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.
Next sessions
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Endomorphisms via Splittings
Speaker : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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Schéma de signature à clé publique : Frobénius-UOV
Speaker : Gilles Macario-Rat - Orange
L'exposé présente un schéma de signature à clé publique post-quantique inspiré du schéma UOV et introduisant un nouvel outil : les formes de Frobénius. L'accent est mis sur le rôle et les propriétés des formes de Frobénius dans ce nouveau schéma : la simplicité de description, la facilité de mise en oeuvre et le gain inédit sur les tailles de signature et de clé qui bat RSA-2048 au niveau de[…]