The Research and Design of ECC Fast Algorithm Based on FPGA

The core of elliptic curve cryptographic algorithm (ECC) is the point multiplication algorithm(KP), the performance of the KP determines the performance of the ECC. A new KP parallel scheduling algorithms based on improved NAF is presented in this paper for solving the problem of low speed of KP in prime finite field. By deeply analysing the point addition algorithm and the point doubling algorithm of the Jacobian projective coordinates, designed the point-addition parallel computing algorithm and the point-doubling parallel computing algorithm.The hardware design of the improved algorithm of ECC has completed based on the FPGA development platform of Cyclone IV family.The testing result of hardware shows that a point multiplication operation needs 111, 860 clock cycles. Comparing with the previous algorithms, the computing speed improve 40.3%. If the improved algorithm is implemented based on ASIC, estimating the performance of point multiplication algorithm can reach 72, 393.6 times/s.