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CALC
2001
Springer
161views Cryptology» more  CALC 2001»
14 years 6 days ago
The Shortest Vector Problem in Lattices with Many Cycles
In this paper we investigate how the complexity of the shortest vector problem in a lattice Λ depends on the cycle structure of the additive group Zn /Λ. We give a proof that the...
Mårten Trolin
PKC
2007
Springer
165views Cryptology» more  PKC 2007»
14 years 1 months ago
Deterministic Polynomial Time Equivalence Between Factoring and Key-Recovery Attack on Takagi's RSA
Abstract. For RSA, May showed a deterministic polynomial time equivalence of computing d to factoring N(= pq). On the other hand, Takagi showed a variant of RSA such that the decry...
Noboru Kunihiro, Kaoru Kurosawa
LATIN
2010
Springer
14 years 2 months ago
Gradual Sub-lattice Reduction and a New Complexity for Factoring Polynomials
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type ...
Mark van Hoeij, Andrew Novocin
ANTS
2010
Springer
262views Algorithms» more  ANTS 2010»
13 years 11 months ago
Short Bases of Lattices over Number Fields
Lattices over number elds arise from a variety of sources in algorithmic algebra and more recently cryptography. Similar to the classical case of Z-lattices, the choice of a nice,...
Claus Fieker, Damien Stehlé
CRYPTO
2006
Springer
119views Cryptology» more  CRYPTO 2006»
13 years 11 months ago
Rankin's Constant and Blockwise Lattice Reduction
Abstract Lattice reduction is a hard problem of interest to both publickey cryptography and cryptanalysis. Despite its importance, extremely few algorithms are known. The best algo...
Nicolas Gama, Nick Howgrave-Graham, Henrik Koy, Ph...