FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field

Elliptic curve cryptography (ECC) and Tate pairing are two new types of public-key cryptographic schemes that become popular in recent years. ECC offers a smaller key size compared to traditional methods without sacrificing security level. Tate pairing is a bilinear map commonly used in identity-based cryptographic schemes. Therefore, it is more attractive to implement these schemes by using hardware than by using software because of its computational expensiveness. In this paper, we propose field programmable gate array (FPGA) implementations of the elliptic curve point multiplication in Galois field GF(2283)GF(2283) and Tate pairing computation in GF(2283)GF(2283). Experimental results demonstrate that, compared with previously proposed approaches, our FPGA implementations of ECC and Tate pairing can speed up by 31.6 times and 152 times, respectively.