Digital signature generating/verifying method and system using public key encryption

Abstract

A digital signature generating/verifying method using a public key encryption scheme which ensures high security, reduction in length of the digital signature and independency of the length of the digital signature on that the order of a base point. In generating a digital signature, a first hash value (e) satisfying a condition that e=H(M) is determined for a given message (M) by using a hash function (H), a numerical value (x) is obtained from translation of a random number, a hash value (r) satisfying a condition that r=h(x) is determined by using a hash function (h) whose output value is shorter than that of the first hash function (H), and the digital signature is generated by using the hash values (e) and (r) as determined. For verification of an inputted digital signature, the hash value (e) satisfying the condition that e=H(M) is determined, and for a numerical value (x) obtained from arithmetic operation of a public key (Q), a base point (P) and the inputted digital signature (r, s), a hash value (r′) satisfying a condition that r′=h(x) on the basis of the hash value (re), the digital signature (r, s), the base point (P) and the public key (Q) by using a hash function (h) whose output value is shorter than that of the first hash function (H). The hash value (r′) is then compared with a tally (r) of the inputted digital signature to thereby verify the inputted digital signature.