quantum secure direct communication with mutual authentication using a single basis https://www.zbmath.org/1483.81050 2022-05-16T20:40:13.078697Z "Das, Nayana" https://www.zbmath.org/authors/?q=ai:das.nayana "Paul, Goutam" https://www.zbmath.org/authors/?q=ai:paul.goutam "Majumdar, Ritajit" https://www.zbmath.org/authors/?q=ai:majumdar.ritajit Summary: In this paper, we propose a new theoretical scheme for quantum secure direct communication (QSDC) with user authentication. Different from the previous QSDC protocols, the present protocol uses only one orthogonal basis of single-qubit states to encode the secret message. Moreover, this is a one-time and one-way communication protocol, which uses qubits prepared in a randomly chosen arbitrary basis, to transmit the secret message. We discuss the security of the proposed protocol against some common attacks and show that no eavesdropper can get any information from the quantum and classical channels. We have also studied the performance of this protocol under realistic device noise. We have executed the protocol in IBMQ Armonk device and proposed a repetition code based protection scheme that requires minimal overhead. Efficient quantum private comparison based on entanglement swapping of Bell states https://www.zbmath.org/1483.81052 2022-05-16T20:40:13.078697Z "Huang, Xi" https://www.zbmath.org/authors/?q=ai:huang.xi "Zhang, Shi-Bin" https://www.zbmath.org/authors/?q=ai:zhang.shibin "Chang, Yan" https://www.zbmath.org/authors/?q=ai:chang.yan "Hou, Min" https://www.zbmath.org/authors/?q=ai:hou.min "Cheng, Wen" https://www.zbmath.org/authors/?q=ai:cheng.wen Summary: In this paper, by using entanglement swapping of Bell states, an efficient quantum private comparison(QPC) protocol with a semi-honest party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she is not allowed to conspire with any participants. Moreover, TP cannot get two participants' privacy information except the comparison results. The security analysis shows that the proposed protocol can resist both outsider attacks and insider attacks. Compared with other similar QPC protocols, the proposed one needs neither unitary operations nor the entanglement swapping of multiparticle quantum states, and it only needs the entanglement swapping of Bell states, which makes it more practical. Since three-bit classical information could be compared in each comparison, the proposed protocol has a good performance in its efficiency. Novel quantum private comparison protocol based on locally indistinguishable product states https://www.zbmath.org/1483.81053 2022-05-16T20:40:13.078697Z "Jiang, Dong-Huan" https://www.zbmath.org/authors/?q=ai:jiang.donghuan "Tang, Ke-Ke" https://www.zbmath.org/authors/?q=ai:tang.ke-ke "Xu, Guang-Bao" https://www.zbmath.org/authors/?q=ai:xu.guangbao Summary: In this paper, we propose a two-party quantum private comparison (QPC) protocol using orthogonal product states. This protocol introduces a semi-honest third party who will faithfully execute the protocol and will not conspire with any of the participants. Every participant encodes the hash value of her (his) secret data into a quantum sequence of orthogonal product states. Each of these states comes from a locally indistinguishable set of product states. To ensure information security, each participant splits the quantum sequence of product states that she (he) generates into two single-particle sequences and transmits these two single-particle sequences separately. After the third party calculates and publishes the results, the two participants can know whether their secret information is equal by a simple calculation. Security and efficiency analyses show that our protocol is secure and efficient. Quantum private comparison using single Bell state https://www.zbmath.org/1483.81054 2022-05-16T20:40:13.078697Z "Lang, Yan-Feng" https://www.zbmath.org/authors/?q=ai:lang.yan-feng Summary: Quantum private comparison (QPC) can tell us whether two users' private data are equal or not by quantum technology without disclosing privacy to each other. There are many QPC protocols with diverse procedures and a wide variety of quantum resources. If two forms of quantum states or above are used in a QPC protocol, there will be a need of multiple devices or methods to generate these quantum states, which could bring about some lurking unfavourable effects such as inefficiency and high costs in application. In order to improve the QPC efficiency and reduce costs, a design principle to develop QPC protocols is put forward as a reference in this paper. Also, to take Bell states for example, a QPC protocol with a single Bell state as quantum resource is presented. The protocol is not only simple yet efficient and easy to apply but also of low costs. The analyses show its correctness so it could behave as an alternative way to exercise QPC. Quantum sealed-bid Vickrey auction protocol with semi-quantum bidders https://www.zbmath.org/1483.81055 2022-05-16T20:40:13.078697Z "Li, Zexi" https://www.zbmath.org/authors/?q=ai:li.zexi "Chen, Liuyi" https://www.zbmath.org/authors/?q=ai:chen.liuyi "Zhu, Hongfeng" https://www.zbmath.org/authors/?q=ai:zhu.hongfeng Summary: In this paper, a quantum sealed-bid protocol based on semi-quantum bidders is proposed. The protocol uses Bell states to encrypt message and realizes the process that bidders can directly transmit bidding information to the auction center safely. Its essence is a semi-quantum secure direct communication protocol using Bell states. Unlike most similar protocols, our scheme eliminates the trusted third-party Trent and sets the auction center Charlie as completely honest. Considering that the auction involves human activities, too many quantum servers are not only costly, but also unrealistic. Therefore, we set the bidders as semi-quantum users and implement the Vickrey auction. In addition, the security analysis shows that our scheme has high security and is completely feasible. Quantum dialogue protocol based on Bell entangled states and single photons https://www.zbmath.org/1483.81056 2022-05-16T20:40:13.078697Z "Lu, Yin-Ju" https://www.zbmath.org/authors/?q=ai:lu.yin-ju Summary: In this paper, inspired by \textit{C. Wang} et al.'s deterministic secure quantum communication (DSQC) scheme [Commun. Theor. Phys. 60, No. 4, 397--404 (2013; Zbl 1277.81032)] is put forward also by using Bell states and single photons as quantum resource. The proposed scheme can effectively overcome the active attacks launched by an outside attacker, such the intercept-resend attack, the measure-resend attack, the entangle-measure attack, etc. The information-theoretical efficiency of the proposed scheme is as high as 66.67\%. $$n$$-bit quantum secret sharing protocol using quantum secure direct communication https://www.zbmath.org/1483.81057 2022-05-16T20:40:13.078697Z "Sadeghi-Zadeh, Mohammad Sadegh" https://www.zbmath.org/authors/?q=ai:zadeh.mohammad-sadegh-sadeghi|sadeghizadeh.mohammad-sadegh "Khorrampanah, Mahsa" https://www.zbmath.org/authors/?q=ai:khorrampanah.mahsa "Houshmand, Monireh" https://www.zbmath.org/authors/?q=ai:houshmand.monireh "Aghababa, Hossein" https://www.zbmath.org/authors/?q=ai:aghababa.hossein "Mafi, Yousef" https://www.zbmath.org/authors/?q=ai:mafi.yousef Summary: The proposed quantum secret sharing protocol in this article conveys n bit secret messages from the sender to the n receivers making use of a secure direct communication. In this protocol, all users work together to access their secrets. As a result, the security of the proposed protocol is high. The channel used in this design is an entangled 2n-qubit state. The efficiency of this design has been compared with other designs and it turns out that the efficiency of the proposed protocol is equal to that of the best designs. We demonstrate that this protocol is more efficient than the only n-user confidential subscription plan. Also, all stages of the design in a noisy space have been examined. Flexible for multiple equations about GHZ states and A prototype case https://www.zbmath.org/1483.81058 2022-05-16T20:40:13.078697Z "Wang, Chaonan" https://www.zbmath.org/authors/?q=ai:wang.chaonan "Li, Zexi" https://www.zbmath.org/authors/?q=ai:li.zexi "Zhu, Hongfeng" https://www.zbmath.org/authors/?q=ai:zhu.hongfeng Summary: According to the peculiar entanglement and measurement properties of the three-particle GHZ state, we have systematically analyzed that two GHZ states and three GHZ states satisfy some expressions after exchanging one or two groups of particles respectively, which are described as four interesting and flexible equations. The four equations can deduce that four GHZ states or even $$m$$ GHZ states still satisfy some expressions after exchanging one group and two groups of particles, and they can be summarized as two general flexible equations. Furthermore, we also investigate their application in the field of quantum key agreement based on these equations. In particular, we combine with decoy photons to propose a novel session key sharing protocol, which can guarantee the unconditional security of the protocol. It is feasible to use the existing quantum processing technology to realize the proposed protocol. Multi-party quantum key agreement protocol with authentication https://www.zbmath.org/1483.81059 2022-05-16T20:40:13.078697Z "Wu, Yi-Ting" https://www.zbmath.org/authors/?q=ai:wu.yiting "Chang, Hong" https://www.zbmath.org/authors/?q=ai:chang.hong "Guo, Gong-De" https://www.zbmath.org/authors/?q=ai:guo.gongde "Lin, Song" https://www.zbmath.org/authors/?q=ai:lin.song Summary: Utilizing the advantage of quantum entanglement swapping, a multi-party quantum key agreement protocol with authentication is proposed. In this protocol, a semi-trusted third party is introduced, who prepares Bell states, and sends one particle to multiple participants respectively. After that the participants can share a Greenberger-Horne-Zeilinger state by entanglement swapping. Finally, these participants measure the particles in their hands and obtain an agreement key. Here, classical hash function and Hadamard operation are utilized to authenticate the identity of participants. The correlations of GHZ states ensure the security of the proposed protocol. To illustrated it detailly, the security of this protocol against common attacks is analyzed, which shows that the proposed protocol is secure in theory. A lightweight semi-quantum E-payment protocol based on blockchain https://www.zbmath.org/1483.81060 2022-05-16T20:40:13.078697Z "Xu, Yuguang" https://www.zbmath.org/authors/?q=ai:xu.yuguang.1 "Cheng, Kefan" https://www.zbmath.org/authors/?q=ai:cheng.kefan "Liu, Tianhua" https://www.zbmath.org/authors/?q=ai:liu.tianhua "Zhu, Hongfeng" https://www.zbmath.org/authors/?q=ai:zhu.hongfeng Summary: How to apply E-payment based on quantum cryptography to our daily life is a significant problem. Inspired by the semi-quantum protocols, we present a lightweight semi-quantum E-payment protocol based on blockchain. Our protocol has the following advantages: First, by using semi-quantum cryptography, a classic user Alice can transfer information according to Bell state generated by semi-quantum user Trent. This eliminates the need for participants to have full-quantum capabilities and makes our protocol easier to implement. Moreover, the classic user Alice can perform payment operations on the mobile device. Second, we use controlled quantum teleportation to ensure the anonymity of payment information. Then, three-qubit entangled states are used to make it easier to prepare quantum resources. At last, blockchain technology ensures the traceability of messages. For security, eavesdropping will undoubtedly be found when the $$n$$-bits message is large enough. In addition, the analysis results show that the protocol is secure against some eavesdropping attacks and more lightweight than the existing E-payment protocols. Quantum secure multi-party summation based on Grover's search algorithm https://www.zbmath.org/1483.81061 2022-05-16T20:40:13.078697Z "Zhang, Xin" https://www.zbmath.org/authors/?q=ai:zhang.xin.1|zhang.xin.3|zhang.xin.4|zhang.xin "Lin, Song" https://www.zbmath.org/authors/?q=ai:lin.song "Guo, Gong-De" https://www.zbmath.org/authors/?q=ai:guo.gongde Summary: In this paper, a quantum secure multi-party summation protocol is proposed based on some properties of Grover's search algorithm. In the protocol, each participant's secret input is encoded as a unitary operation on the travelling two-qubit state. With the help of a semi-honest third party, all participants can simultaneously obtain the summation result without disclosing their secret inputs. Only the preparation and measurement of single qubits are required, which makes the proposed protocol feasible using current technology. At last, we demonstrate the correctness and security of the protocol, which can resist various attacks from both external attackers and internal participants. Multi-party quantum key agreement protocol for smart home environment https://www.zbmath.org/1483.81062 2022-05-16T20:40:13.078697Z "Zhu, Hongfeng" https://www.zbmath.org/authors/?q=ai:zhu.hongfeng "Li, Zexi" https://www.zbmath.org/authors/?q=ai:li.zexi "Wang, Xueying" https://www.zbmath.org/authors/?q=ai:wang.xueying "Chen, Liuyi" https://www.zbmath.org/authors/?q=ai:chen.liuyi Summary: The most typical case of applying technology and communication technology to life may be the popular smart home series. Users can remotely control smart devices through mobile phones, which is convenient and fast, greatly changing people's way of life. However, the safe login of smart devices has become a thorny problem. With the emergence of quantum computer, the common encryption method cannot prevent quantum attacks. In addition, a family often has multiple smart devices and multiple family members. Each user can log in to multiple smart devices, and each device can also be logged in by multiple users. Therefore, in view of the above situation, we propose a multi-party quantum session key agreement protocol based on Bell states and single particles, which can be used for multiple participants to negotiate session keys together, and improve the efficiency of users logging in and using smart devices. Moreover, our protocol ensures that each party has an equal opportunity to decide the final shared key, no party can determine the final key individually. Furthermore, security and efficiency analysis show that our protocol can achieve ideal results under the existing quantum technology. Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid https://www.zbmath.org/1483.83029 2022-05-16T20:40:13.078697Z "Yang, Wei" https://www.zbmath.org/authors/?q=ai:yang.wei.4|yang.wei.2|yang.wei.3|yang.wei|yang.wei.1 "Fang, Xiongjun" https://www.zbmath.org/authors/?q=ai:fang.xiongjun "Jing, Jiliang" https://www.zbmath.org/authors/?q=ai:jing.jiliang Summary: The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from the extrema of the total entropy, and the thermodynamical stability criterion are equivalent to the dynamical stability criterion. In this paper, we recast the dynamical criterion for the charged self-gravitating perfect fluid in Einstein-Maxwell theory, and further give the criterion of the star with barotropic condition. In order to obtain the thermodynamical stability criterion, first we get the general formula of the second variation of the total entropy for charged perfect fluid case, and then obtain the thermodynamical criterion for radial perturbation. We show that these two stability criterions are the same, which suggest that the inherent connection between gravity and thermodynamic even when the electric field is taken into account. Phase space analysis of Tsallis agegraphic dark energy https://www.zbmath.org/1483.83030 2022-05-16T20:40:13.078697Z "Huang, Hai" https://www.zbmath.org/authors/?q=ai:huang.hai "Huang, Qihong" https://www.zbmath.org/authors/?q=ai:huang.qihong "Zhang, Ruanjing" https://www.zbmath.org/authors/?q=ai:zhang.ruanjing Summary: Based on the generalized Tsallis entropy and holographic hypothesis, the Tsallis agegraphic dark energy (TADE) was proposed by introducing the timescale as infrared cutoff. In this paper, we analyze the evolution of the universe in the TADE model and the new Tsallis agegraphic dark energy (NTADE) model by considering an interaction between dark matter and dark energy as $$Q=H(\alpha\rho_m+\beta\rho_D)$$. Through the phase space and stability analysis, we find an attractor which represents a late-time accelerated expansion phase can exist only in NTADE model. When $$0\leq\alpha<1$$ and $$\beta=0$$, this attractor becomes a dark energy dominated de Sitter solution and the universe can eventually evolve into an accelerated expansion era which is depicted by the $$\Lambda$$ cold dark matter model. Thus, the expansion history of the universe can be depicted by the NTADE model. Statistical approaches on the apparent horizon entropy and the generalized second law of thermodynamics https://www.zbmath.org/1483.83033 2022-05-16T20:40:13.078697Z "Abreu, Everton M. C." https://www.zbmath.org/authors/?q=ai:abreu.everton-m-c "Neto, Jorge Ananias" https://www.zbmath.org/authors/?q=ai:neto.jorge-ananias Summary: In this work we have investigated the effects of three nongaussian entropies, namely, the modified Rényi entropy (MRE), the Sharma-Mittal entropy (SME) and the dual Kaniadakis entropy (DKE) in the investigation of the generalized second law (GSL) of thermodynamics violation. The GSL is an extension of the second law for black holes. Recently, it was concluded that a total entropy is the sum of the entropy enclosed by the apparent horizon plus the entropy of the horizon itself when the apparent horizon is described by the Barrow entropy. It was assumed that the universe is filled with matter and dark energy fluids. Here, the apparent horizon will be described by MRE, SME, and then by DKE proposals. Since GSL holds for usual entropy, but it is conditionally violated in the extended entropies, this implies that the parameter of these entropies should be constrained in small values in order to obey the GSL of thermodynamics. Hence, we have established conditions where the second law of thermodynamics can or cannot be obeyed considering these three statistical concepts just as it was made in Barrow's entropy. Considering the $$\Lambda CDM$$ cosmology, we will notice that for MRE, SME and DKE, the GSL of thermodynamics is not obeyed for small redshift values. Entropy of Reissner-Nordström-like black holes https://www.zbmath.org/1483.83036 2022-05-16T20:40:13.078697Z "Blagojević, M." https://www.zbmath.org/authors/?q=ai:blagojevic.milutin "Cvetković, B." https://www.zbmath.org/authors/?q=ai:cvetkovic.branislav Summary: In Poincaré gauge theory, black hole entropy is defined canonically by the variation of a boundary term $$\Gamma_H$$, located at horizon. For a class of static and spherically symmetric black holes in vacuum, the explicit formula reads $$\delta \Gamma_H = T \delta S$$, where $$T$$ is black hole temperature and $$S$$ entropy. Here, we analyze a new member of the same class, the Reissner-Nordström-like black hole with torsion [\textit{ J. A.R. Cembranos} and [\textit{J. G. Valcarcel}, New torsion black hole solutions in Poincaré gauge theory,'' J. Cosmol. Astropart. Phys., 01, Article 014 (2017; \url{doi:10.1088/1475-7516/2017/01/014})], where the electric charge of matter is replaced by a gravitational parameter, induced by the existence of torsion. This parameter affects $$\delta \Gamma_H$$ in a way that ensures the validity of the first law. Configuration entropy and confinement-deconfinement transition in higher-dimensional hard wall model https://www.zbmath.org/1483.83052 2022-05-16T20:40:13.078697Z "Lee, Chong Oh" https://www.zbmath.org/authors/?q=ai:lee.chong-oh Summary: We consider a higher-dimensional hard wall model with an infrared (IR) cut-off in asymptotically AdS space and investigate its thermodynamics via the holographic renormalization method. We find a relation between the confinement temperature and the IR cut-off for any dimension. It is also shown that the entropy of $$p$$-branes with the number of coincident branes (the number of the gauge group) $$N$$ jumps from leading order in $$\mathcal{O}(N^0)$$ at the confining low temperature phase to $$\mathcal{O}(N^{\frac{p + 1}{2}})$$ at the deconfining high temperature phase like $$D3$$-branes ($$p = 3$$) case. On the other hand, we calculate the configuration entropy (CE) of various magnitudes of an inverse temperature at an given IR cut-off scale. It is shown that as the inverse temperature grows up, the CE above the critical temperature decreases and AdS black hole (BH) is stable while it below the critical temperature is constant and thermal AdS (ThAdS) is stable. In particular, we also find that the CE below the critical temperature becomes constant and its magnitude increases as a dimension of AdS space increases. Corrections to Hawking radiation and Bekenstein-Hawking entropy of novel four-dimensional black holes in Gauss-Bonnet gravity https://www.zbmath.org/1483.83053 2022-05-16T20:40:13.078697Z "Li, Gu-Qiang" https://www.zbmath.org/authors/?q=ai:li.guqiang "Mo, Jie-Xiong" https://www.zbmath.org/authors/?q=ai:mo.jie-xiong "Zhuang, Yi-Wen" https://www.zbmath.org/authors/?q=ai:zhuang.yi-wen Summary: We make use of the Hamilton-Jacobi and Parikh-Wilczek methods to investigate the Hawking radiation from the event horizon of a new charged anti-de Sitter black hole in four-dimensional Gauss-Bonnet gravity space-time. Both the tunneling rate of charged particles and the Bekenstein-Hawking entropy are evaluated. The emission spectrum is an impure thermal one and consistent with an underlying unitary theory. There is no difference between the emission rate of massive particle and that of massless one. The entropy is modified by a logarithmic term so that the area law of the black hole entropy is violated. It satisfies the first law of black hole thermodynamics and has the same expression as that calculated by Loop Quantum Gravity and String Theory. When the Gauss-Bonnet coupling coefficient is equal to zero, the logarithmic correction vanishes and the Bekenstein-Hawking relation in general relativity is recovered. So our results show the effects of the Gauss-Bonnet modified gravity on the Bekenstein-Hawking entropy and Hawking radiation. Inflation, phase transitions and the cosmological constant https://www.zbmath.org/1483.83083 2022-05-16T20:40:13.078697Z "Bertolami, Orfeu" https://www.zbmath.org/authors/?q=ai:bertolami.orfeu Summary: Cosmological phase transitions are thought to have taken place at the early Universe imprinting their properties on the observable Universe. There is strong evidence that, through the dynamics of a scalar field that lead a second order phase transition, inflation shaped the Universe accounting for the most conspicuous features of the observed Universe. It is argued that inflation has also striking implications for the vacuum energy. Considerations for subsequent second order phase transitions are also discussed. AdS graviton stars and differential configurational entropy https://www.zbmath.org/1483.85002 2022-05-16T20:40:13.078697Z "da Rocha, Roldao" https://www.zbmath.org/authors/?q=ai:da-rocha.roldao-jun|rocha.roldao-da Summary: AdS graviton stars are studied in the differential configurational entropy setup, as solutions of the effective Einstein field equations that backreact to compactification. With the critical central density of AdS graviton stars, the differential configurational entropy is derived and computed, presenting global minima for a wide range of stellar mass magnitude orders. It indicates insular domains of configurational stability for AdS graviton stars near astrophysical neutron star densities. Other relevant features are also reported. Characterization of ionospheric total electron content data using wavelet-based multifractal formalism https://www.zbmath.org/1483.86005 2022-05-16T20:40:13.078697Z "Bhardwaj, Shivam" https://www.zbmath.org/authors/?q=ai:bhardwaj.shivam "Chandrasekhar, E." https://www.zbmath.org/authors/?q=ai:chandrasekhar.e "Seemala, Gopi K." https://www.zbmath.org/authors/?q=ai:seemala.gopi-k "Gadre, Vikram M." https://www.zbmath.org/authors/?q=ai:gadre.vikram-m Summary: Understanding of the spatio-temporal behaviour of nonlinear geophysical signals, such as ionospheric total electron content (TEC) by multifractal analysis brings out the chaotic and intermittent nature of the signal under consideration. Wavelet-based multifractal analysis was performed on TEC data and the horizontal component of the Earth's magnetic field (henceforth referred to as H-component) data recorded during geomagnetic storm events at a few sites in equatorial, mid-latitude and high latitude regions (30\degree S to 80\degree N), confined to a narrow longitude band (35\degree W--80\degree W) (geographic coordinates) during the solar minimum (2008) and solar maximum (2014) years. The study was done using the magnitude cumulant analysis of the wavelet transform. The advantage of this technique, over the well known wavelet transform modulus maxima (WTMM) method in studying the multifractal behaviour of nonlinear signals is explained. Results show that during the major geomagnetic storm events (Dst. Index $$\leq-50$$ nT) both TEC and the H-component data exhibit strong multifractal behavior and that the degree of multifractality (representative of the width of the multifractal spectrum) for the H-component data is more than that of TEC for all latitudes regardless of solar conditions. A nonlinear P-model, representative of multiplicative cascades for the above data sets, also supports the above observation. It has been observed that these observations hold good when multifractal behaviour of TEC data, with and without its dominant diurnal component, is compared with that of H-component data. A statistical hypothesis testing of the above results obtained using bootstrapping technique also establishes the significance level of the multifractal behaviour of the data. Optimality conditions for vector variational inequalities via image space analysis https://www.zbmath.org/1483.90156 2022-05-16T20:40:13.078697Z "Mastroeni, G." https://www.zbmath.org/authors/?q=ai:mastroeni.giandomenico "Pappalardo, M." https://www.zbmath.org/authors/?q=ai:pappalardo.massimo Saddle point and Karush-Kuh-Tucker type optimality conditions for vector variational inequalities in Hausdorff locally convex topological spaces are provided by means of a separation scheme in the framework of image space analysis. Reviewer: Sorin-Mihai Grad (Paris) Entrack: probabilistic spherical regression with entropy regularization for fiber tractography https://www.zbmath.org/1483.92090 2022-05-16T20:40:13.078697Z "Wegmayr, Viktor" https://www.zbmath.org/authors/?q=ai:wegmayr.viktor "Buhmann, Joachim M." https://www.zbmath.org/authors/?q=ai:buhmann.joachim-m Summary: White matter tractography, based on diffusion-weighted magnetic resonance images, is currently the only available in vivo method to gather information on the structural brain connectivity. The low resolution of diffusion MRI data suggests to employ probabilistic methods for streamline reconstruction, i.e., for fiber crossings. We propose a general probabilistic model for spherical regression based on the Fisher-von-Mises distribution, which efficiently estimates maximum entropy posteriors of local streamline directions with machine learning methods. The optimal precision of posteriors for streamlines is determined by an information-theoretic technique, the expected log-posterior agreement concept. It relies on the requirement that the posterior distributions of streamlines, inferred on retest measurements of the same subject, should yield stable results within the precision determined by the noise level of the data source. Average consensus by graph filtering: new approach, explicit convergence rate, and optimal design https://www.zbmath.org/1483.93013 2022-05-16T20:40:13.078697Z "Yi, Jing-Wen" https://www.zbmath.org/authors/?q=ai:yi.jing-wen "Chai, Li" https://www.zbmath.org/authors/?q=ai:chai.li "Zhang, Jingxin" https://www.zbmath.org/authors/?q=ai:zhang.jingxin Editorial remark: No review copy delivered. Research on security trust measure model based on fuzzy mathematics https://www.zbmath.org/1483.93346 2022-05-16T20:40:13.078697Z "Wei, PengCheng" https://www.zbmath.org/authors/?q=ai:wei.pengcheng "He, Fangcheng" https://www.zbmath.org/authors/?q=ai:he.fangcheng Summary: The existing safety measurement model has the disadvantages of poor reliability and stability. In order to improve the reliability of the security trust measurement structure, a fuzzy trust-based security trust measurement model is proposed. The hierarchical fuzzy transmission network is used to establish the mathematical model of the controlled object, and the control objective function is analyzed. The regression analysis model is combined with the convergence constraint function, and the fuzzy adaptive learning is performed according to the security trusted computing output weight, and the parameter analysis is performed. And adjust; on this basis, establish a mathematical model of safety confidence measurement, and perform parameter feedback adjustment and reliability control to improve the reliability of the security trust measurement structure. The simulation results show that the proposed method has good reliability and steady-state convergence, and can effectively improve the reliability calculation ability of the safety confidence measure. It has strong application advantages. Reduced-order observer design for Boolean control networks https://www.zbmath.org/1483.93422 2022-05-16T20:40:13.078697Z "Zhang, Zhihua" https://www.zbmath.org/authors/?q=ai:zhang.zhihua.1 "Leifeld, Thomas" https://www.zbmath.org/authors/?q=ai:leifeld.thomas "Zhang, Ping" https://www.zbmath.org/authors/?q=ai:zhang.ping|zhang.ping.2|zhang.ping.6|zhang.ping.5|zhang.ping.3|zhang.ping.1 Editorial remark: No review copy delivered. On estimation errors in optical communication and location https://www.zbmath.org/1483.93620 2022-05-16T20:40:13.078697Z "Chernoyarov, O. V." https://www.zbmath.org/authors/?q=ai:chernoyarov.oleg-v "Dachian, S." https://www.zbmath.org/authors/?q=ai:dachian.serguei "Kutoyants, Yu. A." https://www.zbmath.org/authors/?q=ai:kutoyants.yury-a "Zyulkov, A. V." https://www.zbmath.org/authors/?q=ai:zyulkov.a-v Summary: We consider several problems of parameter estimation based on observations of inhomogeneous Poisson processes arising in various practical applications of optical communication and location. The intensity function of the observed process consists of a periodic signal depending on an unknown parameter and a constant noise intensity. The asymptotic behavior of maximum likelihood and Bayesian estimators in cases of phase and frequency modulation of signals is described. Particular attention is paid to signals of various regularity (smooth, continuous but nondifferentiable, and of change-point type). Numerical simulations illustrate the results presented. This paper is a survey of results on the behavior of estimators in cases of frequency and phase modulation of signals of various regularity. On the performance analysis of reset attack in cyber-physical systems https://www.zbmath.org/1483.93657 2022-05-16T20:40:13.078697Z "Ni, Yuqing" https://www.zbmath.org/authors/?q=ai:ni.yuqing "Guo, Ziyang" https://www.zbmath.org/authors/?q=ai:guo.ziyang "Mo, Yilin" https://www.zbmath.org/authors/?q=ai:mo.yilin "Shi, Ling" https://www.zbmath.org/authors/?q=ai:shi.ling Editorial remark: No review copy delivered. Optimal input signals for parameter estimation. In linear systems with spatio-temporal dynamics https://www.zbmath.org/1483.94001 2022-05-16T20:40:13.078697Z "Rafajłowicz, Ewaryst" https://www.zbmath.org/authors/?q=ai:rafajlowicz.ewaryst Publisher's description: The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE's as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. \begin{itemize} \item An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. \item New optimality conditions in the time domain and computational algorithms are derived for $$D$$-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing $$D$$-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. \item Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. \item A discussion of the generalizability and possible applications of the results obtained is presented. \end{itemize} Efficient signature verification and key revocation using identity based cryptography https://www.zbmath.org/1483.94002 2022-05-16T20:40:13.078697Z "Guggemos, Tobias" https://www.zbmath.org/authors/?q=ai:guggemos.tobias Publisher's description: We present a solution for signature verification and key revocation in constrained environments, e.g., in the Internet of Things (IoT). Where other mechanisms generate expensive overheads, we achieve revocation through a single multicast message without significant computational or storage overhead. Exploiting Identity Based Cryptography (IBC) complements the approach with efficient creation and verification of signatures. Our solution offers a framework for transforming a suitable signature scheme to a so-called Key Updatable Signature Scheme (KUSS) in three steps. Each step defines mathematical conditions for transformation and precise security notions. Thereby, the framework allows a novel combination of efficient Identity Based Signature (IBS) schemes with revocation mechanisms originally designed for confidentiality in group communications. Practical applicability of our framework is demonstrated by transforming four well-established IBS schemes based on Elliptic Curve Cryptography (ECC). The