Dai, Yu; Lin, Kaizhan; Zhao, Chang-An; Zhou, Zijian Fast subgroup membership testings for \(\mathbb{G}_1, \mathbb{G}_2\) and \(\mathbb{G}_T\) on pairing-friendly curves. (English) Zbl 1523.14051 Des. Codes Cryptography 91, No. 10, 3141-3166 (2023). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 14G50 14Q05 11G20 94A60 11T71 PDFBibTeX XMLCite \textit{Y. Dai} et al., Des. Codes Cryptography 91, No. 10, 3141--3166 (2023; Zbl 1523.14051) Full Text: DOI
Dai, Yu; Zhang, Fangguo; Zhao, Chang-An Fast hashing to \(\mathbb{G}_2\) on pairing-friendly curves with the lack of twists. (English) Zbl 1525.14031 Finite Fields Appl. 91, Article ID 102263, 20 p. (2023). Reviewer: Guillermo Morales Luna (Ciudad de México) MSC: 14G50 14Q05 11G20 94A60 11T71 PDFBibTeX XMLCite \textit{Y. Dai} et al., Finite Fields Appl. 91, Article ID 102263, 20 p. (2023; Zbl 1525.14031) Full Text: DOI
Assoujaa, Ismail; Ezzouak, Siham; Mouanis, Hakima Tower building technique on elliptic curve with embedding degree 18. (English) Zbl 1528.14031 Tatra Mt. Math. Publ. 83, 103-118 (2023). Reviewer: Hayder Hashim (Kufa) MSC: 14G50 94A60 11T71 PDFBibTeX XMLCite \textit{I. Assoujaa} et al., Tatra Mt. Math. Publ. 83, 103--118 (2023; Zbl 1528.14031) Full Text: DOI
Sedlacek, Vladimir; Suchanek, Vojtech; Dufka, Antonin; Sys, Marek; Matyas, Vashek DiSSECT: distinguisher of standard and simulated elliptic curves via traits. (English) Zbl 1515.94091 Batina, Lejla (ed.) et al., Progress in cryptology – AFRICACRYPT 2022. 13th international conference on cryptology in Africa, AFRICACRYPT 2022, Fes, Morocco, July 18–20, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13503, 493-517 (2022). MSC: 94A60 11G07 14H52 11G20 PDFBibTeX XMLCite \textit{V. Sedlacek} et al., Lect. Notes Comput. Sci. 13503, 493--517 (2022; Zbl 1515.94091) Full Text: DOI
El Housni, Youssef; Guillevic, Aurore Families of SNARK-friendly 2-chains of elliptic curves. (English) Zbl 1497.94085 Dunkelman, Orr (ed.) et al., Advances in cryptology – EUROCRYPT 2022. 41st annual international conference on the theory and applications of cryptographic techniques, Trondheim, Norway, May 30 – June 3, 2022. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 13276, 367-396 (2022). MSC: 94A60 14G50 14H52 PDFBibTeX XMLCite \textit{Y. El Housni} and \textit{A. Guillevic}, Lect. Notes Comput. Sci. 13276, 367--396 (2022; Zbl 1497.94085) Full Text: DOI
Rouse, Jeremy; Sutherland, Andrew V.; Zureick-Brown, David [Voight, John] \(\ell\)-adic images of Galois for elliptic curves over \(\mathbb{Q}\)(and an appendix with John Voight). (English) Zbl 1499.14057 Forum Math. Sigma 10, Paper No. e62, 63 p. (2022). Reviewer: Riccardo Pengo (Bonn) MSC: 14H52 11G05 14G35 11F80 11G18 PDFBibTeX XMLCite \textit{J. Rouse} et al., Forum Math. Sigma 10, Paper No. e62, 63 p. (2022; Zbl 1499.14057) Full Text: DOI arXiv
Laurian, Azebaze Guimagang; Emmanuel, Fouotsa; El Mrabet, Nadia; Aminatou, Pecha Njiahouo Faster beta Weil pairing on BLS pairing friendly curves with odd embedding degree. (English) Zbl 07570272 Math. Comput. Sci. 16, No. 2-3, Paper No. 13, 23 p. (2022). MSC: 14H52 PDFBibTeX XMLCite \textit{A. G. Laurian} et al., Math. Comput. Sci. 16, No. 2--3, Paper No. 13, 23 p. (2022; Zbl 07570272) Full Text: DOI
Budroni, Alessandro; Pintore, Federico Efficient hash maps to \(\mathbb{G}_2\) on BLS curves. (English) Zbl 1490.14044 Appl. Algebra Eng. Commun. Comput. 33, No. 3, 261-281 (2022). Reviewer: Guillermo Morales Luna (Ciudad de México) MSC: 14G50 94A60 PDFBibTeX XMLCite \textit{A. Budroni} and \textit{F. Pintore}, Appl. Algebra Eng. Commun. Comput. 33, No. 3, 261--281 (2022; Zbl 1490.14044) Full Text: DOI
