Description
Lattice-based cryptography typically uses lattices with special properties to improve efficiency.
We show how blockwise reduction can exploit lattices with special geometric properties, effectively reducing the required blocksize to solve the shortest vector problem to half of the lattice's rank, and in the case of the hypercubic lattice , further relaxing the approximation factor of blocks to .
We study both provable algorithms and the heuristic well-known primal attack, in the case where the lattice has a first minimum that is almost as short as that of the hypercubic lattice . Remarkably, these near-hypercubic lattices cover Falcon and most concrete instances of the NTRU cryptosystem: this is the first provable result showing that breaking NTRU lattices can be reduced to finding shortest lattice vectors in halved dimension, thereby providing a positive response to a conjecture of Gama, Howgrave-Graham and Nguyen at Eurocrypt 2006.
Infos pratiques
Prochains exposés
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Cycles of pairing-friendly abelian varieties
Orateur : Maria Corte-Real Santos - ENS Lyon
A promising avenue for realising scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. More specifically, such a cycle consists of two elliptic curves E/Fp and E’/Fq that both have a low embedding degree and also satisfy q = #E(Fp) and p = #E’(Fq). These constraints turn out to be rather restrictive; in the decade that has passed since 2-cycles were first[…]-
Cryptography
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