研究有限域(定义在GF(2)上的m维向量空间)的正规基乘法器。基于域元素的正规基表示和多项式基表示可以相互转换,通过分析多项式基下的乘法运算公式,得到利于串行乘法器设计的有效性质。利用该性质,提出了一个新的串行正规基乘法器,该乘法器要求(2m-2)个二值输入的异或门,m个二值输入的与门。在进行具体的硬件实现时,所需要的存储空间为3m+1。 We study normal base multipliers for finite fields (m-dimensional vector spaces defined on GF (2)). The regular basis representation of domain elements and the representation of polynomial basis can be converted into each other. By analyzing the polynomial multiplication formula, the effective property of serial multiplier design is obtained. Using this property, a new serial regular base multiplier is proposed, which requires (2m-2) two-input exclusive-or gates and m binary-input AND gates. In the specific hardware implementation, the required storage space is 3m + 1.