Constructing Collective Signature Schemes Using Problem of Finding Roots Modulo

Abstract

Digital signature schemes are often built based on the difficulty of the discrete logarithm problems, of the problem of factor analysis, of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above. In this paper, we use the new difficult problem, which is to find the w th root in the finite ground field GF(p) to build representative collective signature schemes, but the chosen modulo p has a special structure distinct p = Nt 0 t 1 t 2 + 1, where N is an even number and t 0 , t 1 , t 2 are prime numbers of equal magnitude, about 80 bits. The characteristics of the proposed scheme are: i) The private key of each signer consists of 2 components (K 1 , K 2 ), randomly selected, but the public key has only one component (Y ) calculated by the formula Y = K w 1 1 K w 2 2 ; w 1 = t 0 t 1 and w 2 = t 0 t 2 ; and ii) The generated signature consists of a set of 3 components (e, S 1 , S 2 ). We use the technique of hiding the signer's public key Y, which is the coefficient λ generated by the group nanager, in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.