The Research And Application Of Digital Signature Based On Elliptic Curves

The Elliptic Curve Cryptosystem hasadvantages of high safety, short key length, quick encrypt and decrypt speed and so on, so it will be have the best future than others.Beginning with the discussion of requirements of information security, the foundation of cryptographic techniques is discussed. On the above discussions, the Elliptic Curve Cryptosystem is elaborated in detail. Mathematics foundation, realization principle and the performance of public-key cryptosystems being used widely are compared.Scalar multiplication and point addition in elliptic curves are core operations in elliptic curve cryptosystem. In order to improve the operating speed, the projective coordinates and improving point addition operation are used; the scalar multiplication algorithm is optimized. The optimized algorithm can improve the operating speed of ECC and enhance the availability of ECC, which can be proved by theoretical analysis.Because of Elliptic Curve Cryptosystem's superiority, its application is being extended. The Elliptic Curve Digital Signature Algorithm (ECDSA) is discussed emphasized. Digital signature is one of the most important information security technologies. The security of ECDSA relies on the difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP). The speed of signature generation and signature checking of ECDSA is effectively improved by application of the ECC optimized principle to ECDSA.Based on above discussion, the optimized ECDSA is applied in electronic government system. XML for electronic documents transmission is a developing trend of e-government, which is greatly significant for achieving standardization of electronic documents.The design of XML digital signature based on ECDSA is proposed, then the idea is realized, at last, the feasibility of this idea is proved. The performance of the design is testified in certain degree. Using the optimized ECDSA produce signature in the XML digital signature made the XML signature technology concurrently have the XML digital signature standard and the ECDSA advantages, which is proved by the test, so the thesis research is well practical value.