The Research And Design Of Digital Signature Scheme Based On Elliptic Curves

At present, digital signature and proxy digital signature schemes are almost based on ordinary separate logarithm question. And the security of the schemes couldn't satisfy the request of the people. The schemes based on ECDLP have the higher security. In this paper, it is applied to the domain of digital signature and proxy signature and is unified with special kind of signature schemes. So the schemes have the higher research value.Concentrating on theory, method and application of digital signature and proxy signature , two principal achievements have been obtained in this thesis.First of all, in this paper, an improved digital signature scheme based on elliptic curve was presented. The security and complexity of digital signature was analyzed. This proposed scheme can not only efficiently resist birthday attack, but also improve the security of digital signature. The improved digital signature message recovery scheme may easily realize with low computation. In addition, we examined the improved scheme by means of example. Theprobability of the original digital signature scheme to resist birthday attack is p=1-P_n-1^t/(n-1)^t , but the probalility of the improved digital signature scheme isp=[1-P_n-1^t/(n-1)^t]². Therefore, the security of the improved digital signature scheme isincreased.Second, the security of elliptic curve proxy digital signature scheme by Lin and Peng is analyzed, the original signature scheme can not resist the two forgery attacks. Using anyone of the forgery attacks, original signer can produce a valid proxy signature. On the basis, an improved elliptic curve proxy digital signature scheme concerned is presented in the paper, and this improved scheme can completely resist the two forgery attacks. In addition, the security and complexity of this new scheme is analyzed. In view of this, the improved proxy digital signature can not only resist the two forgery attacks but also retain the full advantages of the proxy digital signature by Lin and Peng.