一种基于有限域的快速乘法器的设计与实现

基于有限域上椭圆曲线公开密匙协议的离散对数计算算法正日益成为热点，而有限域上的计算尤其是乘法计算极大地影响其加／解密速度。为了提高椭圆曲线密码系统的计算速度，需要从很多方面考虑，但其中关键的一点在于如何提高乘法器的速度，且保持其规模在能够接受的范围。在对椭圆曲线的分析基础上提出了一种有限复合域GF((2^m1)^m2)上的快速乘法器。该乘法器采用并行计算和串行计算相结合的原则，在增加少量硬件规模将一次有限域乘法的计算速度由原来的m=m2m1个时钟周期降低到m2个时钟周期，从而极大地提高了乘法器的计算速度。通过FPGA的验证测试证明该方法在速度上完全适合椭圆曲线密码系统。

A Fast Multiplier Design and Implication over Finite Fields

It has become increasingly common to implement a discrete algorithm based on public key protocols on elliptic curves over finite fields The operations, especially multiplication, over finite fields affect greatly the speed of encryption/decryption for ECC To provide a higher computation speed in elliptic curve cryptosystems, many aspects should be considered, among which the key point is to enhance multiplier's speed and to keep its area in proper range For this reason a fast multiplier is described for elliptic curve cryptosystems over finite composite fields GF((2 m 1 ) m 2 ) This multiplier adopts mixed parallel serial approaches The number of clock cycles for one field multiplication can be reduced from the former m=m 2m 1 to the current m 2 with less increase of hardware scales This implementation is provided by FPGA testing to suit ECC