Description
Dans cet exposé, nous étudions des méthodes de résolution de deux types de systèmes polynomiaux structurés : les systèmes bilinéaires et déterminantiels. L'objectif principal est d'étudier les propriétés algébriques de ces systèmes pour en accélérer la résolution et pour borner la complexité des algorithmes de calcul de bases de Gröbner. Ceci passe par l'obtention de nouvelles bornes fines sur la régularité et sur le degré des idéaux associés. Par exemple, on montre que, génériquement, le degré maximal atteint durant le calcul d'une base de Gröbner d'un système affine bilinéaire de K[X,Y] (où X et Y sont deux blocs de variables) est majoré par min(#X,#Y)+1. Ces bornes permettent d'identifier des sous-classes de systèmes bilinéaires et déterminantiels pouvant être résolus en temps polynomial. Afin d'illustrer cette étude, nous montrons comment ces résultats ont été récemment appliqués à la cryptanalyse algébrique de MinRank et de certaines variantes de McEliece. Travail commun avec Jean-Charles Faugère et Mohab Safey El Din.
Prochains exposés
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On the average hardness of SIVP for module lattices of fixed rank
Orateur : Radu Toma - Sorbonne Université
In joint work with Koen de Boer, Aurel Page, and Benjamin Wesolowski, we study the hardness of the approximate Shortest Independent Vectors Problem (SIVP) for random module lattices. We use here a natural notion of randomness as defined originally by Siegel through Haar measures. By proving a reduction, we show it is essentially as hard as the problem for arbitrary instances. While this was[…] -
Attacks and Remedies for Randomness in AI: Cryptanalysis of PHILOX and THREEFRY
Orateur : Yevhen Perehuda - Ruhr-University Bochum
In this work, we address the critical yet understudied question of the security of the most widely deployed pseudorandom number generators (PRNGs) in AI applications. We show that these generators are vulnerable to practical and low-cost attacks. With this in mind, we conduct an extensive survey of randomness usage in current applications to understand the efficiency requirements imposed in[…]-
Cryptography
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Lightweight (AND, XOR) Implementations of Large-Degree S-boxes
Orateur : Marie Bolzer - LORIA
The problem of finding a minimal circuit to implement a given function is one of the oldest in electronics. In cryptography, the focus is on small functions, especially on S-boxes which are classically the only non-linear functions in iterated block ciphers. In this work, we propose new ad-hoc automatic tools to look for lightweight implementations of non-linear functions on up to 5 variables for[…]-
Cryptography
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Symmetrical primitive
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Implementation of cryptographic algorithm
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Algorithms for post-quantum commutative group actions
Orateur : Marc Houben - Inria Bordeaux
At the historical foundation of isogeny-based cryptography lies a scheme known as CRS; a key exchange protocol based on class group actions on elliptic curves. Along with more efficient variants, such as CSIDH, this framework has emerged as a powerful building block for the construction of advanced post-quantum cryptographic primitives. Unfortunately, all protocols in this line of work are[…] -
Endomorphisms via Splittings
Orateur : 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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