Cryptographic identification and digital signature method using efficient elliptic curve

Abstract

A method of identifying user, generating digital signature, and verifying digital signature by selecting a modulus p in the form of p=(2−2−1)/r, p=(2−22− . . . −2+1)/r, p=(2−2−1)/r, p=(2−2+1)/r, and p=(2−22+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 wand public key W=wG; retrieving the prover's public key W; generating a private integer k; combining kand G to form K using p; sending K to the verifier; sending a challenge integer c to the prover; combining c, k, and wto form a response integer v; sending v to the verifier; combining cG, K, and Wusing 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; generating a private integer k; combining kand G to form K using p; combining K and a message M to form an integer h; combining h, k, and wto form an integer s; sending M and (K,s) as a digital signature of M; retrieving W; receiving M and (K,s); combining K and M to form an integer h; and combining h, K, and Wusing p and checking to see if the combination is equal to sG. If so, the digital signature is verified.