The Study Of Digital Signature Based On Elliptic Curve Cryptography

Digital signature is one of the most important technologies in internet. It not only provides integrity authentication of message, identity authentication, but also non-repudiation, unforgeability. Therefore, digital signature greatly ensures the security of systems, such as electric transaction, electric currency, electric purchase, electric publication and intelligent property protect in internet.A high efficiency digital signature scheme adapt to higher real-time needs has been presented in this paper. It based on elliptic curve cryptograph (ECC), which has the most security intense in public key infrastructure (PKI). Combined with the two well-known schemes ECDSA and EC-KCDSA, the design of the presented scheme emphasis on improving computation efficiency with the equivalent security level as the two scheme. Accordingly, its algorithm has two improvements. The first is that no time waste inverse operation through all the process, from key producing, signature calculation to verifying calculation. The second is that use the hamming weight of HASH code of a message instead of HASH code itself to participate in the signature and verifying calculation. The theory analysis as well as experiment result indicate that the new signature scheme cost less time than the two schemes under the premise of equivalent security.Besides, elliptic curve encode has been studied in this paper. Some former researches on this topic embed a plaintext into x-coordinate of points in elliptic curve, but it will occur a plaintext corresponding more than one point in elliptic curve in this way. An improved method based on the KOBLITZ probability arithmetic has been presented. The method not only embeds a plaintext into x-coordinate of a point in elliptic curve but also make the plaintext correlation with y-coordinate of the point. As a result, a plaintext is embedded in one point in elliptic curve.