Abstract: A dual finite fields algorithm for elliptic curve cryptosystem（ECC）is presented. It can be used in two kinds of finite fields, which are Galois fields GF(p) and GF(2m) for arbitrary prime numbers and irreducible polynomials respectively. An arithmetic unit, which can perform all dual Galois fields' arithmetic operations, including addition, subtraction, multiplication, squaring, inversion and division, is designed for the ECC. Furthermore, the authors describes a FPGA implementation of ECC. It can efficiently handle requests for different ECC key length and different curves in GF(p) and GF(2m).

Key words: finite fields, ECC, FPGA implementation

摘要： 提出一种支持椭圆曲线加密体制的双有限域算法。该算法可以同时完成素数域和二进制域上的运算，并且模数p和取模多项式可以任意选取。提出了椭圆曲线加密体制运算单元的设计方法，此运算单元可以同时完成素数域和二进制域上的所有运算，包括加法、减法、乘法、平方、求逆和除法。此外，描述了椭圆曲线加密体制的FPGA实现，最终的电路可以对任意长度密钥进行加密，并且支持素数域和二进制域上的任意椭圆曲线。

关键词: 有限域, 椭圆曲线加密算法, 现场可编程门阵列实现