High-Throughput Low-Complexity Systolic Montgomery Multiplication Over <inline-formula><tex-math notation="LaTeX">$GF(2^{m})$</tex-math></inline-formula> Based on Trinomials

Abstract

Cryptographic computation exploits finite field arithmetic and, in particular, multiplication. Lightweight and fast implementations of such arithmetic are necessary for many sensitive applications. This brief proposed a low-complexity systolic Montgomery multiplication over $GF(2^{m})$ . Our complexity analysis shows that the area complexity of the proposed architecture is reduced compared with the previous work. This has also been confirmed through our application-specific integrated circuit area and time equivalent estimations and implementations. Hence, the proposed architecture appears to be very well suited for high-throughput low-complexity cryptographic applications.