The Design And Fast Implementation Of Signature Scheme Based On The Elliptic Curve

In the open Internet environment, the digital signature plays an important role in establishing safety credible communication environment. The signature scheme based on the elliptic curve is an important branch of digital signature scheme. For the study of elliptic curve cryptosystems, we summarize the results of previous research and carry out the following research in this paper.Firstly, we study the forward secure signature schemes. As we all know, even if the attackers have already been given a signature key by invading a system in t time, he still can't forge signatures before the t time. In other words, the forward secure digital signature provides an assurance that any signatures in the previous periods are still valid before the key compromises. In this paper, after analyzing the existing security problems of some schemes, we propose a forward secure signature scheme based on elliptic curve. And we analyze the security and efficiency of our scheme.Secondly, we study the identity based ring signature scheme. In a ring signature, not only the signature verifier needs to verify the validity of the certificate of all members of the ring, but also the signer needs to verify the other members of the ring. A large number of public key transport and validation greatly influence the efficiency of the scheme. ID-based ring signature solves the distribution and management of certificate for the traditional public key systems infrastructure. In this paper, we propose a new identity based ring signature scheme with multiple attributes. The definition and security requirements of identity based ring signature scheme with multiple attributes are presented. The proposed scheme can be proved to be non-forgeability, anonymity, strongness property, source hiding, non – transferable, weak linked property and signer-admission property.Thirdly, we propose a new signature scheme based on BLS in this paper. The scheme has a tight security reduction to CDH. Since the hardness of the CDH problem is widely believed to be closely related to the hardness of the DL problem. So it provides a guarantee for the security of scheme. In addition, the scheme improves the computing speed of the signature by pre-computing.Finally, in order to improve the efficiency of elliptic curve cryptography implementation, we study the scalar multiplication in the paper. Firstly, the ZLMDR algorithm is proposed to improve the DR algorithm. The improved algorithm compared to the original algorithm on hamming weight and the bit string length is minimum. Then, this paper combines the ZLMDR algorithm with the sliding window method and proposes a more efficient ZLMDR- Sliding window algorithm than the traditional NAF- Sliding window algorithm. And we combine the ZLMDR algorithm and the Shamir algorithm and propose a more efficient ZLMDR-Shamir algorithm than the traditional NAF-Shamir algorithm. At the same time, we improve the MOF algorithm and propose the ZLMOF algorithm. Then we combine the ZLMOF algorithm with the sliding window method and propose a more efficient ZLMOF-Sliding window algorithm than the traditional NAF-Sliding window algorithm. Finally, we combine the ZLMDR algorithm with the Shamir algorithm to propose a more efficient ZLMDR-Shamir algorithm than the traditional NAF-Shamir algorithm.