Description
In this talk, I'll prove some divisibility properties of the cardinality of elliptic curve groups modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas behind the proofs can be used to find new infinite families of elliptic curves with good division properties increasing the success probability of ECM This is a joint work with Razvan Barbulescu, Joppe W. Bos, Thorsten Kleinjung and Peter L. Montgomery.
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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