# An Algebraic Framework for Pseudorandom Functions and Applications to Related-Key Security

3 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : In this work, we provide a new algebraic framework for pseudorandom functions which encompasses many of the existing algebraic constructions, 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 pseudorandom functions by Bellare and Cash (Crypto'10) and by Abdalla et al. (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 framework also yields new results, such as related-key security with respect to arbitrary permutations of polynomials. Our constructions are in the standard model and do not require the existence of multilinear maps.
Document type :
Reports

https://hal.inria.fr/hal-01175788
Contributor : Michel Abdalla Connect in order to contact the contributor
Submitted on : Monday, July 13, 2015 - 1:31:57 AM
Last modification on : Thursday, March 17, 2022 - 10:08:37 AM

### Identifiers

• HAL Id : hal-01175788, version 1

### Citation

Michel Abdalla, Fabrice Benhamouda, Alain Passelègue. An Algebraic Framework for Pseudorandom Functions and Applications to Related-Key Security. [Technical Report] Cryptology ePrint Archive: Report 2015/554, IACR. 2015. ⟨hal-01175788⟩

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