Paper 2015/1037

Cryptanalysis of GGH15 Multilinear Maps

Jean-Sebastien Coron and Moon Sung Lee and Tancrede Lepoint and Mehdi Tibouchi

Abstract

We describe a cryptanalysis of the GGH15 multilinear maps. Our attack breaks in polynomial time the multipartite key-agreement protocol by generating an equivalent user private key. Our attack only applies to GGH15 without safeguards; for GGH15 with safeguards we only have a partial cryptanalysis that can recover any ratio of secret exponents. We also describe attacks against variants of the GGH13 multilinear maps proposed by Halevi (ePrint 2015/866) aiming at supporting graph-induced constraints, as in GGH15.

Note: We describe an extended attack that also breaks GGH15 with the safeguards.