Novel forgery mechanisms in multivariate signature schemes

Multivariate cryptography is listed among the promising candidates for post-quantum cryptography primitives. Its hard problem depends on the difficulty of solving m multivariate quadratic equations in n variables over a finite field, hence the name Multivariate Quadratic Problem (MQP). In this paper, we present three multivariate digital signature forgery mechanisms by a rogue service provider. We also lay out techniques to identify two of such mechanisms. As for a potential signature forgery mechanism via Greatest Common Divisors of evaluated polynomials in the system, it is still an open question on how to detect it. This third strategy seems to inherit the NP-hard difficulties of a random MQP in totality.

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