Description
Les fonctions booléennes sur l'espace $F_2^m$ sont non seulement importantes dans la théorie de codes correcteurs d'erreurs, mais également en cryptographie. Dans ces deux cas, la non-linéarité de ces fonctions est un concept essentiel. Carlet, et Olejar et Stanek ont donné une borne inférieure asymptotique pour la non-linéarité de la plupart d'entre elles. Dans cet exposé, j'améliore cette borne et j'obtiens une limite exacte pour la non-linéarité de la plupart d'entre elles.<br/> Un fait intéressant est le lien de la non-linéarité avec le problème des polynômes réels avec des coefficients aléatoires, qui a été étudié intensivement (cf. les papiers de R. Salem et A. Zygmund, ou de J-P. Kahane et G. Halacz). De plus, en transposant un travail sur les normes dans $L_4$ des polynômes aléatoires, nous étudierons également la "somme des carrés" des fonctions booléennes, qui est lié au critère de propagation pour les fonctions booléennes. Voir les papiers ``Sur la non-linéarité des fonctions booléennes'' dans arXiv, référence: math.NT/0306395 publié dans Acta Arithmetica, vol 115, (2004), 1-22 et ``Asymptotic nonlinearity of Boolean functions'' sur http://iml.univ-mrs.fr/editions/preprint2003/preprint2003.html
Next sessions
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Dual attacks in code-based (and lattice-based) cryptography
Speaker : Charles Meyer-Hilfiger - Inria Rennes
The hardness of the decoding problem and its generalization, the learning with errors problem, are respectively at the heart of the security of the Post-Quantum code-based scheme HQC and the lattice-based scheme Kyber. Both schemes are to be/now NIST standards. These problems have been actively studied for decades, and the complexity of the state-of-the-art algorithms to solve them is crucially[…]-
Cryptography
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Design of fast AES-based Universal Hash Functions and MACs
Speaker : 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
Speaker : 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
Speaker : 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[…]