Implementation And Research Of FPGA Over Elliptic Curve Cryptosystem

With the rapid development of computer technology and network, information security is given more and more attention. As a new public-key cryptography, elliptic curve cryptography has many excellent attributes: short key length, fast speed and high security. These attributes make it an ideal choice for application.Firstly, we generalize and analyze the advantages and present research of Elliptic Curve Cryptography, and illustrate the safety of elliptic curve cryptography; secondly, we study the arithmetic operation in finite field; thirdly we discuss the Elliptic Curve Key Agreement Scheme, Elliptic Curve Encryption Scheme and Elliptic Curve Digital Signature Algorithm; fourthly, the whole design of elliptic curve cryptosystem (ECC) and the hardware structure of the ECC chip are completed; fifthly, the paper particularizes the hardware design of ECC core modules, which includes the operation model of finite field that can operate multiplicate or inverse independently and the model of the elliptic curve scalar multiplication which combines Booth code with amended DA arithmetic; sixthly, a ECC chip based II optimal normal basis of GF(2191) is realized, the result of simulation and application are given; finally, the conclusion summarizes the whole paper and preview the further developments of the work we have done.