Efficient identity-based ring signature scheme with anonymity and system thereof

An identity-based ring signature authentication method comprising:

• generating, by a private key generator, a secret key St by using public parameters (q, G1, G2, e, P, Ppub, g, H1, H2) and identity IDt received from a tth user terminal and transmitting the generated secret key St to the tth user terminal;
• setting, by the terminal, (n−1) values (V1, V2, . . . , Vt−1, Vt+1, . . . , Vn) by choosing an arbitrary random value and generating a first digital signature U on a message m by using the public parameters, the secret key St, a set (L={ID1, . . . , IDn}) of identities of ring members including the identity IDt of a tth user and the (n−1) values;
• generating a digital signature Vt of the tth user by using the first digital signature U, the message m, the set L and the secret key St;
• generating, a plurality of second digital signature including the (n−1) values used to generate the first digital signature U and the digital signature Vt of the tth user;
• generating, a ring signature τ including the first digital signature U and the plurality of second digital signature;
• and
• receiving, by an authentication server, the set L, the message m and the ring signature τ on the message m from the tth user terminal and verifying validity of the received ring signature τ by using the public parameter,
• wherein the public parameters include an elliptic curve group G1 and a multiplicative subgroup G2 of a finite field, each of the G1 and G2 denotes a group of prime order q, a bilinear pairing e, a generator P of the G1, a public key Ppub (=s·P) which is a scalar multiplication of the generator P and a master secret key s of the private key generator, a result (g=e(P, P)) of the bilinear pairing e taking as an input the generator P, a first hash function H1 and a second hash function H2.