Research and design of elliptic curve cryptography

Binary field is considered to be more suitable for hardware implementation of ECC than large prime number domain GF(p). By analyzing the modular arithmetic in binary field and choosing the suitable algorithm, this paper convert all the modular arithmetic to three types of modular arithmetic: modular addition, modular multiplication and modular square, and then design a arithmetic unit. It finishes the computation and storage of data by using the FSM to control storage unit and the other module. The hardware of implementation of ECC which using this arithmetic unit has small area, small storage unit and fast speed, and it is extremely suitable the system which has limited computation ability and storage space.