An Improved Dual Field Modular Inversion Algorithm and VLSI Implementation

Abstract

An improved dual filed modular inversion algorithm which can support inversion operation in both GF(P) and GF(2^m) is proposed in this paper. Compared with previous ones based on Extended Euclidean algorithm, it not only finishes modular inversion arithmetic in dual fields, but also operates much faster by more effective shift operations and avoiding time-consuming magnitude comparison. The simple addition/subtraction becomes the most complex operation in the new algorithm while the multiplication/division is replaced by cheap shifting, and thus only two adders and one subtraction device are required to complete its hardware implementation. The 256-bit modular inversion circuit based on the improved algorithm is implemented in SMIC 0.18 CMOS standard cell technology. The synthesis result indicates that the design is about 17% faster than that of previous algorithms while the area is only 5% larger.