Barbulescu, Razvan; Shinde, Sudarshan A classification of ECM-friendly families of elliptic curves using modular curves. (English) Zbl 1512.11097 Math. Comput. 91, No. 335, 1405-1436 (2022). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11Y05 11G05 11F80 14G35 PDFBibTeX XMLCite \textit{R. Barbulescu} and \textit{S. Shinde}, Math. Comput. 91, No. 335, 1405--1436 (2022; Zbl 1512.11097) Full Text: DOI
Kleinjung, Thorsten; Wesolowski, Benjamin Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic. (English) Zbl 1487.11113 J. Am. Math. Soc. 35, No. 2, 581-624 (2022). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 11Y16 14H52 11T71 PDFBibTeX XMLCite \textit{T. Kleinjung} and \textit{B. Wesolowski}, J. Am. Math. Soc. 35, No. 2, 581--624 (2022; Zbl 1487.11113) Full Text: DOI arXiv
Randriambololona, Hugues The quadratic hull of a code and the geometric view on multiplication algorithms. (English) Zbl 1497.94178 Ballet, Stéphane (ed.) et al., Arithmetic, geometry, cryptography and coding theory, AGC2T, 17th international conference, Centre International de Rencontres Mathématiques, Marseilles, France, June 10–14, 2019. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 770, 267-296 (2021). MSC: 94B27 68W30 12E20 14A25 PDFBibTeX XMLCite \textit{H. Randriambololona}, Contemp. Math. 770, 267--296 (2021; Zbl 1497.94178) Full Text: DOI arXiv
Koshelev, Dmitrii Hashing to elliptic curves of \(j\)-invariant 1728. (English) Zbl 1487.14033 Cryptogr. Commun. 13, No. 4, 479-494 (2021). Reviewer: Jose Capco (Linz) MSC: 14E05 14G15 14G50 14Q20 14K02 14H52 PDFBibTeX XMLCite \textit{D. Koshelev}, Cryptogr. Commun. 13, No. 4, 479--494 (2021; Zbl 1487.14033) Full Text: DOI
Kutas, Péter; Petit, Christophe; Silva, Javier Trapdoor DDH groups from pairings and isogenies. (English) Zbl 1485.94102 Dunkelman, Orr (ed.) et al., Selected areas in cryptography. 27th international conference, Halifax, NS, Canada (virtual event), October 21–23, 2020. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 12804, 431-450 (2021). MSC: 94A60 11G07 14G50 PDFBibTeX XMLCite \textit{P. Kutas} et al., Lect. Notes Comput. Sci. 12804, 431--450 (2021; Zbl 1485.94102) Full Text: DOI Link
Randriambololona, Hugues; Rousseau, Édouard Trisymmetric multiplication formulae in finite fields. (English) Zbl 1480.12001 Bajard, Jean Claude (ed.) et al., Arithmetic of finite fields. 8th international workshop, WAIFI 2020, Rennes, France, July 6–8, 2020. Revised selected and invited papers. Cham: Springer. Lect. Notes Comput. Sci. 12542, 92-111 (2021). MSC: 12-08 12E30 14Q20 68W30 PDFBibTeX XMLCite \textit{H. Randriambololona} and \textit{É. Rousseau}, Lect. Notes Comput. Sci. 12542, 92--111 (2021; Zbl 1480.12001) Full Text: DOI
Ballet, Stéphane; Pieltant, Julia; Rambaud, Matthieu; Randriambololona, Hugues; Rolland, Robert; Chaumine, Jean On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry. (English. Russian original) Zbl 1482.11164 Russ. Math. Surv. 76, No. 1, 29-89 (2021); translation from Usp. Mat. Nauk 76, No. 1, 31-94 (2021). Reviewer: Jeroen Sijsling (Ulm) MSC: 11Y16 68Q25 14H05 12E20 PDFBibTeX XMLCite \textit{S. Ballet} et al., Russ. Math. Surv. 76, No. 1, 29--89 (2021; Zbl 1482.11164); translation from Usp. Mat. Nauk 76, No. 1, 31--94 (2021) Full Text: DOI arXiv
