Description
After the publication of Shor's algorithm, it became evident the most popular public-key cryptographic systems that rely on the integer factorization problem or on the discrete logarithm problem would be easily solvable using large enough quantum computers (if such quantum computers are ever built). That triggered a vivid interest in the research of cryptographic algorithms (mostly public-key cryptographic systems) that are resistant to quantum computers. There are several approaches for designing post-quantum public key algorithms. The main candidates Hash-Based signatures, are Multivariate cryptosystems, Code-based cryptosystems and Lattice-based cryptosystems.<br/> Although Multivariate, Code-based and Lattice-based Cryptosystems rely on different algebraic problems, the goal of this talk is to show that Gr\"obner bases, via algebraic attacks, is a common tool which is underlying the security of these post-quantum public-key algorithms. As such, Gröbner bases is then a fundamental tool to design and analyze public-key schemes in the post-quantum era. In the talk, we will describe two applications. First, an efficient attack against a quantum money scheme proposed at STOC'12 whose security is based on a variant of the Isomorphism of Polynomial. This is [1] a joint work with Marta Conde, and Jean-Charles Faugère. Secondly, we will also show that Gröbner Bases can be used to analyze the security of the Learning With Errors (LWE) problem. Arora and Ge proved few years ago that LWE can be solved by linearizing a system of algebraic equations. We will describe a refined complexity analysis for solving Arora-Ge-style systems of non-linear equations with Gröbner bases for LWE and a variant of LWE BinaryError-LWE. This is [2] a joint work with Martin Albrecht, Carlos Cid, Jean-Charles Faugère, and Robert Fitzpatrick.<br/> [1] Marta Conde Pena, Jean-Charles Faugère, Ludovic Perret. Algebraic Cryptanalysis of a Quantum Money Scheme The Noise-Free Case. PKC'15. [2] Martin R. Albrecht, Carlos Cid, Jean-Charles Faugère, Robert Fitzpatrick, Ludovic Perret. Algebraic Algorithms for LWE Problems. IACR Cryptology ePrint Archive 2014: 1018 (2014).
Prochains exposés
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La crypto-graphie et les crypto-monnaies
Orateur : Daniel Augot - INRIA Saclay—Île-de-France
De nos jours, la requête «crypto» dans un moteur de recherche renvoieaux cryptomonnaies. Mais «crypto means crypto», et on peut se poser laquestion des liens pertinents entre les deux domaines. D'un coté, le monde des cryptomonnaies et de la technologiesous-jacente s'est développé et évolue encore en dehors du mondeacadémique. Il faut suivre d'un coté des posts de blog, des fils dediscussion X[…] -
SoK: Security of the Ascon Modes
Orateur : Charlotte Lefevre - Radboud University
The Ascon authenticated encryption scheme and hash function of Dobraunig et al (Journal of Cryptology 2021) were recently selected as winner of the NIST lightweight cryptography competition. The mode underlying Ascon authenticated encryption (Ascon-AE) resembles ideas of SpongeWrap, but not quite, and various works have investigated the generic security of Ascon-AE, all covering different attack[…] -
Comprehensive Modelling of Power Noise via Gaussian Processes with Applications to True Random Number Generators
Orateur : Maciej Skorski - Laboratoire Hubert Curien
The talk examines power noise modelling through Gaussian Processes for secure True Random Number Generators. While revisiting one-sided fractional Brownian motion, we obtain novel contributions by quantifying posterior uncertainty in exact analytical form, establishing quasi-stationary properties, and developing rigorous time-frequency analysis. These results are applied to model oscillator[…]-
Cryptography
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TRNG
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CryptoVerif: a computationally-sound security protocol verifier
Orateur : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
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