International Conference on the Theory and Application of Cryptology and Information Security

Advances in Cryptology -- ASIACRYPT 2015 pp 103-120

Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security

  • Michel Abdalla
  • Fabrice Benhamouda
  • Alain Passelègue
Conference paper

DOI: 10.1007/978-3-662-48797-6_5

Volume 9452 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Abdalla M., Benhamouda F., Passelègue A. (2015) Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security. In: Iwata T., Cheon J. (eds) Advances in Cryptology -- ASIACRYPT 2015. Lecture Notes in Computer Science, vol 9452. Springer, Berlin, Heidelberg

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.

Keywords

Pseudorandom functions Multilinear PRFs Aggregate PRFs 

Copyright information

© International Association for Cryptologc Research 2015

Authors and Affiliations

  • Michel Abdalla
    • 1
  • Fabrice Benhamouda
    • 1
  • Alain Passelègue
    • 1
  1. 1.ENS, CNRS, INRIA, and PSLParisFrance