Cryptanalysis of Gu's ideal multilinear map

In March, 2015 Gu Chunsheng proposed a candidate ideal multilinear map [9]. An ideal multilinear map allows to perform as many multiplications as desired, while in κ-multilinear maps like GGH [5] or CLT [3,4] one we can perform at most a predetermined number κ of multiplications. In this note, we show that the extraction Multilinear Computational Diffie-Hellman problem (extMCDH) 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 [9] are not secure either.