GF（2^n）域上的一种Ⅱ型优化正规基乘法器及其FPGA实现

An Optimal Normal Basis Type Ⅱ Multiplier over GF(2~n) for FPGAs

有限域GF(2n)上的椭圆曲线密码体制以其密钥短,安全强度高的优点正在获得广泛的重视和应用.该密码体制最主要的运算是有限域上的乘法运算.本文提出了一种基于Ⅱ型优化正规基的乘法器,该乘法器具有Massey—Omura乘法器的优点,又避免了其不足,易于编程,适合FPGA实现.实验表明,该算法简单,快速.

The elliptic curve cryptosystems over the finite field GF(2n) receive considerable attention and are widely used because of their small key size and high security. Multiplication operation over the finite field GF(2n) is the crucial arithmetic operation. This paper presents a multiplication algorithm for the optimal normal basis type Ⅱ. The algorithm has the advantage of Massey-Omura multiplication algorithm and eliminate its deficiency.The test shows that this algorithm is simple,fast and is easy to be implemented by FPGA.