Research And Implementation Over Elliptic Curve Cryptosystem

With the rapid development of the internet, information security is given more and more attention. The information exchange becomes larger and larger. It is a difficult problem to meet the demand with the traditional software encryption method, so the hardware implementation appeared. As new public-key cryptography, elliptic curve cryptography has some excellent attributes: short length of the key, fast speed of the process, high level of the security. All of these make it an ideal choice for the application. In fact, it is one of standards of the next generation to the public-key cryptography.In the paper, based on the generalization and analytical study to the present research of the Elliptic Curve Cryptography (ECC), the blue map of the ECC is given to complete an independent system. First, we study the arithmetic operation in the finite field, in which several theorems and useful inferences of the ECC are presented. Secondly, fast hardware implementation of the elliptic curve cryptography arithmetic is the hotspot direction in the ECC research, so the hardware implementations of the finite field operations are given with optimal normal basis, the design of the ECC core modules are completed, which includes the elliptic curve scalar multiplication which combines NAF code with amended arithmetic. Finally , the result of simulation and application are given, in which the conclusion summarizes that ECC scalar multiplication modules based on II optimal normal bases completes a computing needs time 11 ms at 50 MHZ frequency of the work in GF (2¹⁹¹).