Radix-4 Semi-Systolic Architecture for Montgomery Multiplication over GF(2m)

Abstract

Arithmetic operations over finite fields have been applied in a variety of fields such ascryptographic algorithms and error correction codes.The most basic and critical operation over finite fields is the multiplication. Various architectures, such as systolic, semi-systolic array, and so forth, to calculate the multiplication over GF(2m) have been developed. However, many existing multipliers have some shortcomings, including long latency and/or AT (area-time) complexity.In this paper,a radix-4 multiplier using the semi-systolic architecture in finite fields based on Montgomery multiplication.The proposed architecture has the low-latency as compared to other multipliers. Although the area complexity of our multiplier is slightly increased, our multiplier saves time complexity as compared to other multipliers. Considering AT complexity, the proposed multiplier saves about 54.2% and 27.9% as compared to Huang and Kim-Kim, respectively.