Abstract
The MQ problem, which consists in solving a system of multivariate quadratic polynomials over finite field, has attracted the attention of researchers for the development of public-key cryptosystems because (1) it’s NP-complete, (2) there is no known polynomial-time algorithm for it’s solution, even in the quantum computational model, and (3) enable cryptographic primitives of practical interest. In 2011, Sakumoto, Shirai and Hiwatari presented two new zero-knowledge identification protocols based exclusively on the MQ problem. The 3-pass identification protocol of Sakumoto et al. has knowledge error 2/3. In this paper, we propose an improvement that reduces the knowledge error to 1/2. The result is a protocol that reduces the total communication needed and requires a smaller number of rounds for the same security level.
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