Description
Dans cet exposé je présenterai deux méthodes différentes pour la construction des équations des courbes non-hyperelliptiques de genre $3$ provenant des facteurs Q-simples A_f principalement polarisés de J(X_0(N)), où X_0(N) repésente la courbe modulaire associée à Gamma_0(N)$. La première méthode, qui ne s'applique qu'aux courbes modulaires, est basée sur le calcul du morphisme canonique des courbes non hyperelliptiques de genre 3 en utilisant des relations algébriques entre éléments d'une base integrale de l'espace S_2 (A_f) des cusp forms. Ces courbes admettent tous des modèles définis sur Q avec des petits coefficients. L'autre méthode est basée sur la résolution explicite du problème de Torelli en dimension 3 : A partir d'une variété abélienne A=C^3 /(Z^3+W Z^3) donnée par sa matrice de périodes W dans H_3 et provenant de la Jacobienne d'une courbe non hyperelliptique de genre 3, trouver l'équation d'un bon modèle de cette courbe (à isomorphisme près).
Next sessions
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On the average hardness of SIVP for module lattices of fixed rank
Speaker : 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
Speaker : 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
Speaker : 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
Speaker : 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
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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