Paper 2002/080

Applications of Multilinear Forms to Cryptography

Dan Boneh and Alice Silverberg


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.

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Published elsewhere. MINOR revision.Topics in Algebraic and Noncommutative Geometry, eds. C. G. Melles et al., Contemporary Mathematics 324, AMS (2003), 71-90
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asilverb @ uci edu
2018-04-30: last of 2 revisions
2002-06-24: received
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      author = {Dan Boneh and Alice Silverberg},
      title = {Applications of Multilinear Forms to Cryptography},
      howpublished = {Cryptology ePrint Archive, Paper 2002/080},
      year = {2002},
      note = {\url{}},
      url = {}
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