基于GF(2^(m))域上Ⅱ型最优正规基的模乘算法及实现

Modular Multiplication Algorithm and Implementation Based on Type-ⅡOptimal Normal Basis over GF(2^(m))

论文提出了一种利用Ⅱ型正规基进行乘法运算的新方案。通过一种有效的线性变换,将GF(2m)上的正规基转换成在GF(2^(m))上的m项多项式。这种多项式可以使用任何多项式乘法算法进行相乘,然后再利用上述变换的逆过程将乘积转换回正规基。此方案所需的XOR和AND运算为M(m)+2m log_(2)(m/2),其中M(m)取决于选用的多项式乘法算法。相较于其他的正规基乘法具有更小的资源占用量。通过FPGA综合实践表明,该方案能够显著减少LUTs数量。

In this paper,a new method of using typeⅡnormal basis for multiplication is proposed.By an efficient linear transformation,the regular basis of GF(2^(m))is transformed into m-term polynomials over GF(2^(m))。This polynomial can be multiplied using any polynomial multiplication algorithm and then converted back to a normal basis using the inverse of the transformation described above.The XOR/AND operations required for this scheme are M(m)+2m log_(2)(m^(2)),where M(m)depends on the polynomial multiplication algorithm chosen.Compared with other normal basis methods,it has smaller resource consumption.The FPGA comprehensive practice shows that this scheme can significantly reduce the number of LUTs.