Description
We describe an algorithm of Harvey, improved and implemented by Harvey and Sutherland, which given a hyperelliptic curve of genus g over Q computes its zeta function over F_p for all p <= N in such a way that the average time per prime is polynomial in g and log(N). The method is based on p-adic cohomology, specifically the algorithms of Kedlaya and Harvey; the key new observation is that one can set up the cohomology computation in a manner which is almost entirely independent of p, and thus reuse much of the computation.
Next sessions
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Key Attack on the ACDGV Matrix Encryption Scheme
Speaker : Anmoal Porwal - Technical University of Munich
I will present our key-recovery attack on the ACDGV public-key encryption scheme proposed at ASIACRYPT 2024 by Aragon, Couvreur, Dyseryn, Gaborit, and Vinçotte. The secret key is a Gabidulin code hidden by appending random rows and columns and by left- and right-multiplication with invertible matrices. Our attack exploits the resulting algebraic structure to recover an equivalent secret key. It[…]-
Cryptography
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Asymmetric primitive
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Module Learning With Errors and Structured Extrapolated Dihedral Cosets
Speaker : Jinwei Zheng - Télécom Paris
The Module Learning With Errors (MLWE) problem is the fundamental hardness assumption underlying the key encapsulation and signature schemes ML-KEM and ML-DSA, which have been selected by NIST for post-quantum cryptography standardization. Understanding its quantum hardness is crucial for assessing the security of these standardized schemes. Inspired by the equivalence between LWE and[…]-
Cryptography
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