Method for identification based on bilinear diffie-hellman problem

A method for identification, comprising the steps of:

• (a) generating system parameters G1, G2, P and ê and storing the system parameters in a memory by a system administrator, wherein G1 and G2 are cyclic groups of order m, P is a generator on the cyclic group G1, ê is a bilinear map defined as
• ê:
• G1×G1G2;
• (b) generating a private key <a1, a2, . . . an> and a public key v and storing the public key v in the memory by a prover or the system administrator, wherein a1, a2, . . . an are randomly chosen in Zm* where Zm* is a multiplicative group of order m;
• (c) generating random numbers r1, r2, . . . rn∈Zm* for obtaining an evidence (x, Q) and sending the evidence (x, Q) to a verifier by the prover;
• (d) receiving the evidence (x, Q), selecting a randomly selected number a ω□Zm* to obtain a query R, storing the evidence (x, Q) and the randomly selected number ω in the memory and sending the query R to the prover by the verifier;
• (e) receiving the query R, computing a temporary value S to obtain a response Y and sending the response Y to the verifier by the prover;
• and
• (f) determining a legitimacy of the prover by employing the system parameters G1, G2, P and ê, the public key v, the evidence (x, Q) and the randomly selected number ω by the verifier.