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

Conference paper

DOI: 10.1007/978-3-662-47989-6_19

Volume 9215 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Abdalla M., Benhamouda F., Passelègue A. (2015) An Algebraic Framework for Pseudorandom Functions and Applications to Related-Key Security. In: Gennaro R., Robshaw M. (eds) Advances in Cryptology -- CRYPTO 2015. CRYPTO 2015. Lecture Notes in Computer Science, vol 9215. Springer, Berlin, Heidelberg


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.

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.ENS, CNRS, INRIA, and PSLÉcole normale supérieureParis Cedex 05France