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EUROCRYPT
2005
Springer

Floating-Point LLL Revisited

13 years 9 months ago
Floating-Point LLL Revisited
The Lenstra-Lenstra-Lov´asz lattice basis reduction algorithm (LLL or L3 ) is a very popular tool in public-key cryptanalysis and in many other fields. Given an integer d-dimensional lattice basis with vectors of norm less than B in an n-dimensional space, L3 outputs a socalled L3 -reduced basis in polynomial time O(d5 n log3 B), using arithmetic operations on integers of bit-length O(d log B). This worst-case complexity is problematic for lattices arising in cryptanalysis where d or/and log B are often large. As a result, the original L3 is almost never used in practice. Instead, one applies floating-point variants of L3 , where the long-integer arithmetic required by Gram-Schmidt orthogonalisation (central in L3 ) is replaced by floating-point arithmetic. Unfortunately, this is known to be unstable in the worst-case: the usual floating-point L3 is not even guaranteed to terminate, and the output basis may not be L3 -reduced at all. In this article, we introduce the L2 algorithm,...
Phong Q. Nguyen, Damien Stehlé
Added 27 Jun 2010
Updated 27 Jun 2010
Type Conference
Year 2005
Where EUROCRYPT
Authors Phong Q. Nguyen, Damien Stehlé
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