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The authors study the problem of finding efficiently computable non-degenerate multilinear maps from Gn 1 to G2, where G1 and G2 are groups of the same prime order, and where computing discrete logarithms in G1 is hard. They 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. This paper studies some questions in linear algebra and cryptography. Interesting problems in cryptography have recently been solved using Weil or Tate pairings on supersingular elliptic curves, or more generally on supersingular abelian varieties. These applications include one-round three-party key exchange , identity-based encryption , and short digital signatures.
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