Description
The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The running-time of the number field sieve depends on the quality of the chosen polynomials. The quality of the chosen polynomials can be modeled in terms of size and root properties. In this talk, we will describe some better algorithms to select polynomials with good size and root properties.<br/> The talk will be based on papers, Shi Bai, Cyril Bouvier, Alexander Kruppa and Paul Zimmermann. Better polynomials for GNFS. Math. Comp, 2015.<br/> Shi Bai, Richard Brent and Emmanuel Thomé. Root optimization of polynomials in the number field sieve. Math. Comp, 2015.
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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