Research On Digital Signatures Based On Conic Curves Over Ring Z_n

Conic cuvre cryptography was introduced by Prof.Cao Zhen-fu in1998.Compared with ECC, plaintext embedding,inverse operation,computing element order and point in curves are facility.when the standard binary systym was adopted to compute the integral multiple of an element of a group ,the time can be saved approximately by 1/4.The main research results in this paper include:1. By attack to the digital signature scheme based on the conic curve over Zn proposed by Yang etc, secret key can be gained by public key and the signature .So the signature scheme is not security. A new digital signature scheme is proposed by choosing the parameter again. It can resist the attack in the paper and make comprehensively use of the difficulties in the factorizing large integer and computing discrete logarithm on finite group, increasing the security of it.2. Based on the new scheme broadcasting and sequential multi-signature digital scheme are structured,the former has the advantage to obtain the same signature parameter without exchanging data for many times among signers;the latter has the advantage of the size of the multi-signature not to be dependent on the number of the signers.