Research On Digital Signature Scheme Based On Elliptic Curve

Digital signature is the signature of electronic form. It is the important technique guarantee of electronic business, electronic government affairs and electronic finance system. At the same level of security, the elliptic curve cryptography (ECC) has smaller secret keys and higher signature efficiency than other cryptosystems. Based on the advantage of ECC, the elliptic curve digital signature algorithm (ECDSA) has higher competition ability than other cryptosystems. So the elliptic curve digital signature has an imperative application foreground.The domestic and foreign research present situation is analyzed in this paper, and several kinds of signature schemes based on the ECC are proposed to prompt the signature efficiency and security. Firstly, the present situation of digital signature scheme with the specified receiver is analysed, and a digital signature scheme based on elliptic curve with the specified receiver is proposed, which combines the idea of signature with the specified receiver and the superiority of elliptic curve cryptosystem. Then the security and efficiency of the signature scheme are analysed. Meanwhile having expanded the scheme, a (t, n) threshold signature scheme with the specified receiver is proposed. Secondly, in order to disperse the power of verifier and prevent from abusing the signature, a threshold shared verification signature scheme is proposed. Finally, the Wang et al.'s scheme is pointed out that the scheme is not security if a attacker can solve discrete logarithm problems and the attacker can forge the signature of messages. In order to improve the security, a signature scheme based on two hard problem assumptions is proposed. The security of the scheme is based on the difficulties of simultaneously solving the elliptic curve and quadratic residue. A attacker can't forge the signature of messages even if a attacker can solve theelliptic curve discrete logarithm problems or quadratic residue problem in the scheme.