Paper 2015/867

Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security

Michel Abdalla, 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.

Metadata
Available format(s)
PDF
Publication info
A major revision of an IACR publication in ASIACRYPT 2015
DOI
10.1007/978-3-662-48797-6_5
Keywords
Pseudorandom functionsMultilinear PRFsAggregate PRFs
Contact author(s)
fabrice benhamouda @ ens fr
History
2015-11-25: revised
2015-09-08: received
See all versions
Short URL
https://ia.cr/2015/867
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/867,
      author = {Michel Abdalla and Fabrice Benhamouda and Alain Passelègue},
      title = {Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security},
      howpublished = {Cryptology ePrint Archive, Paper 2015/867},
      year = {2015},
      doi = {10.1007/978-3-662-48797-6_5},
      note = {\url{https://eprint.iacr.org/2015/867}},
      url = {https://eprint.iacr.org/2015/867}
}
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