A Multivariate Public-Key Cryptosystem (MPKC) is a public-key cryptosystem where the public map P, or trapdoor one-way function, is given as a set of m polynomial of a small degree d equations over n variables in a finite field F . Usually d = 2, hence the alternate name “Multivariate Quadratic” (MQ). To decrypt, authenticate or sign digitally, a user must, for a given m-tuple z = (z1, . . . , ...