Paper 2015/759

Cryptanalysis of Gu's ideal multilinear map

Alice Pellet-Mary and Damien Stehle

Abstract

In March, 2015 Gu Chunsheng proposed a candidate ideal multilinear map [eprint 2015/269]. An ideal multilinear map allows to perform as many multiplications as desired, while in k-multilinear maps like GGH [EC 2013] or CLT [CR2013, CR2015] one we canperform at most a predetermined number k of multiplications. In this note, we show that the extraction Multilinear Computational Diffie-Hellman problem (ext-MCDH) associated to Gu's map can be solved in polynomial-time: this candidate ideal multilinear map is insecure. We also give intuition on why we think that the two other ideal multilinear maps proposed by Gu in [eprint 2015/269] are not secure either.