Clarisse, Rémi; Duquesne, Sylvain; Sanders, Olivier Curves with fast computations in the first pairing group. (English) Zbl 1520.94046 Krenn, Stephan (ed.) et al., Cryptology and network security. 19th international conference, CANS 2020, Vienna, Austria, December 14–16, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12579, 280-298 (2020). MSC: 94A60 14G50 14H52 PDFBibTeX XMLCite \textit{R. Clarisse} et al., Lect. Notes Comput. Sci. 12579, 280--298 (2020; Zbl 1520.94046) Full Text: DOI
Bouvier, Cyril; Imbert, Laurent Faster cofactorization with ECM using mixed representations. (English) Zbl 1483.11264 Kiayias, Aggelos (ed.) et al., Public-key cryptography – PKC 2020. 23rd IACR international conference on practice and theory of public-key cryptography, Edinburgh, UK, May 4–7, 2020. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 12111, 483-504 (2020). MSC: 11Y05 11T71 94A60 14G50 PDFBibTeX XMLCite \textit{C. Bouvier} and \textit{L. Imbert}, Lect. Notes Comput. Sci. 12111, 483--504 (2020; Zbl 1483.11264) Full Text: DOI Link
Guillevic, Aurore; Masson, Simon; Thomé, Emmanuel Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation. (English) Zbl 1448.94202 Des. Codes Cryptography 88, No. 6, 1047-1081 (2020). MSC: 94A60 11T71 14G50 PDFBibTeX XMLCite \textit{A. Guillevic} et al., Des. Codes Cryptography 88, No. 6, 1047--1081 (2020; Zbl 1448.94202) Full Text: DOI
Oliveira, Thomaz; López, Julio; Cervantes-Vázquez, Daniel; Rodríguez-Henríquez, Francisco Koblitz curves over quadratic fields. (English) Zbl 1466.94034 J. Cryptology 32, No. 3, 867-894 (2019). MSC: 94A60 11T71 14G50 PDFBibTeX XMLCite \textit{T. Oliveira} et al., J. Cryptology 32, No. 3, 867--894 (2019; Zbl 1466.94034) Full Text: DOI
Fouotsa, Emmanuel; Pecha, Aminatou; El Mrabet, Nadia Beta Weil pairing revisited. (English) Zbl 1438.14003 Afr. Mat. 30, No. 3-4, 371-388 (2019). MSC: 14H52 PDFBibTeX XMLCite \textit{E. Fouotsa} et al., Afr. Mat. 30, No. 3--4, 371--388 (2019; Zbl 1438.14003) Full Text: DOI
Fotiadis, Georgios; Konstantinou, Elisavet Generating pairing-friendly elliptic curve parameters using sparse families. (English) Zbl 1496.94043 J. Math. Cryptol. 12, No. 2, 83-99 (2018). Reviewer: Michael J. Jacobson jun. (Calgary) MSC: 94A60 11G20 14G50 14H52 PDFBibTeX XMLCite \textit{G. Fotiadis} and \textit{E. Konstantinou}, J. Math. Cryptol. 12, No. 2, 83--99 (2018; Zbl 1496.94043) Full Text: DOI Link
Duquesne, Sylvain; El Mrabet, Nadia; Haloui, Safia; Rondepierre, Franck Choosing and generating parameters for pairing implementation on BN curves. (English) Zbl 1401.94151 Appl. Algebra Eng. Commun. Comput. 29, No. 2, 113-147 (2018). MSC: 94A60 11T71 14G50 PDFBibTeX XMLCite \textit{S. Duquesne} et al., Appl. Algebra Eng. Commun. Comput. 29, No. 2, 113--147 (2018; Zbl 1401.94151) Full Text: DOI
Guillevic, Aurore; Morain, François; Thomé, Emmanuel Solving discrete logarithms on a 170-bit MNT curve by pairing reduction. (English) Zbl 1418.11159 Avanzi, Roberto (ed.) et al., Selected areas in cryptography – SAC 2016. 23rd international conference, St. John’s, NL, Canada, August 10–12, 2016. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 10532, 559-578 (2017). MSC: 11T71 94A60 14G50 PDFBibTeX XMLCite \textit{A. Guillevic} et al., Lect. Notes Comput. Sci. 10532, 559--578 (2017; Zbl 1418.11159) Full Text: DOI arXiv
