Applications of Multilinear Forms to Cryptography

Dan Boneh; Alice Silverberg

Paper 2002/080

Applications of Multilinear Forms to Cryptography

Dan Boneh and Alice Silverberg

Abstract

We study the problem of finding efficiently computable non-degenerate multilinear maps from $G_1^n$ to $G_2$, where $G_1$ and $G_2$ are groups of the same prime order, and where computing discrete logarithms in $G_1$ is hard. We present several applications to cryptography, explore directions for building such maps, and give some reasons to believe that finding examples with $n>2$ may be difficult.

Note: In the April 2018 revised version, a correction was made to the proof of Corollary 7.6, and more details are now given in that proof.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Minor revision. Topics in Algebraic and Noncommutative Geometry, eds. C. G. Melles et al., Contemporary Mathematics 324, AMS (2003), 71-90
Contact author(s): asilverb @ uci edu
History: 2018-04-30: last of 2 revisions; 2002-06-24: received; See all versions
Short URL: https://ia.cr/2002/080
License: CC BY

BibTeX

@misc{cryptoeprint:2002/080,
      author = {Dan Boneh and Alice Silverberg},
      title = {Applications of Multilinear Forms to Cryptography},
      howpublished = {Cryptology {ePrint} Archive, Paper 2002/080},
      year = {2002},
      url = {https://eprint.iacr.org/2002/080}
}