The quantum-resistant digital signature schemes based on new hard problems

Abstract

In this paper, we propose a family of quantum-resistant digital signature schemes built on novel hard problems defined over finite fields. These problems are, to the best of current knowledge, computationally intractable and therefore not susceptible to Shor’s quantum algorithm. Based on these problems, we present three concrete signature schemes with standard key-generation, signing, and verification procedures. We prove the correctness of each scheme and analyze its security against secret-key recovery and forgery attacks. Performance comparisons with representative post-quantum candidates illustrate that the proposed schemes achieve competitive key and signature sizes and efficient signing/verification times, making them attractive for practical deployment.