### Multilinear Maps Using Ideal Lattices without Encodings of Zero

Gu Chunsheng

##### Abstract

Garg, Gentry and Halevi (GGH) described the first candidate multilinear maps using ideal lattices. However, Hu and Jia recently presented an efficient attack for two applications based on the GGH map, multipartite Diffie-Hellman key exchange and an instance of witness encryption using 3-exact cover problem. In this paper, we describe a modification construction of multilinear maps from ideal lattices without encodings of zero by introducing random matrices to avoid the zeroing attack problem. The security of our construction depends upon new hardness assumption, which is seemingly closely related to hardness problems of lattices. Furthermore, we present multipartite Diffie-Hellman key exchange protocol using our construction, and an instance of witness encryption using 3-exact cover problem based on a variant of our construction.

Available format(s)
Publication info
Preprint. MINOR revision.
Keywords
Multilinear mapsIdeal latticesMultipartite Diffie-Hellman key exchangeWitness EncryptionZeroizing attack
Contact author(s)
chunsheng_gu @ 163 com
History
2015-05-26: last of 6 revisions
See all versions
Short URL
https://ia.cr/2015/023

CC BY

BibTeX

@misc{cryptoeprint:2015/023,
author = {Gu Chunsheng},
title = {Multilinear Maps Using Ideal Lattices without Encodings of Zero},
howpublished = {Cryptology ePrint Archive, Paper 2015/023},
year = {2015},
note = {\url{https://eprint.iacr.org/2015/023}},
url = {https://eprint.iacr.org/2015/023}
}

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