Description
By a well-known result of Dwork the zeta functions of the fibers in a one-parameter family of hypersurfaces can be described in terms of p-adic holomorphic functions. This result was used by A. Lauder in order to formulate a deter- ministic algorithm that computes the zeta function of a hypersurface in polynomial time. In this talk we describe a similiar method for elliptic curves which is based on rigid cohomology rather than Dwork cohomology. In contrast to Dwork's theory, rigid cohomology is closely related to the notions of classical algebraic geometry. We give an overview on the theoretical background, describe the essential steps of the algorithm and comment on the problem of p-adic precision estimates. We also report on computational results obtained by a MAGMA implementation. In the last part we explain the relation between both theories and how Lauder's general algorithm can be reformulated in terms of rigid cohomology. This shows up similiarities as well as differences between the two approaches.
Prochains exposés
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Key Attack on the ACDGV Matrix Encryption Scheme
Orateur : 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
Orateur : 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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