Research On Digital Signature Based On Elliptic Curve

With the rapid development of information technology and its applications in various fields, information security becomes increasingly important. Since the information is transmitted, saved, processed and other processes in open communication networks, information is vulnerable to various attacks. Digital signature has played a very important role to better identify the signer's identity and information to ensure the accuracy of information sources. Compared with other public-key cryptosystem, ECC has many advantages. It has small computational load, tiny key size, short length, a small amount of the overall algorithm and the computing speed and other advantages, therefore, elliptic curve cryptography combined with the digital signature has broad application prospects.This paper analyzes the background and significance of elliptic curve digital signature, the current researches of elliptic curve cryptosystem, public key cryptosystem, and elliptic curve cryptography based on good understandings of basic theories, wide readings in literature and in-depth studies. Then three elliptic curve digital signature schemes of applicable in different fields are proposed. Firstly, this article analyzes the current situation of authentication cryptography (IBE cryptography), combines cryptographic authentication elliptic curve cryptography, and proposes an elliptic curve digital signature with the function of authentication program(which is named the Scheme 1). This scheme not only owns the features of s forward security and public verifiability but also has other security features.Secondly, in order to meet the requirement that more than one person wants to sign a message at the same time, this article decentralizes the signers' powers to prevent their abuse of the powers, and proposes an elliptic curve (t, n) threshold digital signature scheme (which is also named Scheme 2). Since this scheme doesn't need a trusted center and can release phases of the signatures without the secret communications, it has high security. Then, this article proposes a digital signature scheme based on elliptic curve discrete logarithm problem and the discrete logarithm problem in the finite field on the digital signature scheme (which is also named Scheme 3)., Even in the cases that the elliptic curve discrete logarithm problem or the discrete logarithm problem in the finite field are cracked, the attacker can't pass the validation through its false message signature. Finally, this article analyzes the safety and efficiency of the three signature schemes and gets the result that the three signature schemes have good security and efficiency.