Constructing Collective Signature Schemes Using Problem of Finding Roots Modulo

Digital signature schemes in general and representative collective digital schemes, particular, are often built based on the difficulty of discrete logarithm problem finite field, elliptic curve, factor analysis, finding roots modulo large primes or a combination difficult problems mentioned above. In this paper, we use new problem, which is to find with root ground field GF(p) build but chosen p has special structure distinct p=Nt_0 t_1 t_2+1, where N an even number t0, t1, t2 prime numbers equal magnitude, about 80 bits. The characteristics proposed scheme are: i) private key each signer consists 2 components (K_1, K_2), randomly selected, public only one component (Y) calculated by formula Y= K_1^ (w_1) K_2^ (w_2); w_1 = t_0 w_2 t_2; ii) generated set 3 (e, S1, S2). We technique hiding signer's Y, coefficient λ group manager, process forming enhance privacy all members signing collective.