Description
I will describe an algorithm for computing the zeta function of an arbitrary hyperelliptic curve in characteristic 2. This is a generalisation of an earlier method of myself and Wan, which tackled a restricted class of curves. The algorithm reduces the problem to that of computing the L-function of an additive character sum over an open subset of the projective line. This latter task can be achieved using the Dwork-Reich trace formula, Dwork's analytic construction of an additive character, and a method for `cohomological reduction' similar to the `Hermite reduction' algorithm used in the symbolic integration of rational functions. The talk is based upon joint work with Daqing Wan. See http://web.comlab.ox.ac.uk/oucl/work/alan.lauder/ for a version of the earlier paper, which has now appeared in LMS JCM, and also two other related papers.
Prochains exposés
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Combining Partial Sums and FFT for the Fastest Known Attack on 6‑Round AES
Orateur : Shibam Ghosh - Inria
The partial-sums technique introduced by Ferguson et al. (2000) achieved a 6‑round AES attack with time complexity 2^{52} S‑box evaluations, a benchmark that has stood since. In 2014, Todo and Aoki proposed a comparable approach based on the Fast Fourier Transform (FFT). In this talk, I will show how to combine partial sums with FFT to get "the best of both worlds". The resulting attack on 6[…]-
Cryptography
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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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