security of the resulting group Identity Based Signature (gIBS) schemes is carefully analyzed with techniques of Provable Security. We design and implement a testbed for evaluating these kind of cryptographic schemes on different computing- and networking hardware, typical for constrained environments. Measurements on this testbed provide evidence that the transformations are practicable and efficient. The revocation complexity in turn is significantly reduced compared to existing solutions. Some of our new schemes even outperform the signing process of the widely used Elliptic Curve Digital Signature Algorithm (ECDSA). The presented transformations allow future application on schemes beyond IBS or ECC. This includes use cases dealing with Post-Quantum Cryptography, where the revocation efficiency is similarly relevant. Our work provides the basis for such solutions currently under investigation. Protecting privacy through homomorphic encryption. Based on 6 workshops on homomorphic encryption standardization https://www.zbmath.org/1483.94003 2022-05-16T20:40:13.078697Z Publisher's description: This book summarizes recent inventions, provides guidelines and recommendations, and demonstrates many practical applications of homomorphic encryption. This collection of papers represents the combined wisdom of the community of leading experts on Homomorphic Encryption. In the past 3 years, a global community consisting of researchers in academia, industry, and government, has been working closely to standardize homomorphic encryption. This is the first publication of whitepapers created by these experts that comprehensively describes the scientific inventions, presents a concrete security analysis, and broadly discusses applicable use scenarios and markets. This book also features a collection of privacy-preserving machine learning applications powered by homomorphic encryption designed by groups of top graduate students worldwide at the Private AI Bootcamp hosted by Microsoft Research.The volume aims to connect non-expert readers with this important new cryptographic technology in an accessible and actionable way. Readers who have heard good things about homomorphic encryption but are not familiar with the details will find this book full of inspiration. Readers who have preconceived biases based on out-of-date knowledge will see the recent progress made by industrial and academic pioneers on optimizing and standardizing this technology. A clear picture of how homomorphic encryption works, how to use it to solve real-world problems, and how to efficiently strengthen privacy protection, will naturally become clear. The articles of mathematical interest will be reviewed individually. Advances in cryptology -- CRYPTO 2021. 41st annual international cryptology conference, CRYPTO 2021, virtual event, August 16--20, 2021. Proceedings. Part I https://www.zbmath.org/1483.94004 2022-05-16T20:40:13.078697Z The articles of this volume will be reviewed individually. For the preceding conference see [Zbl 1475.94010; Zbl 1475.94011; Zbl 1475.94012]. For Parts II--IV of the proceedings of the present conference see [Zbl 07386996; Zbl 07386997; Zbl 07386998]. Indexed articles: \textit{Liu, Yanyi; Pass, Rafael}, On the possibility of basing cryptography on $$\mathsf{EXP}\ne \mathsf{BPP}$$, 11-40 [Zbl 07500821] \textit{Beyne, Tim}, Linear cryptanalysis of FF3-1 and FEA, 41-69 [Zbl 07500822] \textit{Tao, Chengdong; Petzoldt, Albrecht; Ding, Jintai}, Efficient key recovery for all HFE signature variants, 70-93 [Zbl 07500823] \textit{Rosulek, Mike; Roy, Lawrence}, Three halves make a whole? Beating the half-gates lower bound for garbled circuits, 94-124 [Zbl 07500824] \textit{Garillot, François; Kondi, Yashvanth; Mohassel, Payman; Nikolaenko, Valeria}, Threshold Schnorr with stateless deterministic signing from standard assumptions, 127-156 [Zbl 07500825] \textit{Kılınç Alper, Handan; Burdges, Jeffrey}, Two-round trip Schnorr multi-signatures via delinearized witnesses, 157-188 [Zbl 07500826] \textit{Nick, Jonas; Ruffing, Tim; Seurin, Yannick}, MuSig2: simple two-round Schnorr multi-signatures, 189-221 [Zbl 07500827] \textit{Rotem, Lior; Segev, Gil}, Tighter security for Schnorr identification and signatures: a high-moment forking lemma for $${\varSigma }$$-protocols, 222-250 [Zbl 07500828] \textit{Yuen, Tsz Hon; Esgin, Muhammed F.; Liu, Joseph K.; Au, Man Ho; Ding, Zhimin}, DualRing: generic construction of ring signatures with efficient instantiations, 251-281 [Zbl 07500829] \textit{Chatterjee, Rohit; Garg, Sanjam; Hajiabadi, Mohammad; Khurana, Dakshita; Liang, Xiao; Malavolta, Giulio; Pandey, Omkant; Shiehian, Sina}, Compact ring signatures from learning with errors, 282-312 [Zbl 07500830] \textit{Chia, Nai-Hui; Chung, Kai-Min; Yamakawa, Takashi}, A black-box approach to post-quantum zero-knowledge in constant rounds, 315-345 [Zbl 07500831] \textit{Ananth, Prabhanjan; Chung, Kai-Min; Placa, Rolando L. La}, On the concurrent composition of quantum zero-knowledge, 346-374 [Zbl 07500832] \textit{Shmueli, Omri}, Multi-theorem designated-verifier NIZK for QMA, 375-405 [Zbl 07500833] \textit{Bartusek, James; Coladangelo, Andrea; Khurana, Dakshita; Ma, Fermi}, On the round complexity of secure quantum computation, 406-435 [Zbl 07500834] \textit{Alon, Bar; Chung, Hao; Chung, Kai-Min; Huang, Mi-Ying; Lee, Yi; Shen, Yu-Ching}, Round efficient secure multiparty quantum computation with identifiable abort, 436-466 [Zbl 07500835] \textit{Bartusek, James; Coladangelo, Andrea; Khurana, Dakshita; Ma, Fermi}, One-way functions imply secure computation in a quantum world, 467-496 [Zbl 07500836] \textit{Alagic, Gorjan; Brakerski, Zvika; Dulek, Yfke; Schaffner, Christian}, Impossibility of quantum virtual black-box obfuscation of classical circuits, 497-525 [Zbl 07500837] \textit{Aaronson, Scott; Liu, Jiahui; Liu, Qipeng; Zhandry, Mark; Zhang, Ruizhe}, New approaches for quantum copy-protection, 526-555 [Zbl 07500838] \textit{Coladangelo, Andrea; Liu, Jiahui; Liu, Qipeng; Zhandry, Mark}, Hidden cosets and applications to unclonable cryptography, 556-584 [Zbl 07500839] \textit{Hosoyamada, Akinori; Iwata, Tetsu}, On tight quantum security of HMAC and NMAC in the quantum random oracle model, 585-615 [Zbl 07500840] \textit{Hosoyamada, Akinori; Sasaki, Yu}, Quantum collision attacks on reduced SHA-256 and SHA-512, 616-646 [Zbl 07500841] \textit{Boneh, Dan; Drake, Justin; Fisch, Ben; Gabizon, Ariel}, \textsf{Halo Infinite}: proof-carrying data from additive polynomial commitments, 649-680 [Zbl 07500842] \textit{Bünz, Benedikt; Chiesa, Alessandro; Lin, William; Mishra, Pratyush; Spooner, Nicholas}, Proof-carrying data without succinct arguments, 681-710 [Zbl 07500843] \textit{Chiesa, Alessandro; Yogev, Eylon}, Subquadratic SNARGs in the random oracle model, 711-741 [Zbl 07500844] \textit{Bootle, Jonathan; Chiesa, Alessandro; Sotiraki, Katerina}, Sumcheck arguments and their applications, 742-773 [Zbl 07500845] \textit{Ràfols, Carla; Zapico, Arantxa}, An algebraic framework for universal and updatable SNARKs, 774-804 [Zbl 07500846] Analysis of critical damage in the communication network. III: Analysis of internode flows https://www.zbmath.org/1483.94005 2022-05-16T20:40:13.078697Z "Malashenko, Y. E." https://www.zbmath.org/authors/?q=ai:malashenko.yu-e "Nazarova, I. A." https://www.zbmath.org/authors/?q=ai:nazarova.irina-a The paper presents an interesting approach to analyzing critical damage in communication networks. As the critical damage, the authors accepted a subset of edges, removing which at least for one pair of nodes breaks all possible connection paths. For each pair of source-destination vertices, two criteria are used to estimate the decrease in the flow for each damage from the given set. At the first step, all destructive actions are determined at which the maximal possible flow for some selected pair of nodes become zero (the first criterion). At the next step, for such a pair, all damages are found at which the maximal flow was below the permissible level but greater than zero (the second criterion). Finally, based on the data obtained, diagrams of the maximal permissible flows between each pair of vertices are formed for all critical damage from the given set. In this paper, the authors consider and analyze three types of damage: destruction of the minimal cut separating the source-destination pair in an intact network, destruction of the minimal cut in a network with unit capacities, and destruction of all edges incident to a vertex. The computational experiments are carried out for all possible combinations of source-destination pairs of vertices, considering the transmission direction. The results of the consequences of destructive influences on network systems with various structural features are further analyzed -- the authors analyze two network models, so-called core, and ring networks. The capacities of edges are chosen at random from the segment [900, 999] and are equal for coinciding edges in both networks. In this study, the authors continue their earlier study of the flow method of the a priori analysis of the structural invulnerability of a network in the case of a certain type of failure. The choice as the structural damage of cuts that are minimal in terms of throughput and the number of edges, as well as separating a certain vertex from the network, is determined by the logic of the study. The search for the most vulnerable source-destination pairs for the indicated damage is carried out according to two criteria (the zeroing of the flow and the flow falling below a predetermined level), which makes it possible to estimate in advance how the structure retains the standard performance of the network system after destruction. When carrying out the computational experiment, the methods of flow programming with a polynomial estimate of the computational complexity are used. As presented by the authors, the proposed calculation scheme is relatively simple and amenable to parallelization. Therefore, when investigating the vulnerability of large networks, even clusters of personal computers with various operating systems could be used. \par For Part I and II see [the authors, J. Comput. Syst. Sci. Int. 59, No. 5, 745--754 (2020; Zbl 1459.94006); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upravl. 2020, No. 5, 106--115 (2020); J. Comput. Syst. Sci. Int. 59, No. 6, 918--927 (2020; Zbl 1459.94005); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upravl. 2020, No. 6, 109--119 (2020)]. Reviewer: Józef Woźniak (Gdańsk) Trust framework for attack resilience in MANET using AODV https://www.zbmath.org/1483.94006 2022-05-16T20:40:13.078697Z "Wadhwani, Ganesh Kumar" https://www.zbmath.org/authors/?q=ai:wadhwani.ganesh-kumar "Khatri, Sunil Kumar" https://www.zbmath.org/authors/?q=ai:khatri.sunil-kumar "Mutto, S. K." https://www.zbmath.org/authors/?q=ai:mutto.s-k Summary: Mobile Ad-hoc network (MANET) is a collection of arbitrary moving autonomous nodes having routing capabilities. Theoretically, nodes are expected to cooperate with each other to facilitate communication with not directly connected nodes but in real scenario some of the nodes may be malicious. These compromised/malicious nodes may be part of the network or any other node trying to intrude in the network. A trust based framework is proposed in this paper to make the network resilient to malicious nodes. Trust is calculated using route request and route reply counter to make it simple and scalable. Ad Hoc On-Demand Distance Vector (AODV) routing protocol is used as the basic protocol. Performance analysis is done by varying malicious node density and calculating packet loss \& average packet delay. It shows that the proposed framework along with trust calculating mechanism is giving better results as compared to basic routing protocol AODV in the presence of malicious nodes. Image edge sharpening via heaviside substitution and structure recovery https://www.zbmath.org/1483.94007 2022-05-16T20:40:13.078697Z "Deng, Liang-Jian" https://www.zbmath.org/authors/?q=ai:deng.liangjian "Guo, Weihong" https://www.zbmath.org/authors/?q=ai:guo.weihong "Huang, Ting-Zhu" https://www.zbmath.org/authors/?q=ai:huang.ting-zhu Summary: In this paper, we propose a simple but efficient method to sharpen image edges. Starting from an image with blurry edges, we improve edge sharpness using transformed approximated Heaviside functions (AHFs) for better visualization. In particular, we provide an efficient method for directly computing the scaling and shifting factors of the transformed AHFs, so that blurred edges can be improved accurately. To recover more image structures, we give a sharp edge-preserving reconstruction model that is based on the result of the edge sharpening strategy. A gradient descent algorithm can efficiently solve the reconstruction model. Moreover, we apply the proposed method to image super-resolution and deblurring. Extensive experimental results demonstrate that the proposed method can efficiently obtain competitive performance, both visually and quantitatively. For the entire collection see [Zbl 1477.62002]. An encryption algorithm for grey-scale image based on bit-plane decomposition and diffuse representation https://www.zbmath.org/1483.94008 2022-05-16T20:40:13.078697Z "Houas, A." https://www.zbmath.org/authors/?q=ai:houas.a "Rezki, B." https://www.zbmath.org/authors/?q=ai:rezki.b "Mokhtari, Z." https://www.zbmath.org/authors/?q=ai:mokhtari.zouhir Summary: In this work, the authors construct a new algorithm to encrypt images of grey-scale type. After the decomposition of the image into 8 bit-planes, the key-image for the encryption and decryption algorithm are got by the representation of the 8 bit-planes in the new introduced basis. The decryption is done by subtraction between each encrypted image and key-image to obtain the 8 bit-planes from which we can restitute the original image without loss of information. The effectiveness of our proposed scheme is confirmed by some experimental results. Two-step blind deconvolution of UPC-a barcode images https://www.zbmath.org/1483.94009 2022-05-16T20:40:13.078697Z "Kim, Bohyun" https://www.zbmath.org/authors/?q=ai:kim.bohyun "Lou, Yifei" https://www.zbmath.org/authors/?q=ai:lou.yifei Summary: Barcodes are widely used in supermarkets and tracking systems. One noticeable difficulty in barcode recognition is caused by blurring artifacts. For example, a focal blur may occur when the data is captured at a far distance, and motion blur is often inevitable under a low light condition. To decipher the barcode, many barcode reading systems may require more information than the image alone, e.g., the digits written below the barcode and/or a blurring kernel that describes how the data is blurred from a clean image. In this paper, we propose a method to recover a clean barcode from the blurred data without any additional information (e.g. information on the blurring kernel and so on). In particular, we propose a two-step procedure for blind deconvolution of barcode images. In the first step, we estimate the blurring kernel by exploiting a barcode structure with an exclusive search of the first two digits. Using the estimated kernel, we rely on a non-blind deconvolution technique to restore the entire barcode. We conduct numerical experiments based on both synthetic and real data, showing the efficiency and accuracy of the proposed method. For the entire collection see [Zbl 1477.62002]. Dual algorithm for truncated fractional variation based image denoising https://www.zbmath.org/1483.94010 2022-05-16T20:40:13.078697Z "Liang, Haixia" https://www.zbmath.org/authors/?q=ai:liang.haixia "Zhang, Juli" https://www.zbmath.org/authors/?q=ai:zhang.juli Summary: Fractional-order derivative is attracting more and more attention of researchers in image processing because of its better property in restoring more texture than the total variation. To improve the performance of fractional-order variation model in image restoration, a truncated fractional-order variation model was proposed in [\textit{R. H. Chan} and \textit{H.