Advances in Cryptology – CRYPTO 2013

Volume 8042 of the series Lecture Notes in Computer Science pp 476-493

Practical Multilinear Maps over the Integers

  • Jean-Sébastien CoronAffiliated withUniversity of Luxembourg
  • , Tancrède LepointAffiliated withCryptoExpertsÉcole Normale Supérieure
  • , Mehdi TibouchiAffiliated withNTT Secure Platform Laboratories

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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.