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).
Next sessions
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Présentations des nouveaux doctorants Capsule
Speaker : Alisée Lafontaine et Mathias Boucher - INRIA Rennes
2 nouveaux doctorants arrivent dans l'équipe Capsule et présenteront leurs thématiques de recherche. Alisée Lafontaine, encadrée par André Schrottenloher, présentera son stage de M2: "Quantum rebound attacks on double-block length hash functions" Mathias Boucher, encadré par Yixin Shen, parlera des algorithmes quantiques et des réseaux euclidiens. -
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[…] -
CryptoVerif: a computationally-sound security protocol verifier
Speaker : 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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