Digital Signature Scheme Based on the Conjugate Twisted Root Extraction Problem

Abstract

Digital signatures are important primitives for building secure systems and are widely used in internet and electronic commerce for authencation. The most famous digital signature schemes are based on either the intractability of the integer factorization problem or the discrete logarithmic problem over finite fields. With Shor's algorithm on a quantum computer, these problems become tractable. Hence developments of signature schemes which are not based on these problems are crucial for maintaining information security. This paper introduces the conjugate twisted root extraction problem, and proposes a digital signature scheme based on a group of 2 × 2 matrices over N-truncated one variable polynomials. Its security relies on the cojugate twisted e-th root extraction problem. We prove that an adversary cannot forge a signature on a document unless the adversary extracts the e-th root in this group. The performance and other security issues are also discussed.