Cryptographic identification and digital signature method using efficient elliptic curve

A method of identifying user, generating digital signature, and verifying digital signature by selecting a modulus p in the form of p=(2^dk-2^ck-1)/r, p=(2^dk-2^(d-1)k+2^(d-2)k- . . . -2^k+1)/r, p=(2^dk-2^ck-1)/r, p=(2^dk-2^ck+1)/r, and p=(2^4k-2^3k+2^2k+1)/r, selecting an elliptic curve E and an order q; selecting a basepoint G; generating a private key w; generating a public key W=wG; distributing p, E, q, G, and W to at least a prover, a verifier, and a signer; generating the prover's private key w_p and public key W_p=w_pG; retrieving the prover's public key W_p; generating a private integer k_p; combining k_p and G to form K using p; sending K to the verifier; sending a challenge integer c to the prover; combining c, k_p, and w_p to form a response integer v; sending v to the verifier; combining cG, K, and W_p using p and checking to see if the combination is equal to vG. If not so, stop. Otherwise, generating, by the signer, the signer's private key w_s; generating a private integer k_s; combining k_s and G to form K using p; combining K and a message M to form an integer h; combining h, k_s, and w_s to form an integer s; sending M and (K,s) as a digital signature of M; retrieving W_p; receiving M and (K,s); combining K and M to form an integer h; and combining h, K, and W_p using p and checking to see if the combination is equal to sG. If so, the digital signature is verified.