-X. Liang}, J. Oper. Res. Soc. China 7, No. 4, 561--578 (2019; Zbl 1438.94005)]. In this paper, we propose a dual approach to solve this truncated fractional-order variation model on noise removal. The proposed algorithm is based on the dual approach proposed by \textit{A. Chambolle} [J. Math. Imaging Vis. 20, No. 1--2, 89--97 (2004; Zbl 1366.94048)]. Conversely, the Chambolle's dual approach can be treated as a special case of the proposed algorithm with fractional order $$\alpha = 1$$. The work of this paper modifies the result in [\textit{J. Zhang} et al., ibid. 43, No. 1, 39--49 (2012; Zbl 1255.68278)], where the convergence is not analysed. Based on the truncation, the convergence of the proposed dual method can be analysed and the convergence criteria can be provided. In addition, the accuracy of the reconstruction is improved after the truncation is taken. An anisotropic local method for boundary detection in images https://www.zbmath.org/1483.94011 2022-05-16T20:40:13.078697Z "Lund, Margaret" https://www.zbmath.org/authors/?q=ai:lund.margaret "Howard, Marylesa" https://www.zbmath.org/authors/?q=ai:howard.marylesa "Wu, Dongsheng" https://www.zbmath.org/authors/?q=ai:wu.dongsheng "Crum, Ryan S." https://www.zbmath.org/authors/?q=ai:crum.ryan-s "Miller, Dorothy J." https://www.zbmath.org/authors/?q=ai:miller.dorothy-j "Akin, Minta C." https://www.zbmath.org/authors/?q=ai:akin.minta-c Summary: Boundary detection is a powerful tool for quantitative image analysis that allows researchers to extract crucial information about a scene. Many methods rely on sharp changes in luminance, chromaticity, or texture in order to correctly predict edge locations between regions, and images without these features have proven difficult to partition. We present a supervised statistical boundary detection method based on image segmentation that incorporates spatial information to locate boundaries in images with low contrast between classes, heteroskedasticity, and objects whose intensity values vary spatially. Similar to its predecessor, the algorithm incorporates user-selected training data to place each pixel into the most probable class based on the statistics of local training data. The major contribution of this work is in the algorithm using a single insensitive parameter to restrict the statistics to be calculated on anisotropic (elliptical) local training data since pixels that lie along a boundary are assumed to be most informative of the boundary location. The algorithm's success is demonstrated on images from the Berkeley Segmentation Dataset and on X-ray images of olivine sand under dynamic compaction loading. Additionally, because of the statistical nature of the algorithm, maps showing the uncertainty in the boundary location are provided. For the entire collection see [Zbl 1477.62002]. Two-stage geometric information guided image reconstruction https://www.zbmath.org/1483.94012 2022-05-16T20:40:13.078697Z "Qin, Jing" https://www.zbmath.org/authors/?q=ai:qin.jing "Guo, Weihong" https://www.zbmath.org/authors/?q=ai:guo.weihong Summary: In compressive sensing, it is challenging to reconstruct image of high quality from very few noisy linear projections. Existing methods mostly work well on piecewise constant images but not so well on piecewise smooth images such as natural images, medical images that contain a lot of details. We propose a two-stage method called GeoCS to recover images with rich geometric information from very limited amount of noisy measurements. The method adopts the shearlet transform that is mathematically proven to be optimal in sparsely representing images containing anisotropic features such as edges, corners, spikes etc. It also uses the weighted total variation (TV) sparsity with spatially variant weights to preserve sharp edges but to reduce the staircase effects of TV. Geometric information extracted from the results of stage I serves as an initial prior for stage II which alternates image reconstruction and geometric information update in a mutually beneficial way. GeoCS has been tested on incomplete spectral Fourier samples. It is applicable to other types of measurements as well. Experimental results on various complicated images show that GeoCS is efficient and generates high-quality images. For the entire collection see [Zbl 1477.62002]. Application of the optimized 1-bit tensor completion method in the recovery of noisy digital images https://www.zbmath.org/1483.94013 2022-05-16T20:40:13.078697Z "Shahrezaei, Mohsen" https://www.zbmath.org/authors/?q=ai:shahrezaei.mohsen "Shojaeifard, Alireza" https://www.zbmath.org/authors/?q=ai:shojaeifard.alireza "Yazdani, Hamid Reza" https://www.zbmath.org/authors/?q=ai:yazdani.hamid-reza (no abstract) Patch-based image restoration using expectation propagation https://www.zbmath.org/1483.94014 2022-05-16T20:40:13.078697Z "Yao, Dan" https://www.zbmath.org/authors/?q=ai:yao.dan "McLaughlin, Stephen" https://www.zbmath.org/authors/?q=ai:mclaughlin.stephen "Altmann, Yoann" https://www.zbmath.org/authors/?q=ai:altmann.yoann A simple recovery framework for signals with time-varying sparse support https://www.zbmath.org/1483.94015 2022-05-16T20:40:13.078697Z "Durgin, Natalie" https://www.zbmath.org/authors/?q=ai:durgin.natalie "Grotheer, Rachel" https://www.zbmath.org/authors/?q=ai:grotheer.rachel "Huang, Chenxi" https://www.zbmath.org/authors/?q=ai:huang.chenxi "Li, Shuang" https://www.zbmath.org/authors/?q=ai:li.shuang "Ma, Anna" https://www.zbmath.org/authors/?q=ai:ma.anna "Needell, Deanna" https://www.zbmath.org/authors/?q=ai:needell.deanna "Qin, Jing" https://www.zbmath.org/authors/?q=ai:qin.jing Summary: Sparse recovery methods have been developed to solve multiple measurement vector (MMV) problems. These methods seek to reconstruct a collection of sparse signals from a small number of linear measurements, exploiting not only the sparsity but also certain correlations between the signals. Typically, the assumption is that the collection of signals shares a common joint support, allowing the problem to be solved more efficiently (or with fewer measurements) than solving many individual, single measurement vector (SMV) subproblems. Here, we relax this stringent assumption so that the signals may exhibit a changing support, a behavior that is much more prominent in applications. We propose a simple windowed framework that can utilize any traditional MMV method as a subroutine, and exhibits improved recovery when the MMV method incorporates prior information on signal support. In doing so, our framework enjoys natural extensions of existing theory and performance of such MMV methods. We demonstrate the value of this approach by using different MMV methods as subroutines within the proposed framework and applying it to both synthetic and real-world data. For the entire collection see [Zbl 1477.62002]. Wavelet invariants for statistically robust multi-reference alignment https://www.zbmath.org/1483.94016 2022-05-16T20:40:13.078697Z "Hirn, Matthew" https://www.zbmath.org/authors/?q=ai:hirn.matthew-j "Little, Anna" https://www.zbmath.org/authors/?q=ai:little.anna-v Summary: We propose a nonlinear, wavelet-based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the statistical properties of this representation given a large number of independent corruptions of a target signal. We prove the nonlinear wavelet-based representation uniquely defines the power spectrum but allows for an unbiasing procedure that cannot be directly applied to the power spectrum. After unbiasing the representation to remove the effects of the additive noise and random dilations, we recover an approximation of the power spectrum by solving a convex optimization problem, and thus reduce to a phase retrieval problem. Extensive numerical experiments demonstrate the statistical robustness of this approximation procedure. Faster Johnson-Lindenstrauss transforms via Kronecker products https://www.zbmath.org/1483.94017 2022-05-16T20:40:13.078697Z "Jin, Ruhui" https://www.zbmath.org/authors/?q=ai:jin.ruhui "Kolda, Tamara G." https://www.zbmath.org/authors/?q=ai:kolda.tamara-g "Ward, Rachel" https://www.zbmath.org/authors/?q=ai:ward.rachel-a Summary: The Kronecker product is an important matrix operation with a wide range of applications in signal processing, graph theory, quantum computing and deep learning. In this work, we introduce a generalization of the fast Johnson-Lindenstrauss projection for embedding vectors with Kronecker product structure, the Kronecker fast Johnson-Lindenstrauss transform (KFJLT). The KFJLT reduces the embedding cost by an exponential factor of the standard fast Johnson-Lindenstrauss transform's cost when applied to vectors with Kronecker structure, by avoiding explicitly forming the full Kronecker products. We prove that this computational gain comes with only a small price in embedding power: consider a finite set of $$p$$ points in a tensor product of $$d$$ constituent Euclidean spaces $$\bigotimes_{k=d}^1\mathbb{R}^{n_k}$$, and let $$N = \prod_{k=1}^dn_k$$. With high probability, a random KFJLT matrix of dimension $$m \times N$$ embeds the set of points up to multiplicative distortion ($$1\pm \varepsilon$$) provided $$m \gtrsim \varepsilon^{-2}\,\log^{2d-1}(p)\,\log N$$. We conclude by describing a direct application of the KFJLT to the efficient solution of large-scale Kronecker-structured least squares problems for fitting the CP tensor decomposition. The optimization algorithm for blind processing of high frequency signal of capacitive sensor https://www.zbmath.org/1483.94018 2022-05-16T20:40:13.078697Z "Ma, Yuanjia" https://www.zbmath.org/authors/?q=ai:ma.yuanjia Summary: At present, the high frequency signal processing algorithm of capacitive sensor based on RBF has the problems of poor filtering effect and high level of signal detection and poor quality of signal separation. In this paper, an optimization algorithm for blind processing of high frequency signal of capacitive sensor is proposed. Based on the gradient method, and the calculation way of improved variance gradient estimation, the gradient of square single- error sample is taken as the estimation of mean square error to filter the capacitive sensor signal, and adjust the filtering step by adjusting the threshold, which can enhance the filtering effect of the sensor signal; The detection threshold is calculated by determining the false alarm probability. The decision condition is used to detect the target signal and get the high accuracy sensor signal. The initialization separation matrix is set according to the number of observation signals, and the correlation matrix of the source signal can be calculated, so as to achieve the efficient separation of high frequency signals. The experiment shows that the algorithm can effectively solve the problems existing in the current signal processing algorithm, and it is reliable. Inverting spectrogram measurements via aliased Wigner distribution deconvolution and angular synchronization https://www.zbmath.org/1483.94019 2022-05-16T20:40:13.078697Z "Perlmutter, Michael" https://www.zbmath.org/authors/?q=ai:perlmutter.michael "Merhi, Sami" https://www.zbmath.org/authors/?q=ai:merhi.sami "Viswanathan, Aditya" https://www.zbmath.org/authors/?q=ai:viswanathan.aditya "Iwen, Mark" https://www.zbmath.org/authors/?q=ai:iwen.mark-a Summary: We propose a two-step approach for reconstructing a signal $$\mathfrak{x}\in\mathbb{C}^d$$ from subsampled discrete short-time Fourier transform magnitude (spectogram) measurements: first, we use an aliased Wigner distribution deconvolution approach to solve for a portion of the rank-one matrix $$\widehat{\mathfrak{x}}\widehat{\mathfrak{x}}^\ast$$. Secondly, we use angular synchronization to solve for $$\widehat{\mathfrak{x}}$$ (and then for $$\mathfrak{x}$$ by Fourier inversion). Using this method, we produce two new efficient phase retrieval algorithms that perform well numerically in comparison to standard approaches and also prove two theorems; one which guarantees the recovery of discrete, bandlimited signals $$\mathfrak{x}\in\mathbb{C}^d$$ from fewer than $$d$$ short-time Fourier transform magnitude measurements and another which establishes a new class of deterministic coded diffraction pattern measurements which are guaranteed to allow efficient and noise robust recovery. Self-triggered network coordination over noisy communication channels https://www.zbmath.org/1483.94020 2022-05-16T20:40:13.078697Z "Shi, Mingming" https://www.zbmath.org/authors/?q=ai:shi.mingming "Tesi, Pietro" https://www.zbmath.org/authors/?q=ai:tesi.pietro "De Persis, Claudio" https://www.zbmath.org/authors/?q=ai:de-persis.claudio Editorial remark: No review copy delivered. RBFNN-based minimum entropy filtering for a class of stochastic nonlinear systems https://www.zbmath.org/1483.94021 2022-05-16T20:40:13.078697Z "Yin, Xin" https://www.zbmath.org/authors/?q=ai:yin.xin "Zhang, Qichun" https://www.zbmath.org/authors/?q=ai:zhang.qichun "Wang, Hong" https://www.zbmath.org/authors/?q=ai:wang.hong.7 "Ding, Zhengtao" https://www.zbmath.org/authors/?q=ai:ding.zhengtao Editorial remark: No review copy delivered. Information-based physics, influence, and forces https://www.zbmath.org/1483.94022 2022-05-16T20:40:13.078697Z "Walsh, James Lyons" https://www.zbmath.org/authors/?q=ai:walsh.james-lyons "Knuth, Kevin H." https://www.zbmath.org/authors/?q=ai:knuth.kevin-h Summary: In recent works, Knuth and Bahreyni have demonstrated that the concepts of space and time are emergent in a coarse-grained model of direct particle-particle influence. In addition, Knuth demonstrated that observer-made inferences regarding the free particle, which is defined as a particle that influences others, but is not itself influenced, result in a situation identical to the Feynman checkerboard model of the Dirac equation. This suggests that the same theoretical framework that gives rise to an emergent spacetime is consistent with quantum mechanics. In this paper, we begin to explore the effect of influence on the emergent properties of a particle. This initial study suggests that when a particle is influenced, it is interpreted as accelerating in a manner consistent with special relativity implying that, at least in this situation, influence can be conceived of as a force. For the entire collection see [Zbl 1470.00021]. On large-scale dynamic topic modeling with nonnegative CP tensor decomposition https://www.zbmath.org/1483.94023 2022-05-16T20:40:13.078697Z "Ahn, Miju" https://www.zbmath.org/authors/?q=ai:ahn.miju "Eikmeier, Nicole" https://www.zbmath.org/authors/?q=ai:eikmeier.nicole "Haddock, Jamie" https://www.zbmath.org/authors/?q=ai:haddock.jamie "Kassab, Lara" https://www.zbmath.org/authors/?q=ai:kassab.lara "Kryshchenko, Alona" https://www.zbmath.org/authors/?q=ai:kryshchenko.alona "Leonard, Kathryn" https://www.zbmath.org/authors/?q=ai:leonard.kathryn "Needell, Deanna" https://www.zbmath.org/authors/?q=ai:needell.deanna "Madushani, R. W. M. A." https://www.zbmath.org/authors/?q=ai:madushani.r-w-m-a "Sizikova, Elena" https://www.zbmath.org/authors/?q=ai:sizikova.elena "Wang, Chuntian" https://www.zbmath.org/authors/?q=ai:wang.chuntian Summary: There is currently an unprecedented demand for large-scale temporal data analysis due to the explosive growth of data. Dynamic topic modeling has been widely used in social and data sciences with the goal of learning latent topics that emerge, evolve, and fade over time. Previous work on dynamic topic modeling primarily employ the method of nonnegative matrix factorization (NMF), where slices of the data tensor are each factorized into the product of lower-dimensional nonnegative matrices. With this approach, however, information contained in the temporal dimension of the data is often neglected or underutilized. To overcome this issue, we propose instead adopting the method of nonnegative CANDECOMP/PARAFAC (CP) tensor decomposition (NNCPD), where the data tensor is directly decomposed into a minimal sum of outer products of nonnegative vectors, thereby preserving the temporal information. The viability of NNCPD is demonstrated through application to both synthetic and real data, where significantly improved results are obtained compared to those of typical NMF-based methods. The advantages of NNCPD over such approaches are studied and discussed. To the best of our knowledge, this is the first time that NNCPD has been utilized for the purpose of dynamic topic modeling, and our findings will be transformative for both applications and further developments. For the entire collection see [Zbl 1477.62002]. Analysis and processing aspects of data in big data applications https://www.zbmath.org/1483.94024 2022-05-16T20:40:13.078697Z "Rahul, Kumar" https://www.zbmath.org/authors/?q=ai:rahul.kumar "Banyal, Rohitash Kumar" https://www.zbmath.org/authors/?q=ai:banyal.rohitash-kumar "Goswami, Puneet" https://www.zbmath.org/authors/?q=ai:goswami.puneet Summary: Data analysis and processing is playing an important role because of the large amount of data generated through various sources of big data. It is an important component in big data-based applications. Data qualities are the main concern in the data acquisition, transformation and data pre-processing under big data applications. Data pre-processing is required because of inconsistent, noisy and incomplete data generation in big data applications. Data analysis basically encompasses different methods and a function applicable to data's to detect characteristics such as data type, size, format, patterns and so on. Based on data format, it's easy to identify data qualities for further use in various applications. Moreover, data analysis and processing includes various steps such as data qualities identification, statistical analysis of data, defining modeling, and hypothetical testing of model and result from analysis. Raw data is unused data and required analysis, filtering, and processing in any system. This paper deals with the analysis and processing aspects of raw data and cleaned data in big data applications. This paper also deals with data cleaning and its implementation concepts. Beating Fredman-Komlós for perfect $$k$$-hashing https://www.zbmath.org/1483.94025 2022-05-16T20:40:13.078697Z "Guruswami, Venkatesan" https://www.zbmath.org/authors/?q=ai:guruswami.venkatesan "Riazanov, Andrii" https://www.zbmath.org/authors/?q=ai:riazanov.andrii Summary: We say a subset $$C \subseteq \{ 1 , 2 , \ldots , k \}^n$$ is a $$k$$-hash code (also called $$k$$-separated) if for every subset of $$k$$ codewords from $$C$$, there exists a coordinate where all these codewords have distinct values. Understanding the largest possible rate (in bits), defined as $$( \log_2 | C |) / n$$, of a $$k$$-hash code is a classical problem. It arises in two equivalent contexts: (i) the smallest size possible for a perfect hash family that maps a universe of $$N$$ elements into $$\{1, 2, \ldots, k \}$$, and (ii) the zero-error capacity for decoding with lists of size less than $$k$$ for a certain combinatorial channel.