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Abstract: In recent years, methods based on lattice reduction have been used repeatedly for the cryptanalytic attack of various systems. Even if they do not rest on highly sophisticated theories, these methods may look a bit intricate to the practically oriented cryptographers, both from the mathematical and the algorithmic point of view. The aim of the present paper is to explain what can be achieved by lattice reduction algorithms, even without understanding of the actual mechanisms involved. Two... (Update)
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BibTeX entry: (Update)
A Joux, J Stern, "Lattice Reduction: a Toolbox for the Cryptanalyst", to appear in Journal of Cryptology http://citeseer.ist.psu.edu/article/joux94lattice.html More
@article{ joux98lattice,
author = "Antoine Joux and Jacques Stern",
title = "Lattice Reduction: {A} Toolbox for the Cryptanalyst",
journal = "Journal of Cryptology: the journal of the International Association for Cryptologic Research",
volume = "11",
number = "3",
month = "Summer",
pages = "161--185",
year = "1998",
url = "citeseer.ist.psu.edu/article/joux94lattice.html" }
Citations (may not include all citations):227 Factoring polynomials with rational coefficients (context) - Lenstra, Lenstra et al. - 1982
124 The Art of Computer Programming: Vol (context) - Knuth - 1969
100 Integer programming with a fixed number of variables (context) - Lenstra - 1983
70 Hiding information and signatures in trapdoor knapsacks (context) - Merkle, Hellman - 1978
61 A design principle for hash functions (context) - Damgard - 1989
60 Lattice basis reduction: Improved practical algorithms and s.. - Schnorr, Euchner - 1991
60 Solving low-density subset sum problems (context) - Lagarias, Odlyzko - 1983
51 A hierarchy of polynomial time lattice basis reduction algor.. (context) - Schnorr - 1987
49 Improved low-density subset sum algorithms - Coster, Joux et al. - 1992
33 A polynomial-time algorithm for breaking the basic Merkle-He.. (context) - Shamir - 1982
29 Disquisitiones arithmeticae (context) - Gauss
23 the Lagarias-Odlyzko algorithm for the subset sum problems (context) - Frieze - 1986
23 Geometrie der Zahlen (context) - Minkowski - 1910
22 Sur les formes quadratiques (context) - Korkine, Zolotarev
21 Reconstructing truncated integer variables satisfying linear.. (context) - Frieze, Hastad et al. - 1988
18 A more efficient algorithm for lattice basis reduction (context) - Schnorr - 1988
16 Breaking iterated knapsacks (context) - Brickell - 1985
14 Inferring a sequence generated by a linear congruence (context) - Plumstead - 1982
13 de M. Hermite `a M. Jacobi sur diff (context) - Hermite
12 On breaking generalized knapsack public key cryptosystems (context) - Adleman - 1983
8 Secret linear congruential generators are not cryptographica.. (context) - Stern - 1987
7 Recherches d'arithm'etique (context) - Lagrange
7 The knapsack hash-function proposed at crypto'89 can be brok.. (context) - Camion, Patarin - 1991
6 Inferring sequences produced by a linear congruential genera.. (context) - Boyar - 1989
5 Deciphering a linear congruential encryption (context) - Knuth - 1980
4 Cryptanalysis of another knapsack cryptosystem (context) - Joux, Stern - 1991
3 The cryptanalysis of a new publickey cryptosystem based on m.. (context) - Chee, Joux et al. - 1991
3 Cryptanalysis of a public-key cryptosystem based on approxim.. (context) - Stern, Toffin - 1990
2 La R'eduction de R'eseaux en Cryptographie (context) - Joux - 1993
2 A practical attack against knapsack based hash functions - Granboulan, Joux - 1994
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