The Research Of Digital Signature Based On Elliptic Curve Cryptography

With the high-speed development and application of computers and network technology,the informatization level becomes more and more advanced in the modern society. Digital signature can generate a secure, fast, long-distance signing through digital communications network,digital signature can ensure the integrity of information transmission, authenticate the identity of the sender, prevent the occurrence of transaction disputes,and so on.Elliptic curve cryptography is a public key cryptosystem,which based on the intractability of discrete logarithm problem in elliptic curve point group. Elliptic curve cryptographic algorithm is a efficient and safe signature algorithm ,which realize DSA by way of elliptic curve cryptography,and provides the highest encryption strength forper-bit data.In this paper, analyzes the mathematical theory of public key cryptosystem firstly,and then studys the principle and process technology of digital signature deeply.studys the mathematical theory of elliptic curve in finited field systematically.analyzes the point addtion and multiplication operation.Although elliptic curve cryptography has the advantages of high safety and short private key,it's operation efficiency is restricted for the complexity of mathematicl calculation on elliptic curve. This paper presents a modified algorithm for point multiplication,the algorithm is based on the window non-adjacent form algorithm,it can increase the signature and verify digital signature operation in computation speed,so improves the operating efficiency of digital signature system.Finally,implements a digital signature system based on ECDSA with the Eclipse in the Java platform. After several tests,the system achieved signatures and verification for information and documents perfectly,compared with the traditional system of ECDSA signature, the system has some advantages in signature efficiency.