Description
Finding a short non zero vector in an Euclidean lattice is a well-studied problem which has proven useful to construct many cryptographic primitives. The current best asymptotic algorithm to find a relatively short vector in an arbitrary lattice is the BKZ algorithm. This algorithm recovers a vector which is at most $2^{n^{\alpha}}$ times larger than the shortest non zero vector in time $2^{n^{1-\alpha}}$ for any $\alpha$ between 0 and 1.<br/> In order to gain in efficiency, it is sometimes interesting to use structured lattices instead of general lattices. An example of such structured lattices are ideal lattices. One may then wonder whether, on the security front, it is easier to find short vectors in a structured lattice or not. Until 2016, there was no known algorithm which would perform better on ideal lattices than the BKZ algorithm (either classically or quantumly). In 2016 and 2017, Cramer-Ducas-Peikert-Regev and Cramer-Ducas-Wesolowski proposed a quantum algorithm that finds a $2^{\sqrt n}$ approximation of the shortest non zero vector in polynomial time. However, the BKZ algorithm remained the best algorithm in the classical setting or for approximation factor smaller than $2^{\sqrt n}$ in the quantum setting.<br/> In this talk, I will present an algorithm that extends the one of Cramer et al. and improves upon the BKZ algorithm for ideal lattices, both quantumly and classically. This algorithm is heuristic and non uniform (i.e., it requires an exponential time pre-processing).<br/> lien: http://desktop.visio.renater.fr/scopia?ID=723420***3028&autojoin
Prochains exposés
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Lie algebras and the security of cryptosystems based on classical varieties in disguise
Orateur : Mingjie Chen - KU Leuven
In 2006, de Graaf et al. proposed a strategy based on Lie algebras for finding a linear transformation in the projective linear group that connects two linearly equivalent projective varieties defined over the rational numbers. Their method succeeds for several families of “classical” varieties, such as Veronese varieties, which are known to have large automorphism groups. In this talk, we[…]-
Cryptography
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Some applications of linear programming to Dilithium
Orateur : Paco AZEVEDO OLIVEIRA - Thales & UVSQ
Dilithium is a signature algorithm, considered post-quantum, and recently standardized under the name ML-DSA by NIST. Due to its security and performance, it is recommended in most use cases. During this presentation, I will outline the main ideas behind two studies, conducted in collaboration with Andersson Calle-Vierra, Benoît Cogliati, and Louis Goubin, which provide a better understanding of[…] -
Wagner’s Algorithm Provably Runs in Subexponential Time for SIS^∞
Orateur : Johanna Loyer - Inria Saclay
At CRYPTO 2015, Kirchner and Fouque claimed that a carefully tuned variant of the Blum-Kalai-Wasserman (BKW) algorithm (JACM 2003) should solve the Learning with Errors problem (LWE) in slightly subexponential time for modulus q = poly(n) and narrow error distribution, when given enough LWE samples. Taking a modular view, one may regard BKW as a combination of Wagner’s algorithm (CRYPTO 2002), run[…]-
Cryptography
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CryptoVerif: a computationally-sound security protocol verifier
Orateur : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
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Structured-Seed Local Pseudorandom Generators and their Applications
Orateur : Nikolas Melissaris - IRIF
We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a[…]-
Cryptography
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