Vitse, Vanessa Field extensions and index calculus on algebraic curves. (English) Zbl 1430.11164 Bassa, Alp (ed.) et al., Arithmetic, geometry, cryptography and coding theory. 15th international conference on arithmetic, geometry, cryptography, and coding theory (AGCT), CIRM, Luminy, France, May 18–22, 2015. Proceedings. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 686, 187-199 (2017). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 11T71 14H25 14H40 94A60 PDFBibTeX XMLCite \textit{V. Vitse}, Contemp. Math. 686, 187--199 (2017; Zbl 1430.11164) Full Text: DOI HAL
Hisil, Huseyin; Costello, Craig Jacobian coordinates on genus 2 curves. (English) Zbl 1377.94053 J. Cryptology 30, No. 2, 572-600 (2017). MSC: 94A60 14G50 14Q05 PDFBibTeX XMLCite \textit{H. Hisil} and \textit{C. Costello}, J. Cryptology 30, No. 2, 572--600 (2017; Zbl 1377.94053) Full Text: DOI
Novoselov, S. A. On bounds for balanced embedding degree. (Russian. English summary) Zbl 1490.14045 Prikl. Diskretn. Mat. 2016, No. 2(32), 63-86 (2016). MSC: 14G50 11T71 11G20 PDFBibTeX XMLCite \textit{S. A. Novoselov}, Prikl. Diskretn. Mat. 2016, No. 2(32), 63--86 (2016; Zbl 1490.14045) Full Text: DOI MNR
Montanari, Andrea Effective compression maps for torus-based cryptography. (English) Zbl 1403.94072 Des. Codes Cryptography 79, No. 1, 1-17 (2016). MSC: 94A60 14G50 14E05 PDFBibTeX XMLCite \textit{A. Montanari}, Des. Codes Cryptography 79, No. 1, 1--17 (2016; Zbl 1403.94072) Full Text: DOI
Gorla, Elisa; Massierer, Maike Index calculus in the trace zero variety. (English) Zbl 1333.14025 Adv. Math. Commun. 9, No. 4, 515-539 (2015). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 14G50 11G25 11Y40 11T71 PDFBibTeX XMLCite \textit{E. Gorla} and \textit{M. Massierer}, Adv. Math. Commun. 9, No. 4, 515--539 (2015; Zbl 1333.14025) Full Text: DOI arXiv
Barreto, Paulo S. L. M.; Costello, Craig; Misoczki, Rafael; Naehrig, Michael; Pereira, Geovandro C. C. F.; Zanon, Gustavo Subgroup security in pairing-based cryptography. (English) Zbl 1370.94485 Lauter, Kristin (ed.) et al., Progress in cryptology – LATINCRYPT 2015. 4th international conference on cryptology and information security in Latin America, Guadalajara, Mexico, August 23–26, 2015. Proceedings. Cham: Springer (ISBN 978-3-319-22173-1/pbk; 978-3-319-22174-8/ebook). Lecture Notes in Computer Science 9230, 245-265 (2015). MSC: 94A60 14G50 PDFBibTeX XMLCite \textit{P. S. L. M. Barreto} et al., Lect. Notes Comput. Sci. 9230, 245--265 (2015; Zbl 1370.94485) Full Text: DOI
Gorla, Elisa; Massierer, Maike Point compression for the trace zero subgroup over a small degree extension field. (English) Zbl 1319.14033 Des. Codes Cryptography 75, No. 2, 335-357 (2015). Reviewer: Guillermo Matera (Buenos Aires) MSC: 14G50 11G25 14H52 11T71 PDFBibTeX XMLCite \textit{E. Gorla} and \textit{M. Massierer}, Des. Codes Cryptography 75, No. 2, 335--357 (2015; Zbl 1319.14033) Full Text: DOI arXiv
Mihăilescu, Preda; Rassias, Michael Th. Computational number theory and cryptography. (English) Zbl 1312.94079 Daras, Nicholas J. (ed.), Applications of mathematics and informatics in science and engineering. Selected papers based on the presentations at the 2nd international conference on applications of mathematics and informatics in military sciences, AMIMS, April 12–13, 2013, Hellenic Military Academy, Vari Attikis, Greece. Cham: Springer (ISBN 978-3-319-04719-5/hbk; 978-3-319-04720-1/ebook). Springer Optimization and Its Applications 91, 349-373 (2014). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 94A60 11Y16 11Y05 11G20 14G50 81P70 PDFBibTeX XMLCite \textit{P. Mihăilescu} and \textit{M. Th. Rassias}, Springer Optim. Appl. 91, 349--373 (2014; Zbl 1312.94079) Full Text: DOI