Digital Signature Scheme Based on a New Hard Problem

Factorizing composite number n = qr, where q and r are two large primes, and finding discrete logarithm modulo large prime number p are two dicult computational problems which are usually put into the base of dierent digital signature schemes (DSSes). This paper introduces a new hard computational problem that consists in finding the kth roots modulo large prime p = Nk 2 + 1, where N is an even number and k is a prime with the length jkj ‚ 160. Diculty of the last problem is estimated as O( p k). It is proposed a new DSS with the public key y = x k mod p, where x is the private key. The signature corresponding to some message M represents a pair of the jpjbit numbers S and R calculated as follows: R = t k mod p and S = tx f(R;M) mod p, where f(R;M) is a compression function. The verification equation is S k mod p = y f(R;M) R mod p. The