Biblio

Elliptic Curve Cryptography (ECC) provides high security levels with shorter keys than other public-key cryptosystems such as RSA. Usually modular inversion operation is a choke point in realizing the public-key cryptosystem. Based on the Extended Euclidean Algorithm, this work proposes an efficient FPGA implementation of ECC modular inversion over F256. According to this proposed algorithm, one modular inversion requires 320 clock cycles with a maximum clock frequency of 144.011MHz on a Xilinx Virtex-7 FPGA device which gives a computation time of 2.22μs. On the other words, our scenario can perform 450 thousand times division operations in one second approximately. Compared to other available literature, our scheme presented in this paper provides a high performance FPGA implementation of 256-bit modular inversion over F256. This makes the elliptic curve cryptography have important practical value in hardware implementation.