Practical Multilinear Maps over the Integers

  • Jean-Sébastien Coron
  • Tancrède Lepoint
  • Mehdi Tibouchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8042)

Abstract

Extending bilinear elliptic curve pairings to multilinear maps is a long-standing open problem. The first plausible construction of such multilinear maps has recently been described by Garg, Gentry and Halevi, based on ideal lattices. In this paper we describe a different construction that works over the integers instead of ideal lattices, similar to the DGHV fully homomorphic encryption scheme. We also describe a different technique for proving the full randomization of encodings: instead of Gaussian linear sums, we apply the classical leftover hash lemma over a quotient lattice. We show that our construction is relatively practical: for reasonable security parameters a one-round 7-party Diffie-Hellman key exchange requires less than 40 seconds per party. Moreover, in contrast with previous work, multilinear analogues of useful, base group assumptions like DLIN appear to hold in our setting.

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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Jean-Sébastien Coron
    • 1
  • Tancrède Lepoint
    • 2
    • 3
  • Mehdi Tibouchi
    • 4
  1. 1.University of LuxembourgLuxembourg
  2. 2.CryptoExpertsFrance
  3. 3.École Normale SupérieureFrance
  4. 4.NTT Secure Platform LaboratoriesJapan

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