摘要
提出了一种并行的有限域GF(2m)乘法器结构.有限域乘法由多项式乘法和模不可约多项式f(x)两步实现.把多项式被乘数和乘数各自平分成3个子多项式,多项式乘法由子多项式的乘法和加法实现.当多项式的度m=500时,与传统的Mastrivito多项式乘法相比,所提出的多项式乘法结构可以减少33.1%的异或门,减少33.3%的与门.为了简化,采用特殊不可约多项式来产生有限域.此有限域乘法器结构适合高安全度的椭圆曲线密码算法的VLSI设计.
The parallel multiplier architecture over Galois field GF(2~m) was proposed. The finite field multiplication requires two steps: polynomial multiplication and reduction modulo the irreducible f(x). The polynomial multiplicand and multiplicator are equally split into three sub-polynomials, respectively. The polynomial multiplication is performed by sub-polynomial multiplications and additions. When the degree m of the finite field is 500, compared to the traditional Mastrivito polynomial multiplication, it can reduce the number of the XOR gates by 33.1%, and that of the AND gates by 33.3%. To simplify reduction modulo, the special polynomials are used to generate finite field. The proposed multiplier architecture suits elliptic curve cryptosystems with large finite field.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
2005年第4期636-639,644,共5页
Journal of Shanghai Jiaotong University
基金
国家高技术发展计划(863)资助项目(2003AA141040)
关键词
超大规模集成电路
有限域
乘法器
椭圆曲线密码
very large scale integration (VLSI)
finite field
multiplier
elliptic curve cryptosystems
