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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Random lattices that are modules over the ring of integers
Orateur : Nihar Gargava - Institut de Mathématiques d'Orsay
We investigate the average number of lattice points within a ball where the lattice is chosen at random from the set of unit determinant ideal or modules lattices of some cyclotomic number field. The goal is to consider the space of such lattice as a probabilistic space and then study the distribution of lattice point counts. This is inspired by the connections of this problem to lattice-based[…]-
Cryptography
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Schéma de signature à clé publique : Frobénius-UOV
Orateur : Gilles Macario-Rat - Orange
L'exposé présente un schéma de signature à clé publique post-quantique inspiré du schéma UOV et introduisant un nouvel outil : les formes de Frobénius. L'accent est mis sur le rôle et les propriétés des formes de Frobénius dans ce nouveau schéma : la simplicité de description, la facilité de mise en oeuvre et le gain inédit sur les tailles de signature et de clé qui bat RSA-2048 au niveau de[…] -
Yoyo tricks with a BEANIE
Orateur : Xavier Bonnetain - Inria
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Cryptography
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Symmetrical primitive
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