Description
Strong lattice reduction is the key element for most attacks against lattice-based cryptosystems. Between the strongest but impractical HKZ reduction and the weak but fast LLL reduction, there have been several attempts to find efficient trade-offs. Among them, the BKZ algorithm introduced by Schnorr and Euchner in 1991 seems to achieve the best time/quality compromise in practice. However, no reasonable time complexity upper bound was known so far for BKZ. We give a proof that after O~(n^3/k^2) calls to a k-dimensional HKZ reduction subroutine, BKZ_k returns a basis such that the norm of the first vector is at most ~= gamma_k ^ (n/2(k-1)) * det(L)^(1/n). The main ingredient of the proof is the analysis of a linear dynamic system related to the algorithm.
Prochains exposés
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Adelic reduction of module lattices
Orateur : Henry Bambury - DGA-MI et Inria Rennes
We give a strict generalisation of the LLL algorithm over number fields, based on the reduction theory of $GL(n)$ over the adele ring of a number field. Our algorithm is free of heuristics, with rigorous bounds on output quality and complexity. -- based on joint work with Seungki Kim, Changmin Lee and Phong Nguyen ---
Cryptography
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