Research And Application Of Elliptic Curve Digital Signature

Nowadays, networks technique is applied more and more, people pay more attention to the security of the information in networks. Digital signature is one of the technic that ensure information safety. It plays an important factor in protecting integrality, unforgeability, undeniability and veriiiability of the information. Elliptic curve cryptography is the most secure public key cryptography, which is based on the intractability of the elliptic curve discrete logarithm problem (ECDLP). And it has become a major subject of the cryptography at home and broad. In this paper, the general signature, proxy signature and threshold signature scheme are discussed in detail, then a digital signature system for LAN is developed.Firstly, the basic knowlodge of the elliptic curve cryptography is introduced. Then, general computation of the points on the elliptic curve and the ways to implement them are discussed. The capability to withstand the attacks to the ECDLP is analyzed, and then a security criterion is proposed. The security criterion can prevent the elliptic curve from being attacked. The algorithms to generate a secure elliptic curve are presented in detail. To make the signature functions suitable for variable conditions, a threshold signature and a proxy signature scheme are designed based on ECDLP.Based on the theory above, an application programme is developed. The algorithm module can be used to implement the algorithms based on elliptic curve. And an elliptic curve digital signature system for LAN based on the module is developed. The general signature scheme, the threshold signature scheme and the proxy signature scheme in this paper have high security, they are capable to withstand types of attacks, conspiracy attack and forge attack included. The programme developed in this paper has some characteristics including expandability, divisibility, independence, portability stability and length adjustability. The elliptic curve digital signature system in this paper has characteristics of high security, handling facility and function diversification.