Paper 2013/183

Practical Multilinear Maps over the Integers

Jean-Sebastien Coron, Tancrede Lepoint, and Mehdi Tibouchi


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 about $25$ seconds per party.

Note: An extended abstract will appear at Crypto 2013. This is the full version.

Available format(s)
Public-key cryptography
Publication info
A minor revision of an IACR publication in CRYPTO 2013
Contact author(s)
jscoron @ tranef com
2017-07-07: last of 4 revisions
2013-04-01: received
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      author = {Jean-Sebastien Coron and Tancrede Lepoint and Mehdi Tibouchi},
      title = {Practical Multilinear Maps over the Integers},
      howpublished = {Cryptology ePrint Archive, Paper 2013/183},
      year = {2013},
      note = {\url{}},
      url = {}
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