Cryptology ePrint Archive: Report 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.

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Original Publication (with minor differences): Topics in Algebraic and Noncommutative Geometry, eds. C. G. Melles et al., Contemporary Mathematics 324, AMS (2003), 71-90

Date: received 24 Jun 2002, last revised 30 Apr 2018

Contact author: asilverb at uci edu

Available format(s): PDF | BibTeX Citation

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.

Version: 20180430:223037 (All versions of this report)

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