Public-Key Identification Schemes Based on Multivariate Cubic Polynomials

Solving a system of multivariate polynomials over a finite field is a promising problem in cryptography. Recently, Sakumoto et al. proposed public-key identification schemes based on the quadratic version of the problem, which is called the MQ problem. However, it is still an open question whether or not it is able to build efficient constructions of public-key identification based on multivariate polynomials of degree greater than two. In this paper, we tackle the cubic case of this question and construct public-key identification schemes based on the cubic version of the problem, which is called the MC problem. The MQ problem is a special case of the MC problem. Our schemes consist of a protocol which is zero-knowledge argument of knowledge for the MC problem under the assumption of the existence of a non-interactive commitment scheme. For a practical parameter choice, the efficiency of our scheme is highly comparable to that of the schemes based on the MQ problem. Furthermore, the parallel version of our scheme also achieves the security under active attack with some additional cost.

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