240-bit collective signature protocol in a non-cyclic finite group

Abstract

The article describes a collective digital signature protocol based on the difficulty of the discrete logarithm problem modulo a composite number that is a product of two strong primes having the 2:1 size ratio. The usage of difficult problems provide signature protocol with security improvement, because the probability to break the protocol has been reduced significant. This can be achieved due to the appearance of breakthrough solutions in the area of the factoring problem and the discrete logarithm modulo a prime problem. One of the features of the protocol is using the non-cyclic finite group. After selecting appropriate parameters which provide 80-bit security, the size of the proposed collectively signature is 240 bits and is not dependent on the number of signers.