\\ A general upper bound of $$k! / k^{k - 1}$$ on the rate of a $$k$$-hash code (in the limit of large $$n)$$ was obtained by \textit{M. L. Fredman} and \textit{J. Komlos} [SIAM J. Algebraic Discrete Methods 5, 61--68 (1984; Zbl 0525.68037)] for any $$k \geq 4$$. While better bounds have been obtained for $$k = 4$$, their original bound has remained the best known for each $$k \geq 5$$. In this work, we present a method to obtain the first improvement to the Fredman-Komlós bound for every $$k \geq 5$$. A random encoding method for secure data communication: an extension of sequential coding https://www.zbmath.org/1483.94026 2022-05-16T20:40:13.078697Z "Chaturvedi, Atul" https://www.zbmath.org/authors/?q=ai:chaturvedi.atul "Shukla, Varun" https://www.zbmath.org/authors/?q=ai:shukla.varun "Misra, Manoj Kumar" https://www.zbmath.org/authors/?q=ai:misra.manoj-kumar Summary: The security of data communication is very important in all aspects. \textit{V. Shukla} and \textit{A. Mishra} [A new sequential coding method for secure data communication'', in: 2020 IEEE international conference on computing, power and communication technologies (GUCON), Galgotias University, Greater Noida, UP, India, October 2--4, 2020. Danvers, MA: IEEE. 529--533 (2020; \url{doi:10.1109/GUCON48875.2020.9231252})] had proposed a secure sequential coding method. They have shown the results for text secret messages only. In this paper, firstly we extend their scheme by showing the results for image secret messages. Secondly, we upgrade their scheme by proposing the similar method by using random encoding. Random encoding enhances the level of security. A separate section is provided for security analysis and associated advantages. New approach of adapttve secure transmission through flat fading channel based on three-pass protocol https://www.zbmath.org/1483.94027 2022-05-16T20:40:13.078697Z "Abbas, Mustafa S." https://www.zbmath.org/authors/?q=ai:abbas.mustafa-s "Al-Salih, Ahmed M." https://www.zbmath.org/authors/?q=ai:al-salih.ahmed-m "Obeis, Nawfal Turki" https://www.zbmath.org/authors/?q=ai:obeis.nawfal-turki Summary: The three-pass protocol is one of the frameworks in cryptography, which provides the privacy of exchanging information safely without distribution of secret or public keys between users. The three-pass protocol method has been put into use within a wireless network environment to transmit confidential data between two nodes with the presence of passive eavesdropper through a flat fading channel that affects the bit error rate. This led to the impact on the confidentiality of the transmission. Therefore, there are multiple challenges to ensure the confidentiality of the transmission and to improve the error rate. In this paper, the data has been encrypted using a One-Time Pad algorithm, and the channel of transmission is authenticated using Hash function. Moreover, the high values of signal to noise ratio have been increased in order to enhance the rate of bit error, so both the confidentiality of the transmission and its error rate are improved. The analysis of the flat fading channel performance is based on the perceptual quality at the rated Signal to Noise Ratio (SNR). Performance analysis of NTRU algorithm with non-post-quantum algorithms https://www.zbmath.org/1483.94028 2022-05-16T20:40:13.078697Z "Abouaroek, Musaeed" https://www.zbmath.org/authors/?q=ai:abouaroek.musaeed "Ahmad, Khaleel" https://www.zbmath.org/authors/?q=ai:ahmad.khaleel Summary: In opportunistic networks, the nodes connect to each other wirelessly and use the store-carry-forward technique to transmit the data from one node to another node. The nodes in opportunistic networks are heterogeneous, having high mobility, limited power, low density, short radio range, and numerous security threats to unauthorized nodes. The fundamental challenge in an opportunistic network is to secure and protect the information during communication in networks to achieve the user's confidence. This issue is technically resolved by incorporating the cryptography algorithms that make both the virtual and modern world in a safer position. Asymmetric Cryptography makes information unintelligible to an unauthorized user and provides confidentiality to genuine users. Encryption and decryption technology are solutions to protect data from unauthorized users. There are many opportunistic network algorithms in the existing literature that provide optimal performance. However, in this research work, we propose the NTRU post-quantum algorithm because of its high performance, low cost, and fast execution during encryption and decryption of the data over the network. We also implemented and analyzed the performance of the proposed NTRU algorithm and compared its results with the Elliptic Curve Cryptography and ElGamal algorithm. After the result analysis, we conclude that our proposed technique is highly effective and secure. The soft graphic integer sub-decomposition method for elliptic scalar multiplication https://www.zbmath.org/1483.94029 2022-05-16T20:40:13.078697Z "Ajeena, Ruma Kareem K." https://www.zbmath.org/authors/?q=ai:ajeena.ruma-kareem-k Summary: A new version of the ISD method for computing a scalar multiplication on elliptic curve defined over prime field has been proposed. This version is called the soft graphic ISD (SG-ISD) method. The SG-ISD method employed the connected sub-graphs of undirected simple graph, which formed a soft graph $$(F, A)$$ generated by a set valued function $$F$$, to represent the sub-scalars of ISD method. Thus, undirected simple graph can be proved as the SG-ISD version. On the SG-ISD method, the binary representations, which are all edges of the ISD sub-scalars that forms a nonempty set $$A$$, has been done directly from the connected sub-graphs. So, every ISD version of a scalar $$k$$ is proven mathematically as the SG-ISD version of $$k$$ in an elliptic scalar multiplication $$kP$$. New experimental results on the proposed SG-ISD method are presented. The computational complexities of the original ISD and proposed SG-ISD methods are determined mathematically on the basis of the counting operations. These operations are elliptic curve and finite field operations. The comparison results on these computational complexities of the ISD and SG-ISD methods have been discussed. The experiments on the computational complexities reveal that the SG-ISD method is faster than the ISD method. Thus, the SG-ISD method is considered as an efficient algorithm in comparison with the original ISD for cryptographic applications. Lattice attacks on NTRU and LWE: a history of refinements https://www.zbmath.org/1483.94030 2022-05-16T20:40:13.078697Z "Albrecht, Martin R." https://www.zbmath.org/authors/?q=ai:albrecht.martin-r "Ducas, Léo" https://www.zbmath.org/authors/?q=ai:ducas.leo Summary: The authors provide an overview of the advances and techniques used in the field of lattice reduction algorithms. Four decades after its invention, the LLL algorithm still plays a significant role in cryptography, not least as it has become one of the main tools to assess the security of a new wave of lattice-based cryptosystems intended for the new post-quantum cryptographic standard. The runtime of the LLL algorithm was always well understood, but the quality of its output, i.e., how short its output vectors were, could be hard to predict, even heuristically. Yet, an important aspect in the evaluation of the new lattice schemes is accurate predictions of the hardness of the underlying lattice problems, which crucially relies on estimating the 'shortness' of the vectors that can be efficiently found using lattice reduction and enumeration. The authors have been on the forefront of improving such estimators and build upon their expertise in this chapter. For the entire collection see [Zbl 1479.94004]. Scalar multiplication in elliptic curve libraries https://www.zbmath.org/1483.94031 2022-05-16T20:40:13.078697Z "Alimoradi, Reza" https://www.zbmath.org/authors/?q=ai:alimoradi.reza "Arkian, Hamid Reza" https://www.zbmath.org/authors/?q=ai:arkian.hamid-reza "Razavian, Seiied-Mohammad-Javad" https://www.zbmath.org/authors/?q=ai:razavian.seiied-mohammad-javad "Ramzi, Ali" https://www.zbmath.org/authors/?q=ai:ramzi.ali Summary: With the advent of elliptic curve cryptography (ECC); it grew unusually quickly because it had a smaller key size compared with that of the RSA cryptography system. Many researches are being done nowadays to make this type of cryptography more efficient. These investigations are about improving efficiency of both algorithm and method of implementations. This paper studies and analyzes some software libraries which support elliptic curve computations. Scalar multiplication is a major operation in ECC. Therefore, this study implements some methods of scalar multiplication by two software libraries LiDIA and MIRACL and compares the results at the end. The elliptic scalar multiplication graph and its application in elliptic curve cryptography https://www.zbmath.org/1483.94032 2022-05-16T20:40:13.078697Z "Aljamaly, Karrar Taher R." https://www.zbmath.org/authors/?q=ai:aljamaly.karrar-taher-r "Ajeena, Ruma Kareem K." https://www.zbmath.org/authors/?q=ai:ajeena.ruma-kareem-k Summary: In this work, a new graph has been defined as a main point to design a new version of an asymmetric encryption scheme. This graph is formed based on the scalar multiplication operation on elliptic curve defined over a prime field, which is called an elliptic scalar multiplication (ESM) graph. Some mathematical facts to show the ESM graph is a complete graph are proved theoretically. On the complete elliptic scalar multiplication (CESM) graph, an asymmetric encryption algorithm has been implemented. Fast computations on the proposed algorithm are Z obtained through the matrices representation and determination of the minimum spanning tree (MST) to compute the ciphertext. More secure computations with the CESM graphic encryption algorithm in comparison with the previous asymmetric encryption algorithms. So, the CESM graphic asymmetric encryption algorithm is considered as a new sight for elliptic curve cryptographic usages. Light-weighted cryptographic algorithms for energy efficient applications https://www.zbmath.org/1483.94033 2022-05-16T20:40:13.078697Z "Bhatt, Devershi Pallavi" https://www.zbmath.org/authors/?q=ai:bhatt.devershi-pallavi "Raja, Linesh" https://www.zbmath.org/authors/?q=ai:raja.linesh "Sharma, Shilpa" https://www.zbmath.org/authors/?q=ai:sharma.shilpa Summary: Despite of increasing awareness about information security after the digitization movement and ransomware attack, small business and the general public who perform digital transactions are being attacked. Cryptography has an important place in Security as it works on the data rather than the machine or the network. Data is being transmitted through whichever way, it can be hidden and kept safe by using the right kind of Cryptographic algorithms. But apart from security the pervasive computing and embedded systems create a huge possibility for small and light weighted algorithms, specific applications like WSN need such mechanisms like data aggregation, light-weighted cryptography to enhance the lifetime of the network [\textit{A. Kumari} et al., ibid. 22, No. 4, 521--530 (2019; Zbl 07475904)], underwater WSN. In this paper, the need and comparison of light weight cryptographic algorithms is discussed. Bijective s-boxes of different sizes obtained from quasi-cyclic cod https://www.zbmath.org/1483.94034 2022-05-16T20:40:13.078697Z "Bikov, Dusan" https://www.zbmath.org/authors/?q=ai:bikov.dusan "Bouyukliev, İliya" https://www.zbmath.org/authors/?q=ai:bouyukliev.iliya-georgiev "Bouyuklieva, Stefka" https://www.zbmath.org/authors/?q=ai:bouyuklieva.stefka Summary: The aim of this paper is to construct S-boxes of different sizes with good cryptographic properties. An algebraic construction for bijective S-boxes is described. It uses quasi-cyclic representations of the binary simplex code. Good S-boxes of sizes 4, 6, 8, 9, 10, 11, 12, 14, 15, 16 and 18 are obtained. Ring learning with errors: a crossroads between post-quantum cryptography, machine learning and number theory https://www.zbmath.org/1483.94035 2022-05-16T20:40:13.078697Z "Blanco-Chacón, Iván" https://www.zbmath.org/authors/?q=ai:blanco-chacon.ivan Summary: The present survey is intended to serve as a comprehensive account of the main areas of the cryptography based on the ring learning with errors problem. We cover the major topics, from their mathematical foundations to the main primitives, as well as several open ends and recent progress with an emphasis in the connections with algebraic number theory. This work is based to a certain extent on an invited course and a seminar given by the author at the Basque Center for Applied Mathematics in 2018 and at the ICIAM 2019. Efficient modular arithmetic https://www.zbmath.org/1483.94036 2022-05-16T20:40:13.078697Z "Bos, Joppe W." https://www.zbmath.org/authors/?q=ai:bos.joppe-w "Kleinjung, Thorsten" https://www.zbmath.org/authors/?q=ai:kleinjung.thorsten "Page, Dan" https://www.zbmath.org/authors/?q=ai:page.dan Summary: The authors discuss how to realise efficient modular arithmetic in practice on a range of platforms. They cover generic modular multiplication routines such as the popular Montgomery multiplication as well as special routines for primes of a specific shape. Moreover, especially fast methods are outlined that might produce errors with a very small probability. Such faster sloppy reduction' techniques are especially beneficial in cryptanalytic settings. The authors have all been involved in various cryptographic and cryptanalytic record-setting software implementations. In this chapter they explain how to select the most efficient modular arithmetic routines for the cryptologic implementation task at hand. For the entire collection see [Zbl 1479.94004]. \textsf{FAST}: disk encryption and beyond https://www.zbmath.org/1483.94037 2022-05-16T20:40:13.078697Z "Chakraborty, Debrup" https://www.zbmath.org/authors/?q=ai:chakraborty.debrup "Ghosh, Sebati" https://www.zbmath.org/authors/?q=ai:ghosh.sebati "Mancillas-López, Cuauhtemoc" https://www.zbmath.org/authors/?q=ai:mancillas-lopez.cuauhtemoc "Sarkar, Palash" https://www.zbmath.org/authors/?q=ai:sarkar.palash Summary: This work introduces \textsf{FAST} which is a new family of tweakable enciphering schemes. Several instantiations of \textsf{FAST} are described. These are targeted towards two goals, the specific task of disk encryption and a more general scheme suitable for a wide variety of practical applications. A major contribution of this work is to present detailed and careful software implementations of all of these instantiations. For disk encryption, the results from the implementations show that \textsf{FAST} compares very favourably to the IEEE disk encryption standards XCB and EME2 as well as the more recent proposal AEZ. \textsf{FAST} is built using a fixed input length pseudo-random function and an appropriate hash function. It uses a single-block key, is parallelisable and can be instantiated using only the encryption function of a block cipher. The hash function can be instantiated using either the Horner's rule based usual polynomial hashing or hashing based on the more efficient Bernstein-Rabin-Winograd polynomials. Security of \textsf{FAST} has been rigorously analysed using the standard provable security approach and concrete security bounds have been derived. Based on our implementation results, we put forward \textsf{FAST} as a serious candidate for standardisation and deployment. A novel image encryption algorithm based on chaotic billiards https://www.zbmath.org/1483.94038 2022-05-16T20:40:13.078697Z "Charif, Khalid" https://www.zbmath.org/authors/?q=ai:charif.khalid "Guennoun, Zine El Abidine" https://www.zbmath.org/authors/?q=ai:el-abidine-guennoun.zine Summary: In this paper, a novel symmetric image encryption algorithm is proposed on the basis of the chaotic billiard (Sinai billiard). These chaotic systems, characterized by the highest degree of chaos, have been recently introduced in cryptography. The design of the algorithm relies on the random walk of three-point particles that move freely in the billiard. It includes several rounds of the confusion and diffusion processes. In each ciphering round, the permutation of the image pixels is performed according to the random numbers obtained from the output of a particle system, by using a new calculation technique. Thus, the pixel values are hidden by the pseudo-random sequences generated by the systems of the other two particles. The simulation results demonstrate that the algorithm is simple to implement and is highly secure. It has successfully passed all security tests and has shown the desirable properties in a good secure cryptosystem. Practical FHE parameters against lattice attacks https://www.zbmath.org/1483.94039 2022-05-16T20:40:13.078697Z "Cheon, Jung Hee" https://www.zbmath.org/authors/?q=ai:cheon.jung-hee "Son, Yongha" https://www.zbmath.org/authors/?q=ai:son.yongha "Yhee, Donggeon" https://www.zbmath.org/authors/?q=ai:yhee.donggeon Summary: We give secure parameter suggestions to use sparse secret vectors in \textsf{LWE} based encryption schemes. This should replace existing security parameters, because homomorphic encryption (HE) schemes use quite different variables from the existing parameters. In particular, HE schemes using sparse secrets should be supported by experimental analysis, here we summarize existing attacks to be considered and security levels for each attacks. Based on the analysis and experiments, we compute optimal scaling factors for CKKS. Sieving for twin smooth integers with solutions to the Prouhet-Tarry-Escott problem https://www.zbmath.org/1483.94040 2022-05-16T20:40:13.078697Z "Costello, Craig" https://www.zbmath.org/authors/?q=ai:costello.craig "Meyer, Michael" https://www.zbmath.org/authors/?q=ai:meyer.michael-josef-heinz|meyer.michael-m "Naehrig, Michael" https://www.zbmath.org/authors/?q=ai:naehrig.michael Summary: We give a sieving algorithm for finding pairs of consecutive smooth numbers that utilizes solutions to the Prouhet-Tarry-Escott (PTE) problem. Any such solution induces two degree-$$n$$ polynomials, $$a(x)$$ and $$b(x)$$, that differ by a constant integer $$C$$ and completely split into linear factors in $$\mathbb{Z}[x]$$. It follows that for any $$\ell \in \mathbb{Z}$$ such that $$a(\ell ) \equiv b(\ell ) \equiv 0 \bmod{C}$$, the two integers $$a(\ell )/C$$ and $$b(\ell )/C$$ differ by 1 and necessarily contain $$n$$ factors of roughly the same size. For a fixed smoothness bound $$B$$, restricting the search to pairs of integers that are parameterized in this way increases the probability that they are $$B$$-smooth. Our algorithm combines a simple sieve with parametrizations given by a collection of solutions to the PTE problem. The motivation for finding large twin smooth integers lies in their application to compact isogeny-based post-quantum protocols. The recent key exchange scheme B-SIDH and the recent digital signature scheme SQISign both require large primes that lie between two smooth integers; finding such a prime can be seen as a special case of finding twin smooth integers under the additional stipulation that their sum is a prime $$p$$. When searching for cryptographic parameters with $$2^{240} \le p <2^{256}$$, an implementation of our sieve found primes $$p$$ where $$p+1$$ and $$p-1$$ are $$2^{15}$$-smooth; the smoothest prior parameters had a similar sized prime for which $$p-1$$ and $$p+1$$ were $$2^{19}$$-smooth. In targeting higher security levels, our sieve found a 376-bit prime lying between two $$2^{21}$$-smooth integers, a 384-bit prime lying between two $$2^{22}$$-smooth integers, and a 512-bit prime lying between two $$2^{28}$$-smooth integers. Our analysis shows that using previously known methods to find high-security instances subject to these smoothness bounds is computationally infeasible. For the entire collection see [Zbl 1475.94010]. Randomness improvement of chaotic maps for image encryption in a wireless communication scheme using PIC-microcontroller via ZigBee channels https://www.zbmath.org/1483.94041 2022-05-16T20:40:13.078697Z "García-Guerrero, E. E." https://www.zbmath.org/authors/?q=ai:garcia-guerrero.e-e "Inzunza-González, E." https://www.zbmath.org/authors/?q=ai:inzunza-gonzalez.e "López-Bonilla, O. R." https://www.zbmath.org/authors/?q=ai:lopez-bonilla.o-r "Cárdenas-Valdez, J. R." https://www.zbmath.org/authors/?q=ai:cardenas-valdez.jose-r "Tlelo-Cuautle, E." https://www.zbmath.org/authors/?q=ai:tlelo-cuautle.esteban Summary: Recently, a lot of research has been done in chaotic cryptography field using different kinds of chaotic systems, like chaotic maps, which are being considered as one of the secure and efficient methods to protect confidential information. This article highlights that the main cryptography requirements demand that the new embedded cryptosystems have to be more efficient and secure, it means that they must be faster and offer greater security. For instance, the new cryptosystems require to be compatible with the new telecommunication protocols and, in addition, to be efficient in energy consumption. In this manner, this article introduces a process to improve the randomness of five chaotic maps that are implemented on a PIC-microcontroller. The improved chaotic maps are tested to encrypt digital images in a wireless communication scheme, particularly on a machine-to-machine (M2M) link, via ZigBee channels. We show that function \textit{mod} 255 improves the randomness of the pseudo-random number generators (PRNG), which is verified performing NIST SP 800-22 statistical tests, histograms, phase-plane analysis, entropy, correlation of adjacent pixels, differential attacks, and using digital images of size $$256\times 256$$ and $$512\times 512$$ pixels. A comparative analysis is presented versus related works that also use chaotic encryption and classic algorithms, such as: AES, DES, 3DES and IDEA. The security analysis confirms that the proposed process to improve the randomness of chaotic maps, is appropriate to implement an encryption scheme that is secure and robust against several known attacks and other statistical tests. Finally, it was experimentally verified that this chaotic encryption scheme can be used in practical applications such as M2M and Internet of things (IoT). Computing discrete logarithms https://www.zbmath.org/1483.94042 2022-05-16T20:40:13.078697Z "Granger, Robert" https://www.zbmath.org/authors/?q=ai:granger.robert-a "Joux, Antoine" https://www.zbmath.org/authors/?q=ai:joux.antoine Summary: The authors discuss the question how hard is it to compute discrete logarithms in various groups?''. It details the key ideas and constructions behind the most efficient algorithms for solving the discrete logarithm problem (DLP) with a focus on the recent advances related to finite fields of extension degree >1. A highlight is the rapid development, in the period 2012--2014, of quasi-polynomial time algorithms to solve the DLP in finite fields of fixed charaterstic. Both authors contributed significantly to this development, albeit on competing teams. For this book, in Chapter 5, they join forces and explain how different ideas eventually led to the fall of the fixed characteristic finite-field discrete logarithm problem. For the entire collection see [Zbl 1479.94004]. RSA, DH and DSA in the wild https://www.zbmath.org/1483.94043 2022-05-16T20:40:13.078697Z "Heninger, Nadia" https://www.zbmath.org/authors/?q=ai:heninger.nadia Summary: The author outlines the various cryptographic pitfalls one can -- but really should not -- make in practice. Often it is possible to bypass the hard' mathematical problem a cryptosystem is based upon, and instead take advantage of implementation, deployment or protocol mistakes to extract the private key. Often, the techniques used are excellent examples of the interplay of mathematics and computer science, requiring a combination of ingenuity to find the core idea and perseverance to exploit the weakness in practice. The author gives a wide-ranging overview of the multitude of cryptographic implementation vulnerabilities that have been found in the past decades and their impact in practice, including a fair number where she was personally involved in identifying the vulnerability. In this chapter, she wonders whether, after several decades of implementation chaos and catastrophic vulnerabilities, we are doomed, but concludes that there is hope yet by bringing into practice the lessons learned. For the entire collection see [Zbl 1479.94004]. Non-zero inner product encryption schemes from various assumptions: LWE, DDH and DCR https://www.zbmath.org/1483.94044 2022-05-16T20:40:13.078697Z "Katsumata, Shuichi" https://www.zbmath.org/authors/?q=ai:katsumata.shuichi "Yamada, Shota" https://www.zbmath.org/authors/?q=ai:yamada.shota Summary: In non-zero inner product encryption (NIPE) schemes, ciphertexts and secret keys are associated with vectors and decryption is possible whenever the inner product of these vectors does not equal zero. So far, much effort on constructing bilinear map-based NIPE schemes have been made and this has lead to many efficient schemes. However, the constructions of NIPE schemes without bilinear maps are much less investigated. The only known other NIPE constructions are based on lattices, however, they are all highly inefficient due to the need of converting inner product operations into circuits or branching programs. To remedy our rather poor understanding regarding NIPE schemes without bilinear maps, we provide two methods for constructing NIPE schemes: a direct construction from lattices and a generic construction from schemes for inner products (LinFE). For our first direct construction, it highly departs from the traditional lattice-based constructions and we rely heavily on new tools concerning Gaussian measures over multi-dimensional lattices to prove security. For our second generic construction, using the recent constructions of LinFE schemes as building blocks, we obtain the first NIPE constructions based on the DDH and DCR assumptions. In particular, we obtain the first NIPE schemes without bilinear maps or lattices. For the entire collection see [Zbl 1408.94007]. Analysis of variability and degree of non-linearity of HC-128 https://www.zbmath.org/1483.94045 2022-05-16T20:40:13.078697Z "Kumar, Arvind" https://www.zbmath.org/authors/?q=ai:kumar.arvind "Mishra, P. R." https://www.zbmath.org/authors/?q=ai:mishra.prasanna-raghaw "Pal, S. K." https://www.zbmath.org/authors/?q=ai:pal.sayan-kumar|pal.sankar-kumar|pal.surya-kant|pal.saibal-kumar|pal.sudipta-kumar|pal.sankar-kr|pal.shiv-kumar|pal.sudip-kumar|pal.surjya-k|pal.swapan-kr|pal.sandip-kumar "Ojjela, Odelu" https://www.zbmath.org/authors/?q=ai:ojjela.odelu Summary: HC-128 is a strong candidate of eSTREAM Project. The resistance of this algorithm against cryptanalytic attacks has been analyzed by several researchers. We analyze its security in terms of its variability and non-linearity. A strong crypto-algorithm should have full variability. By variability of an algorithm' we mean the number of distinct sequences, the algorithm can produce. Full variability means that the algorithm produces as many distinct sequences as there are key-IV pairs. There are research papers which indicate that the algorithm may have the full variability. However, no concrete proof is given. In this paper we present a deterministic proof of full variability of HC-128. Non-linearity plays an important role in determining the security of a crypto-algorithm. Because of the complicated nature of the algorithm, determining the exact degree of the HC-128 function is quite difficult. In this paper, we demonstrate that the degree of non-linearity of key and IV setup function of HC-128 is very high and it is computationally hard to invert the cipher with the knowledge of key stream only. Competing secure text encryption in intranet using elliptic curve cryptography https://www.zbmath.org/1483.94046 2022-05-16T20:40:13.078697Z "Kumari, Arpana" https://www.zbmath.org/authors/?q=ai:kumari.arpana "Kapoor, Vivek" https://www.zbmath.org/authors/?q=ai:kapoor.vivek Summary: Privacy and Security is one of the major requirements of every network. Intranet based applications are used to avoid third party data sharing or prevent sensitive communication from spying or sniffing from Internet service providers. Intranet applications are used to provide safe and secure communication within network and overcome dependency from ISP. It is used by sensitive departments like military, Navy, ISRO and many more. This work attempts to provide secure communication architecture to achieve 'confidentiality and data integrity in more strong way. Secure communication among pear-to-pear devices is important as it accesses remotely in a convenient, controlled and efficient way. For validation and authentication, the cryptographic technique is used. Intranet application connects multiple systems through the network, every organization have their own intranet network. The proposed system implements a secure system using Elliptic curve cryptography for cryptographic algorithm and integrate checksum estimation method. Data is divided into chunks for processing and key is generated for further process. Java technology is used to validate the performance of the proposed model in the context of key generation, encryption, decryption, and checksum calculation. Review on spatial domain image steganography techniques https://www.zbmath.org/1483.94047 2022-05-16T20:40:13.078697Z "Lakshmi Sirisha, B." https://www.zbmath.org/authors/?q=ai:lakshmi-sirisha.b "Chandra Mohan, B." https://www.zbmath.org/authors/?q=ai:chandra-mohan.b Summary: Steganography techniques leads main role in embedding process of secret information into cover information in order to provide good security. These techniques are very essential, when sending the confidential information from one place to another place in the field of defense and medical. Hence, it is a challenging and important task to hide the secret information in to cover information. This review provides classification of steganography techniques, existing and proposed techniques with advantages and disadvantages. As per observations of existing methods, much amount of information hides using spatial domain techniques than transform domain techniques. This review mainly focuses on the spatial domain image steganography techniques. Blockchain. Bitcoin https://www.zbmath.org/1483.94048 2022-05-16T20:40:13.078697Z "Lezaun, Mikel" https://www.zbmath.org/authors/?q=ai:lezaun.mikel (no abstract) A novel Niederreiter-like cryptosystem based on the $$(u|u + \upsilon)$$-construction codes https://www.zbmath.org/1483.94049 2022-05-16T20:40:13.078697Z "Mahdjoubi, Roumaissa" https://www.zbmath.org/authors/?q=ai:mahdjoubi.roumaissa "Cayrel, Pierre Louis" https://www.zbmath.org/authors/?q=ai:cayrel.pierre-louis "Akleylek, Sedat" https://www.zbmath.org/authors/?q=ai:akleylek.sedat "Kenza, Guenda" https://www.zbmath.org/authors/?q=ai:kenza.guenda Summary: In this paper, we present a new variant of the Niederreiter Public Key Encryption (PKE) scheme which is resistant against recent attacks. The security is based on the hardness of the Rank Syndrome Decoding (RSD) problem and it presents a $$(u|u + \upsilon)$$-construction code using two different types of codes: Ideal Low Rank Parity Check (ILRPC) codes and $$\lambda$$-Gabidulin codes. The proposed encryption scheme benefits are a larger minimum distance, a new efficient decoding algorithm and a smaller ciphertext and public key size compared to the Loidreau's variants and to its IND-CCA secure version. Lattice-based integer factorisation: an introduction to Coppersmith's method https://www.zbmath.org/1483.94050 2022-05-16T20:40:13.078697Z "May, Alexander" https://www.zbmath.org/authors/?q=ai:may.alexander Summary: The author investigates the use of LLL to factor integers as pioneered by Coppersmith. Conceptually, Coppersmith's method can be deceptively simple: given additional information about an integer to factor (e.g., the knowledge that an RSA key pair (N; $$e$$) has a small corresponding private exponent $$d$$), derive a system of equations with a small root that reveals the factorization and use LLL to find