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Paper 2013/183

Practical Multilinear Maps over the Integers

Jean-Sebastien Coron and Tancrede Lepoint and Mehdi Tibouchi

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 about $25$ seconds per party.

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

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown status
Contact author(s)
jscoron @ tranef com
History
2017-07-07: last of 4 revisions
2013-04-01: received
See all versions
Short URL
https://ia.cr/2013/183
License
Creative Commons Attribution
CC BY
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