Cryptology ePrint Archive: Report 2015/867

Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security

Michel Abdalla and Fabrice Benhamouda and Alain Passelègue

Abstract: Since its introduction, pseudorandom functions (PRFs) have become one of the main building blocks of cryptographic protocols. In this work, we revisit two recent extensions of standard PRFs, namely multilinear and aggregate PRFs, and provide several new results for these primitives. In the case of aggregate PRFs, one of our main results is a proof of security for the Naor-Reingold PRF with respect to read-once boolean aggregate queries under the standard Decision Diffie-Hellman problem, which was an open problem. In the case of multilinear PRFs, one of our main contributions is the construction of new multilinear PRFs achieving indistinguishability from random symmetric and skew-symmetric multilinear functions, which was also left as an open problem. In order to achieve these results, our main technical tool is a simple and natural generalization of the recent linear independent polynomial framework for PRFs proposed by Abdalla, Benhamouda, and Passelègue in Crypto 2015, that can handle larger classes of PRF constructions. In addition to simplifying and unifying proofs for multilinear and aggregate PRFs, our new framework also yields new constructions which are secure under weaker assumptions, such as the decisional $k$-linear assumption.

Category / Keywords: Pseudorandom functions, Multilinear PRFs, Aggregate PRFs

Original Publication (with major differences): IACR-ASIACRYPT-2015
DOI: 10.1007/978-3-662-48797-6_5

Date: received 7 Sep 2015, last revised 25 Nov 2015

Contact author: fabrice benhamouda at ens fr

Available format(s): PDF | BibTeX Citation

Version: 20151125:162858 (All versions of this report)

Short URL: ia.cr/2015/867