FPGA implementation of high performance elliptic curve cryptographic processor over GF(2163)GF(2163)

In this paper, we propose a high performance elliptic curve cryptographic processor over GF(2163)GF(2163), one of the five binary fields recommended by National Institute of Standards and Technology (NIST) for Elliptic Curve Digital Signature Algorithm (ECDSA). The proposed architecture is based on the López–Dahab elliptic curve point multiplication algorithm and uses Gaussian normal basis for GF(2163)GF(2163) field arithmetic. To achieve high throughput rates, we design two new word-level arithmetic units over GF(2163)GF(2163) and derive parallelized elliptic curve point doubling and point addition algorithms with uniform addressing based on the López–Dahab method. We implement our design using Xilinx XC4VLX80 FPGA device which uses 24,263 slices and has a maximum frequency of 143 MHz. Our design is roughly 4.8 times faster with two times increased hardware complexity compared with the previous hardware implementation proposed by Shu et al. Therefore, the proposed elliptic curve cryptographic processor is well suited to elliptic curve cryptosystems requiring high throughput rates such as network processors and web servers.