Description
Pseudorandom functions (PRFs) are one of the most fundamental primitives in cryptography. In this work, we provide a new algebraic framework which encompasses many of the existing algebraic PRFs, including the ones by Naor and Reingold (FOCS'97), by Lewko and Waters (CCS'09), and by Boneh, Montgomery, and Raghunathan (CCS'10), as well as the related-key-secure PRFs by Bellare and Cash (Crypto'10) and by Abdalla \etal (Crypto'14). To achieve this goal, we introduce two versions of our framework. The first, termed linearly independent polynomial security, states that the values $(g^{P_1(\vec{a})}, \ldots, g^{P_q(\vec{a})})$ are indistinguishable from a random tuple of the same size, when $P_1, \ldots, P_q$ are linearly independent multivariate polynomials of the secret key vector $\vec{a}$. The second, which is a natural generalization of the first framework, additionally deals with constructions based on the decision linear and matrix Diffie-Hellman assumptions. In addition to unifying and simplifying proofs for existing schemes, our new framework also yields several new results, such as related-key security with respect to arbitrary permutations of polynomials. All our constructions are in the standard model and do not require the existence of multilinear maps.
Prochains exposés
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Présentations des nouveaux doctorants Capsule
Orateur : 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
Orateur : 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
Orateur : 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
Orateur : 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[…]