A multivariate convertible undeniable signature scheme

Abstract

Digital signature is an important cryptographic primitive which can be universally verified. However, this universal verifiability can be ominous in case of e-auction, e-voting, and e-cash, where the verifiability must be restricted. Undeniable signature is a type of digital signature that is mainly used to achieve the goal of access control. In this article, we propose the first multivariate-based quantum secure undeniable signature scheme, which can also be converted into an ordinary signature. The security of this scheme relies on the hardness of multivariate quadratic problem which is computationally hard to solve when defined over any finite field. We deploy Monteiro et al.'s improvement on Sakumoto et al.'s zero-knowledge protocol for the verification process. We discuss the security properties of undeniable signature, viz., completeness, soundness, unforgeability, invisibility, and non-impersonation. Additionally, we show that the proposed undeniable signature has the smallest signature and key sizes among all the existing quantum-resistant undeniable signatures.