A New Digital Signature Scheme Based on Factoring and Discrete Logarithms

Problem statement: A digital signature scheme allows one to sign an electronic message and later the produced signature can be validated by the owner of the message or by any verifier. Most of the existing digital signature schemes were developed based on a single hard problem like factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. Although these schemes appear secure, one day in a near future they may be exploded if one finds a solution of the single hard problem. Approach: To overcome this problem, in this study, we proposed a new signature scheme based on multiple hard problems namely factoring and discrete logarithms. We combined the two problems into both signing and verifying equations such that the former depends on two secret keys whereas the latter depends on two corresponding public keys. Results: The new scheme was shown to be secure against the most five considering attacks for signature schemes. The efficiency performance of our scheme only requires 1203T_mul+Th time complexity for signature generation and 1202T_mul+Th time complexity for verification generation and this magnitude of complexity is considered minimal for multiple hard problems-like signature schemes. Conclusions: The new signature scheme based on multiple hard problems provides longer and higher security level than that scheme based on one problem. This is because no enemy can solve multiple hard problems simultaneously.