Optimization Of Scalar Multiplication In Elliptic Curve Cryptosystem And Fpga Implementation

With the development of information technology, the advanced information security is eagerly desired. The cryptography is the key technology. Public key cryptosystem is adopted, but larger scale keys are required with the computing arts enhanced. The elliptic curve cryptosystem is widely concerned due to the highest security of the same lengthbit. The implement of the cryptosystem is promising. Firstly, the choosing of finite field and the parameters of elliptic curve are put forward. Secondly, the whole computation is divided into two levels: the finite field level and the elliptic curve level. Thirdly, the algorithms on the finite field and over the curve are analyzed and improved respectively. Finally, the selected and improved algorithms are realized in Verilog HDL.The develop flatform is FPGA Advantage issued by Mentor Graphics Company. The software is used to finish the fore-design including the functional simulation and timing simulation. The product of Altera cooperation APEX II series is chosen. And the Quarter II 2.2 is used to finish the synthesis and back-end design, which issued by Altera Company, supporting the newer devices of Altera. The result of the design is of practical value. The improved algorithm on field multiplication leads the less logic elements to implement the scalar multiplication on the elliptic curve. 2,741,998 logic elements are used to construct the structure of scalar multiplication,and it takes 567.69us to multiply in the clock frequency of 100MHz. So the design can be used in the environments limited in resources. It can be used to construct the digital signature, verification and key exchange protocol over the elliptic curve cryptography.