High-Speed Design of Montgomery Inverse Algorithm over GF(2m)

Abstract

Montgomery algorithm has demonstrated its effectiveness in applications like cryptosystems. Most of the existing works on finding the Montgomery inverse of an element over the Galois field are based on the software implementation, which is then extended to derive the scalable hardware architecture. In this work, we consider a fundamental change at the algorithmic level and eliminate the potential problems in hardware implementation which makes the resulting modified Montgomery inverse algorithm over GF(2m) very suitable for hardware realization. Due to its structural simplicity, the modified algorithm can be easily mapped onto a high-speed and possibly low-complexity circuit. Experimental results show that our development can achieve both the area and speed advantages over the previous work when the inversion operation over GF(2m) is under consideration and the improvement becomes more significant when we increase the value of m as in the applications of cryptosystems. The salient property of our development sustains the high-speed operation as well as low hardware complexity over a wide range of m for commercial cryptographic applications and makes it suitable for both the scalable architecture and direct hardware implementation.