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The LLL algorithm. Survey and applications. (English) Zbl 1179.11003
Information Security and Cryptography. Dordrecht: Springer (ISBN 978-3-642-02294-4/hbk; 978-3-642-02295-1/ebook). xiv, 496 p. (2010).

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The articles of this volume will be reviewed individually.
Indexed articles:
Smeets, Ionica; Lenstra, Arjen; Lenstra, Hendrik; Lovász, László; Van Emde Boas, Peter, The history of the LLL-algorithm, 1-17 [Zbl 1230.11002]
Nguyen, Phong Q., Hermite’s constant and lattice algorithms, 19-69 [Zbl 1230.11155]
Vallée, Brigitte; Vera, Antonio, Probabilistic analyses of lattice reduction algorithms, 71-143 [Zbl 1230.11156]
Schnorr, Claus Peter, Progress on LLL and lattice reduction, 145-178 [Zbl 1215.11122]
Stehlé, Damien, Floating-point LLL: Theoretical and practical aspects, 179-213 [Zbl 1186.65052]
Hanrot, Guillaume, LLL: a tool for effective Diophantine approximation, 215-263 [Zbl 1230.11154]
Simon, Denis, Selected applications of LLL in number theory, 265-282 [Zbl 1241.11001]
Klüners, Jürgen, The van Hoeij algorithm for factoring polynomials, 283-291 [Zbl 1234.11163]
Aardal, Karen; Eisenbrand, Friedrich, The LLL algorithm and integer programming, 293-314 [Zbl 1181.90197]
May, Alexander, Using LLL-reduction for solving RSA and factorization problems, 315-348 [Zbl 1237.94078]
Hoffstein, Jeff; Howgrave-Graham, Nick; Pipher, Jill; Whyte, William, Practical lattice-based cryptography: NTRUEncrypt and NTRUSign, 349-390 [Zbl 1191.94090]
Gentry, Craig, The geometry of provable security: some proofs of security in which lattices make a surprise appearance, 391-426 [Zbl 1191.94089]
Micciancio, Daniele, Cryptographic functions from worst-case complexity assumptions, 427-452 [Zbl 1191.94098]
Khot, Subhash, Inapproximability results for computational problems on lattices, 453-473 [Zbl 1237.68101]
Regev, Oded, On the complexity of lattice problems with polynomial approximation factors, 475-496 [Zbl 1237.68102]

MSC:
11-06 Proceedings, conferences, collections, etc. pertaining to number theory
11Y16 Number-theoretic algorithms; complexity
11Y50 Computer solution of Diophantine equations
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94A60 Cryptography
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