the small root. As a result, it becomes possible to explore exponentially sized search spaces, while preserving polynomial time by using the famous LLL lattice reduction algorithm. Yet, exploiting Coppersmith's method in a cryptographic context optimally often involves a number of clever choices related to which system of equations to consider. At first, this is a tantalisingly annoying problem where the choice may appear obvious only in retrospect. The author uses his extensive experience in improving the state of the art to explain the reasoning behind various applications in this chapter. For the entire collection see [Zbl 1479.94004]. About linear and affine equivalence of substitutions https://www.zbmath.org/1483.94051 2022-05-16T20:40:13.078697Z "Pankratov, I. V." https://www.zbmath.org/authors/?q=ai:pankratov.i-v Summary: The results of computer experiments with a software implementation of algorithms for determining the linear and affine equivalence of substitutions are presented. The detailed description of the algorithms is given. Experimental operation time of the algorithms is compared with the theoretical complexity of the problem. Application of cryptography in data privacy using fuzzy graph theory https://www.zbmath.org/1483.94052 2022-05-16T20:40:13.078697Z "Pius, Anu" https://www.zbmath.org/authors/?q=ai:pius.anu "Kirubaharan, D. R." https://www.zbmath.org/authors/?q=ai:kirubaharan.d-r Summary: While exchanging data across different companies, data privacy has become very essential in fuzzy graph theory. Many fuzzy graph theory facilities, include fuzzy logic as plain text transmission, which in turn causes data breach. When sensitive data has to be encrypted, we employ membership functions with varying degrees of fuzzy graph theory. Once our algorithm has finished running, we utilize an auto cryptography encoder to transmit the altered data. After creating the auto cryptography encoder, various organizations may utilize the output data for research analysis as well as for productivity analysis by deploying it in live data environment. Data that has been stored is used by other fuzzy graph theory entities or research analysts to enhance the well-being of individuals. The fuzzy data, however, include various lattice structures to resolve complex problems. Data privacy is put at the risk if sensitive data is revealed. The study that has ensued as a result of this discovery has spurred several privacy-preserving methods to be developed. So, we created a method that encrypts critical information using cryptography technique and, moreover, securely transmits data to many companies. MAKE: a matrix action key exchange https://www.zbmath.org/1483.94053 2022-05-16T20:40:13.078697Z "Rahman, Nael" https://www.zbmath.org/authors/?q=ai:rahman.nael "Shpilrain, Vladimir" https://www.zbmath.org/authors/?q=ai:shpilrain.vladimir Summary: We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over $$\mathbb{Z}_p$$. One of the (semi)groups is additive, and the other one is multiplicative. This allows us to take advantage of both operations on matrices to diffuse information. We note that in our protocol, no power of any matrix or of any element of $$\mathbb{Z}_p$$ is ever exposed, so standard classical attacks on Diffie-Hellman-like protocols are not applicable. History of cryptographic key sizes https://www.zbmath.org/1483.94054 2022-05-16T20:40:13.078697Z "Smart, Nigel P." https://www.zbmath.org/authors/?q=ai:smart.nigel-p "Thomé, Emmanuel" https://www.zbmath.org/authors/?q=ai:thome.emmanuel Summary: The autors provide an overview of improvements over the years in estimating the security level of the main cryptographic hardness assumptions. These improvements heavily rely on the algorithmic innovations discussed in Chapters 2 to 5, but combining all those ideas into concrete key-size recommendations is not immediate. The authors have been at the forefront of cryptanalytic research and recommending cryptographic key sizes and conclude with current recommendations in this Chapter. For the entire collection see [Zbl 1479.94004]. Synthesis of highly nonlinear S-boxes satisfying higher order propagation criterion https://www.zbmath.org/1483.94055 2022-05-16T20:40:13.078697Z "Sokolov, A. V." https://www.zbmath.org/authors/?q=ai:sokolov.alexei-v|sokolov.andrey-v|sokolov.arcady-v|sokolov.andrei-vladimirovich "Zhdanov, O. N." https://www.zbmath.org/authors/?q=ai:zhdanov.o-n Summary: The S-box is the main component of modern block cryptographic algorithms and hash functions. One of the main criteria for the cryptographic quality of an S-boxes is the criterion of a high nonlinearity distance, as well as a propagation criterion of order $$m$$. One of the effective methods for constructing S-boxes is the method of their construction on the basis of a set of Boolean functions with a given level of cryptographic quality. This paper discusses the spectral classes (obtained on the basis of the classification of the Walsh-Hadamard transform coefficient vectors) of Boolean functions of 1\dots 5 variables, for each of which the numbers of Boolean functions that satisfy the propagation criterion of order $$m$$ were found. Using the constructive method among the full set of Boolean functions of 5 variables, a subclass of 12 balanced maximally nonlinear Boolean functions satisfying the propagation criterion PC(4) were found. It is shown that on the basis of this set of Boolean functions, bijective cryptographic S-boxes can be synthesized, which are the best among the entire set of S-boxes of length $$N = 32$$, from the point of view of the criterion of maximum nonlinearity distance and propagation criterion. XTR and tori https://www.zbmath.org/1483.94056 2022-05-16T20:40:13.078697Z "Stam, Martijn" https://www.zbmath.org/authors/?q=ai:stam.martijn Summary: The author discusses how to work efficiently and compactly in certain multiplicative subgroups of finite fields. The emphasis is on XTR, which works in the cyclotomic subgroup of Fp6. The author worked extensively on speeding up XTR and related systems based on algebraic tori and uses his first-hand knowledge to provide a historical perspective of XTR in this Chapter. For the entire collection see [Zbl 1479.94004]. A survey of chosen-prefix collision attacks https://www.zbmath.org/1483.94057 2022-05-16T20:40:13.078697Z "Stevens, Marc" https://www.zbmath.org/authors/?q=ai:stevens.marc Summary: The author surveys the technical advances, impact and usage of collision attacks for the most widely used cryptographic hash functions. Cryptographic hash function are the Swiss army knives within cryptography and are used in many applications including digital signature schemes, message authentication codes, password hashing, cryptocurrencies and content-addressable storage. The author was one of the driving forces in turning initial weaknesses in the compression function into practical attacks against various widely deployed protocols relying on hash function collision resistance for their security. In Chapter 7 he explains how each scenario involves the development of slightly different ideas to exploit weaknesses in especially MD5. For the entire collection see [Zbl 1479.94004]. History of integer factorisation https://www.zbmath.org/1483.94058 2022-05-16T20:40:13.078697Z "Wagstaff, Samuel S. jun." https://www.zbmath.org/authors/?q=ai:wagstaff.samuel-s-jun Summary: The author gives a thorough overview of the hardness of one of the cornerstones of modern public-key cryptography. The history starts with the early effort by Eratosthenes and his sieve, eventually leading to the modern number field sieve, currently the asymptotically fastest general-purpose integer factorisation method known. Also included are special' integer factorisation methods like the elliptic-curve method, where the run-time depends mainly on the size of the unknown prime divisor. Modern factorisation efforts often include a gradual escalation of different methods, so it is essential to be familiar with a wide range of methods and the essence of all relevant algorithms is explained clearly. For the entire collection see [Zbl 1479.94004]. Enhanced lightweight and secure session key establishment protocol for smart home inhabitants https://www.zbmath.org/1483.94059 2022-05-16T20:40:13.078697Z "Dhoot, Anshita" https://www.zbmath.org/authors/?q=ai:dhoot.anshita "Manjul, Manisha" https://www.zbmath.org/authors/?q=ai:manjul.manisha "Devgan, Sonam Kaul" https://www.zbmath.org/authors/?q=ai:devgan.sonam-kaul "Nazarov, A. N." https://www.zbmath.org/authors/?q=ai:nazarov.a-n "Pankaj" https://www.zbmath.org/authors/?q=ai:pankaj.jain|pankaj.t|pankaj.ramdayal|pankaj.|pankaj.rajesh-k|pankaj.kanaujia|pankaj.kamlesh-k|pankaj.ravi|pankaj.kumar|pankaj.n-rajeev|pankaj.pankaj-gautam|pankaj.dhanya-s Summary: The concept behind the wireless communication and the world of information technologies is to create an environment for the users such that they can easily access the smart lifestyle and get interacted with the social world. Session key should be secure enough as every sensor is using a small token to authenticate every network. We are proposing a new, efficient, secure and light-weight protocol in smart home environments to overcome these shortcomings. The quantity demand and investment in research and development, while the other model focuses on a more realistic relationship between the quantity demand and the price. An image watermarking framework based on PSO and FrQWT https://www.zbmath.org/1483.94060 2022-05-16T20:40:13.078697Z "Kumar, Sanoj" https://www.zbmath.org/authors/?q=ai:kumar.sanoj "Singh, Manoj K." https://www.zbmath.org/authors/?q=ai:singh.manoj-kumar "Saini, Deepika" https://www.zbmath.org/authors/?q=ai:saini.deepika Summary: This paper primarily explored the usefulness of singular value decomposition for the image watermarking in pursuit of overcoming its typically experienced issues. For this intention, an efficient watermarking scheme optimized by particle swarm optimization (PSO) is designed based on magic-matrix scrambling method and fractional quaternion wavelet transform (FrQWT). The central idea is to shuffle all picture elements of the watermark using magic-matrix scrambling method followed by its insertion into the fruit amplitude coefficients smartly. Another beauty of the designed proficiency is the usage of PSO algorithm to naturally optimize the parameters involved in watermarking strategy. Finally, the sturdyness of the designed watermarking algorithm is investigated against numerous intentional and unintentional attacks. Development of electronic digital signature algorithms with compound modules and their cryptanalysis https://www.zbmath.org/1483.94061 2022-05-16T20:40:13.078697Z "Kuryazov, D. M." https://www.zbmath.org/authors/?q=ai:kuryazov.d-m Summary: This article proposes options of electronic digital signature algorithms, the cryptographic strength of which is based on the complexity of computing a discrete logarithm in a finite field and the complexity of solving a problem of decomposing a sufficiently large odd number to prime factors, on the hash function used, as well as their cryptanalysis. Unlike existing electronic digital signature algorithms (RSA, El-Gamal) in the proposed new electronic digital signature algorithm signature generation process -- $$s$$, is carried out using a private parameter -- $$\varphi (N)$$. Public key authentication scheme over quaternions https://www.zbmath.org/1483.94062 2022-05-16T20:40:13.078697Z "Valluri, Maheswara Rao" https://www.zbmath.org/authors/?q=ai:valluri.maheswara-rao "Narayan, Shailendra Vikash" https://www.zbmath.org/authors/?q=ai:narayan.shailendra-vikash Summary: Authentication is one of the cryptographic primitives that allows one entity to convince to another of the truth of an assertion without revealing any information other than that the assertion is true. In this paper, public key authentication scheme over quaternions modulo an RSA composite $$n = pq$$, where $$p$$ and $$q$$ are primes of equal size is proposed. Security of the scheme relies on the root extraction problem together with the conjugacy search problem over quaternions modulo $$n$$. Furthermore, issues related to the security, space complexity and computational cost of the scheme are discussed. Linear codes over $$\mathbb{F}_4R$$ and their MacWilliams identity https://www.zbmath.org/1483.94063 2022-05-16T20:40:13.078697Z "Benbelkacem, Nasreddine" https://www.zbmath.org/authors/?q=ai:benbelkacem.nasreddine "Ezerman, Martianus Frederic" https://www.zbmath.org/authors/?q=ai:ezerman.martianus-frederic "Abualrub, Taher" https://www.zbmath.org/authors/?q=ai:abualrub.taher-a Self-dual codes over a family of local rings https://www.zbmath.org/1483.94064 2022-05-16T20:40:13.078697Z "Dougherty, Steven T." https://www.zbmath.org/authors/?q=ai:dougherty.steven-t "Fernández-Córdoba, Cristina" https://www.zbmath.org/authors/?q=ai:fernandez-cordoba.cristina "Ten-Valls, Roger" https://www.zbmath.org/authors/?q=ai:ten-valls.roger A $$[n,k,d]_q$$ code $$C$$ is said to be self-dual if it coincides with its orthogonal space, i.e. $$C=C^\perp$$. Self-dual codes possess many interesting properties and are closely related to many other mathematical structures. For example, they have connections to groups, designs, lattices and other mathematical objects as well. For this reason, investigation of classes of codes that are self-dual is an important area of study in coding theory. In this paper the authors, generalizing some previous works, construct a family of commutative rings $$R_{q,\Delta}$$. After that, they investigate both the structure of these rings and the codes constructed in $$R_{q,\Delta}$$. They determine the parameters that provide the existence of self-dual codes exist and give various constructions of them. Reviewer: Matteo Bonini (Dublin) Left ideals of matrix rings and error-correcting codes https://www.zbmath.org/1483.94065 2022-05-16T20:40:13.078697Z "Ferraz, R. A." https://www.zbmath.org/authors/?q=ai:ferraz.raul-antonio "Polcino Milies, C." https://www.zbmath.org/authors/?q=ai:milies.c-polcino|polcino-milies.cesar "Taufer, E." https://www.zbmath.org/authors/?q=ai:taufer.emanuele Let $$\mathbb{F}_q$$ be the field with $$q$$ elements and denote by $$M_n(\mathbb{F}_q)$$ full ring of $$n \times n$$ matrices. It is known that $$M_n (\mathbb{F}_q)$$ is semi-simple, so every left ideal is generated by just one element and it is possible to prove that such generator is an idempotent. These topics are strictly related to the construction of group codes, once known the ideal and its generator. In this work, the authors focus first on the computations of the number of left ideals in $$M_n(\mathbb{F}_q)$$. Afterwards they compute the number of idempotents generating each ideal, providing a set of idempotent generators of all left ideals of a given rank. Finally, these results are used results for constructing interesting group codes. Some of these codes achieve good performance w.r.t. known ones. Reviewer: Matteo Bonini (Dublin) One-weight codes in some classes of group rings https://www.zbmath.org/1483.94066 2022-05-16T20:40:13.078697Z "Ferraz, Raul Antonio" https://www.zbmath.org/authors/?q=ai:ferraz.raul-antonio "Nascimento Ferreira, Ruth" https://www.zbmath.org/authors/?q=ai:ferreira.ruth-nascimento A $$[n,k,d]_q$$ constant weight (or one-weight) code with parameters is a vector space $$C$$ of codewords of length $$n$$ all having weight fixed weight $$d$$. This class of codes is very studied both in many different metrics due to their interesting properties that have also effect on some applications. In this paper, the authors characterize in the Hamming metric the one-weight group codes $$\mathbb{F}_qG$$ when $$G$$ is a finite abelian group, or when $$G$$ is a cyclic group with $$n$$ elements and $$\gcd(n,q)=1$$. After that, using similar techniques, they also provide a construction of two-weight group codes. Reviewer: Matteo Bonini (Dublin) LCD codes and self-orthogonal codes in finite dihedral group algebras https://www.zbmath.org/1483.94067 2022-05-16T20:40:13.078697Z "Gao, Yanyan" https://www.zbmath.org/authors/?q=ai:gao.yanyan "Yue, Qin" https://www.zbmath.org/authors/?q=ai:yue.qin "Wu, Yansheng" https://www.zbmath.org/authors/?q=ai:wu.yansheng Summary: Let $$\mathbb{F}_q$$ be a finite field with order $$q$$ and $$D_{2n}$$ be the dihedral group with $$2n$$ elements, and $$\gcd (q, 2n) = 1$$. In this article, the authors give precise descriptions and enumerations of linear complementary dual (LCD) codes and self-orthogonal codes in the finite dihedral group algebras $$\mathbb{F}_q[D_{2n}]$$. Some numerical examples are also presented to illustrate the main results. Construction of binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes https://www.zbmath.org/1483.94068 2022-05-16T20:40:13.078697Z "Harada, Masaaki" https://www.zbmath.org/authors/?q=ai:harada.masaaki Let $$\mathbb{F}_q$$ be the finite field with $$q$$ elements, where $$q$$ is a prime power. An $$[n,k]_q$$ code $$C$$ over is said to be LCD code if $$C \cap C^{\perp} = \{ 0 \}$$, where $$C^\perp$$ denotes the dual code of $$C$$. The concept of LCD codes was introduced by Massey and has important relevance in coding for data storage. On the other side, an $$[n,k]_q$$ code $$C$$ is said to be a self-dual code if $$C = C^\perp$$. Even though self dual codes and LCD codes are at the antipodes in terms of properties, the techniques for constructing these codes have often common patterns. In this paper, the authors focus on the construction of LCD codes using already known techniques for self-dual codes for $$q=2,3$$ in the Hamming metric and $$q=4$$ in the Hermitian metric. Reviewer: Matteo Bonini (Dublin) Optimal antiblocking systems of information sets for the binary codes related to triangular graphs https://www.zbmath.org/1483.94069 2022-05-16T20:40:13.078697Z "Kroll, Hans-Joachim" https://www.zbmath.org/authors/?q=ai:kroll.hans-joachim "Taherian, Sayed-Ghahreman" https://www.zbmath.org/authors/?q=ai:taherian.sayed-ghahreman "Vincenti, Rita" https://www.zbmath.org/authors/?q=ai:vincenti.rita Summary: We present AI-systems for the binary codes obtained from the adjacency relation of the triangular graphs $$T(n)$$ for any $$n\geq 5$$. These AI-systems are optimal and have for $$n$$ odd the full error-correcting capability. Two classes of optimal $$p$$-ary few-weight codes from down-sets https://www.zbmath.org/1483.94070 2022-05-16T20:40:13.078697Z "Shi, Minjia" https://www.zbmath.org/authors/?q=ai:shi.minjia "Li, Xiaoxiao" https://www.zbmath.org/authors/?q=ai:li.xiaoxiao In this paper, the authors are interested in constructions of codes over the ring $$\mathbb{F}_p+u\mathbb{F}_p$$, $$u^2=u$$. They present two constructions using so called down-sets and when the down-sets are generated by a single maximal element, the Lee weight distributions of two classes of codes are computed. Further, using the Gray image of these codes the authors obtain two classes of minimal and distance optimal codes. Reviewer: Andrea Svob (Rijeka) Two families of two-weight codes over $$\mathbb{Z}_4$$ https://www.zbmath.org/1483.94071 2022-05-16T20:40:13.078697Z "Shi, Minjia" https://www.zbmath.org/authors/?q=ai:shi.minjia "Xuan, Wang" https://www.zbmath.org/authors/?q=ai:xuan.wang "Solé, Patrick" https://www.zbmath.org/authors/?q=ai:sole.patrick A linear code $$C$$ over $$\mathbb{Z}_4$$ of length $$n$$ is a $$\mathbb{Z}_4$$-submodule of $$\mathbb{Z}_4^n.$$ The Lee weight of $$0,1,2,3 \in \mathbb{Z}_4$$ are $$0,1,2,1,$$ respectively. The Lee weight of any vector $$\mathbf{x}=(x_1,x_2,\ldots,x_n) \in\mathbb{Z}_4^n$$ is define as $$W_L(\mathbf{x})=\sum_{i=1}^{n}W_L(x_i).$$ The linear code $$C$$ is called a two-Lee weight code if all nonzero codewords, i.e. vectors in $$C,$$ have exactly two different Lee weights. The inner product of any vectors $$\mathbf{x}=(x_1,x_2,\ldots,x_n)$$ and $$\mathbf{y}=(y_1,y_2,\ldots,y_n)$$ in $$\mathbb{Z}_4^n$$ is defined by $\mathbf{x} \cdot \mathbf{y}=x_1y_1+x_2y_2+\cdots+x_ny_n.$ The dual code of $$C$$ is defined as $C^\perp=\{\mathbf{x} \in\mathbb{Z}_4^n:~\mathbf{x} \cdot \mathbf{y}=0,~ \forall \mathbf{y} \in C\}.$ A Lee weight projective code $$C$$ of length $$n$$ over $$\mathbb{Z}_4$$ is a linear code such that the minimum nonzero Lee weight of its dual is at least three. In the paper under review, the authors construct two infinite families of two-weight codes over $$\mathbb{Z}_4$$ (Lemma 4.1 and Theorem 4.2 [see also Corollary 4.5]). As by-products, they obtain two infinite families of two-weight projective codes over $$\mathbb{Z}_4$$ (Theorem 4.9 and Corollary 4.10). Reviewer: Djoko Suprijanto (Bandung) A construction of self-dual skew cyclic and negacyclic codes of length $$n$$ over $$\mathbb{F}_{p^n}$$ https://www.zbmath.org/1483.94072 2022-05-16T20:40:13.078697Z "Batoul, Aicha" https://www.zbmath.org/authors/?q=ai:batoul.aicha "Boucher, Delphine" https://www.zbmath.org/authors/?q=ai:boucher.delphine "Boulanouar, Ranya Djihad" https://www.zbmath.org/authors/?q=ai:boulanouar.ranya-djihad We say that a code $$C$$ with generator matrix $$G$$ is isodual if it is equivalent to its dual. A linear code $$C$$ of length $$n$$ and generator matrix $$G$$ is a $$(\theta, \nu)$$-isodual code if $$G\cdot D$$ is a generator matrix of $$C^\bot$$ where $$D$$ is the $$n\times n$$ diagonal matrix with diagonal coefficients $$\nu, \theta(\nu),\ldots, \theta^{n-1}(\nu)$$ where $$\nu\in\mathbb{F}_q^\ast,$$ $$\theta\in\text{Aut}(\mathbb{F}_q)$$ and $$n$$ is a natural number. The authors develop the notion of $$(\theta, \nu)$$-isodual codes, where $$\theta$$ is the Frobenius automorphism in $$\mathbb{F}_{q}$$ and $$\nu\in\mathbb{F}_{q}^\ast.$$ These codes form a subfamily of the family of isodual codes and the $$(\theta, \nu)$$-isodual $$\theta$$-cyclic and $$\theta$$-negacyclic codes are characterised thanks to an equation satisfied by the skew check polynomials of the codes. The special case when $$q=p^n$$ where $$p$$ is a prime number and $$\theta$$ is the Frobenius automorphism over $$\mathbb{F}_{p^n}$$ is studied. A necessary and sufficient condition for the existence of $$(\theta, \nu)$$-isodual as well as a construction and an enumeration formula for self-dual $$\theta$$-cyclic and $$\theta$$-negacyclic codes of length $$n$$ over $$\mathbb{F}_{p^n}$$ are derived. In the last section, a subclass of self-dual $$\theta$$-cyclic codes over $$\mathbb{F}_{p^n}$$ which are self-dual Gabidulin codes are parametrize by a parameter which satisfies a polynomial system. For the entire collection see [Zbl 1470.11003]. Reviewer: Nikolay Yankov (Shumen) A useful tool for constructing linear codes https://www.zbmath.org/1483.94073 2022-05-16T20:40:13.078697Z "Knapp, Wolfgang D." https://www.zbmath.org/authors/?q=ai:knapp.wolfgang-d "Rodrigues, Bernardo G." https://www.zbmath.org/authors/?q=ai:rodrigues.bernardo-gabriel The authors introduce and discuss an elementary tool from the representation theory of finite groups that can be used to construct linear codes invariant under a given permutation group. The tool can be used to achieve theoretical insight as well as a way to explicitly determine generator matrices and weight distributions of codes. The authors use this tool to find, study and sometimes classify several types of codes invariant under various permutation groups, including new codes and codes found previously using graph-theoretical methods. The former include codes obtained by considering invariances under the actions of the Mathieu group $$M_{24}$$, the Conway simple group $$\textrm{Co}_1$$, and some of their subgroups. The latter include binary codes related to triangular graphs, and a 23-dimensional code constructed by Hans-Jörg Schaeffer in 1980 but not previously published. Reviewer: Thomas Britz (Sydney) On the decoding of 1-Fibonacci error correcting codes https://www.zbmath.org/1483.94074 2022-05-16T20:40:13.078697Z "Bellini, Emanuele" https://www.zbmath.org/authors/?q=ai:bellini.emanuele "Marcolla, Chiara" https://www.zbmath.org/authors/?q=ai:marcolla.chiara "Murru, Nadir" https://www.zbmath.org/authors/?q=ai:murru.nadir Perfect codes in some products of graphs https://www.zbmath.org/1483.94075 2022-05-16T20:40:13.078697Z "Bakaein, Samane" https://www.zbmath.org/authors/?q=ai:bakaein.samane "Tavakoli, Mostafa" https://www.zbmath.org/authors/?q=ai:tavakoli.mostafa "Rahbarnia, Freydoon" https://www.zbmath.org/authors/?q=ai:rahbarnia.freydoon Summary: A $$r$$-perfect code in a graph $$G= (V(G),E(G))$$ is a subset $$C$$ of $$V(G)$$ for which the balls of radius $$r$$ centered at the vertices of $$C$$ form a partition of $$V(G)$$. In this paper, we study the existence of perfect codes in corona product and generalized hierarchical product of graphs where the cardinality of $$U$$ is equal to one or two. Also, we give some examples as applications of our results. Explicit list-decodable codes with optimal rate for computationally bounded channels https://www.zbmath.org/1483.94076 2022-05-16T20:40:13.078697Z "Shaltiel, Ronen" https://www.zbmath.org/authors/?q=ai:shaltiel.ronen "Silbak, Jad" https://www.zbmath.org/authors/?q=ai:silbak.jad Summary: A stochastic code is a pair of encoding and decoding procedures (Enc, Dec) where $$\operatorname{Enc}:\{0,1\}^k\times\{0,1\}^d\rightarrow\{0,1\}^n$$. The code is $$(p, L)$$-list decodable against a class $$\mathcal{C}$$ of channel functions'' $$C:\{0,1\}^n\rightarrow\{0,1\}^n$$ if for every message $$m\in\{0,1\}^k$$ and every channel $$C\in\mathcal{C}$$ that induces at most $$pn$$ errors, applying Dec on the `received word'' $$C(\operatorname{Enc}(m,S))$$ produces a list of at most $$L$$ messages that contain $$m$$ with high probability over the choice of uniform $$S\leftarrow\{0,1\}^d$$. Note that both the channel $$C$$ and the decoding algorithm Dec do not receive the random variable $$S$$, when attempting to decode. The rate of a code is $$R=k/n$$, and a code is explicit if Enc, Dec run in time $$\operatorname{poly}(n)$$. \textit{V. Guruswami} and \textit{A. Smith} [J. ACM 63, No. 4, Paper No. 35, 37 p. (2016; Zbl 1407.94009)] showed that for every constants $$0 < p < \frac{1}{2}$$, $$\epsilon > 0$$ and $$c > 1$$ there exist a constant $$L$$ and a Monte Carlo explicit constructions of stochastic codes with rate $$R\geq 1-H(p)-\epsilon$$ that are $$(p, L)$$-list decodable for size $$n^c$$ channels. Here, Monte Carlo means that the encoding and decoding need to share a public uniformly chosen $$\operatorname{poly}(n^c)$$ bit string $$Y$$, and the constructed stochastic code is $$(p, L)$$-list decodable with high probability over the choice of $$Y$$. Guruswami and Smith pose an open problem to give fully explicit (that is not Monte Carlo) explicit codes with the same parameters, under hardness assumptions. In this paper, we resolve this open problem, using a minimal assumption: the existence of poly-time computable pseudorandom generators for small circuits, which follows from standard complexity assumptions by \textit{R. Impagliazzo} and \textit{A. Wigderson} [in: Proceedings of the 29th annual ACM symposium on theory of computing, STOC '97. El Paso, TX, USA, May 4--6, 1997. New York, NY: ACM, Association for Computing Machinery. 220--229 (1999; Zbl 0962.68058)]. Guruswami and Smith also asked to give a fully explicit unconditional constructions with the same parameters against $$O(\log n)$$-space online channels. (These are channels that have space $$O(\log n)$$ and are allowed to read the input codeword in one pass.) We also resolve this open problem. Finally, we consider a tighter notion of explicitness, in which the running time of encoding and list-decoding algorithms does not increase, when increasing the complexity of the channel. We give explicit constructions (with rate approaching $$1-H(p)$$ for every $$p\leq p_0$$ for some $$p_0 >0$$) for channels that are circuits of size $$2^{n^{\Omega(1/d)}}$$ and depth $$d$$. Here, the running time of encoding and decoding is a polynomial that does not depend on the depth of the circuit. Our approach builds on the machinery developed by Guruswami and Smith, replacing some probabilistic arguments with explicit constructions. We also present a simplified and general approach that makes the reductions in the proof more efficient, so that we can handle weak classes of channels. Capturing and shunting energy in chaotic Chua circuit https://www.zbmath.org/1483.94077 2022-05-16T20:40:13.078697Z "Wang, Chunni" https://www.zbmath.org/authors/?q=ai:wang.chunni "Liu, Zhilong" https://www.zbmath.org/authors/?q=ai:liu.zhilong "Hobiny, Aatef" https://www.zbmath.org/authors/?q=ai:hobiny.aatef-d "Xu, Wenkang" https://www.zbmath.org/authors/?q=ai:xu.wenkang "Ma, Jun" https://www.zbmath.org/authors/?q=ai:ma.jun.1|ma.jun Summary: Nonlinear electric devices are critical for building chaotic circuits and the outputs voltage from the capacitor are often detected for further analyzing the dynamics of the nonlinear circuits. Continuous exchange between the electric field energy in the capacitor and magnetic field energy in the induction coil is effective to keep continuous oscillation in the circuit. That is, energy encoding and transmission can regulate the dynamical behaviors in chaotic circuits. In this paper, a branch circuit, which is built by using a capacitor and induction coil, is paralleled with one output end of chaotic Chua circuit, and this external branch circuit is activated to control chaos by pumping energy from Chua circuit and capturing external electromagnetic radiation. From dynamical control view, it explains the mechanism for differential control via capacitor and integral control via induction coil. While in the view of energy encoding, the control branch of circuit built by using a capacitor connected with induction coil in series can capture some external field energy and thus the nonlinear behaviors are controlled by generating equivalent current in the branch of control circuit. The circuit equation and also the dimensionless dynamical system under energy control are obtained, and numerical studies are supplied to confirm the control mechanism from physical view. In the end, it gives possible suggestions to enhance the control effectiveness in experimental way. A new approach to fuzzy sets: application to the design of nonlinear time series, symmetry-breaking patterns, and non-sinusoidal limit-cycle oscillations https://www.zbmath.org/1483.94078 2022-05-16T20:40:13.078697Z "García-Morales, Vladimir" https://www.zbmath.org/authors/?q=ai:garcia-morales.vladimir Summary: It is shown that characteristic functions of sets can be made fuzzy by means of the $$\mathcal{B}_\kappa$$-function, recently introduced by the author, where the fuzziness parameter $$\kappa\in\mathbb{R}$$ controls how much a fuzzy set deviates from the crisp set obtained in the limit $$\kappa\rightarrow 0$$. As applications, we present first a general expression for a switching function that may be of interest in electrical engineering and in the design of nonlinear time series. We then introduce another general expression that allows wallpaper and frieze patterns for every possible planar symmetry group (besides patterns typical of quasicrystals) to be designed. We show how the fuzziness parameter $$\kappa$$ plays an analogous role to temperature in physical applications and may be used to break the symmetry of spatial patterns. As a further, important application, we establish a theorem on the shaping of limit cycle oscillations far from bifurcations in smooth deterministic nonlinear dynamical systems governed by differential equations. Following this application, we briefly discuss a generalization of the Stuart-Landau equation to non-sinusoidal oscillators. Bounds on Shannon functions of lengths of contact closure tests for contact circuits https://www.zbmath.org/1483.94079 2022-05-16T20:40:13.078697Z "Popkov, Kirill A." https://www.zbmath.org/authors/?q=ai:popkov.kirill-andreevich Summary: We consider the problem of synthesis of irredundant two-pole contact circuits which implement $$n$$-place Boolean functions and allow short single fault detection or diagnostic tests of closures of at most $$k$$ contacts. We prove that the Shannon function of the length of a fault detection test is equal to $$n$$ for any $$n$$ and $$k$$, and that the Shannon function of the length of a diagnostic test is majorized by $$n + k(n - 2)$$ for $$n \geq 2$$. Motifs for processes on networks https://www.zbmath.org/1483.94080 2022-05-16T20:40:13.078697Z "Schwarze, Alice C." https://www.zbmath.org/authors/?q=ai:schwarze.alice-c "Porter, Mason A." https://www.zbmath.org/authors/?q=ai:porter.mason-a The number of almost perfect nonlinear functions grows exponentially https://www.zbmath.org/1483.94081 2022-05-16T20:40:13.078697Z "Kaspers, Christian" https://www.zbmath.org/authors/?q=ai:kaspers.christian "Zhou, Yue" https://www.zbmath.org/authors/?q=ai:zhou.yue.1|zhou.yue Summary: Almost perfect nonlinear (APN) functions play an important role in the design of block ciphers as they offer the strongest resistance against differential cryptanalysis. Despite more than 25 years of research, only a limited number of APN functions are known. In this paper, we show that a recent construction by \textit{H. Taniguchi} [Des. Codes Cryptography 87, No. 9, 1973--1983 (2019; Zbl 1419.11138)] provides at least $$\frac{\varphi(m)}{2}\left\lceil\frac{2^m+1}{3m}\right\rceil$$ inequivalent APN functions on the finite field with $${2^{2m}}$$ elements, where $$\varphi$$ denotes Euler's totient function. This is a great improvement of previous results: for even $$m$$, the best known lower bound has been $$\frac{\varphi(m)}{2}\left(\lfloor\frac{m}{4}\rfloor+1\right)$$; for odd $$m$$, there has been no such lower bound at all. Moreover, we determine the automorphism group of Taniguchi's APN functions.