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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Présentations des nouveaux doctorants Capsule
Orateur : Alisée Lafontaine et Mathias Boucher - INRIA Rennes
2 nouveaux doctorants arrivent dans l'équipe Capsule et présenteront leurs thématiques de recherche. Alisée Lafontaine, encadrée par André Schrottenloher, présentera son stage de M2: "Quantum rebound attacks on double-block length hash functions" Mathias Boucher, encadré par Yixin Shen, parlera des algorithmes quantiques et des réseaux euclidiens. -
Design of fast AES-based Universal Hash Functions and MACs
Orateur : Augustin Bariant - ANSSI
Ultra-fast AES round-based software cryptographic authentication/encryption primitives have recently seen important developments, fuelled by the authenticated encryption competition CAESAR and the prospect of future high-profile applications such as post-5G telecommunication technology security standards. In particular, Universal Hash Functions (UHF) are crucial primitives used as core components[…]-
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[…]