Cryptographic computation exploits finite field arithmetic and in particular the multiplication. Lightweight and fast implementations of such arithmetic are necessary for many sensitive applications. This paper 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 to the previous work. This has also been confirmed through our application-specific integrated circuit (ASIC) area and time equivalent estimations and implementations. Hence, the proposed architecture appears to be very well suited for high-throughput low-complexity cryptographic applications.Index Terms-Montgomery multiplication, finite field, trinomials, lightweight and high throughput cryptographic architectures.
I. INTRODUCTIONFinite field arithmetic has important applications in a number of fields such as digital signal processing and cryptography. Particularly, modern cryptographic algorithms rely heavily on finite field arithmetic. One of the most important finite field operations is multiplication by which other such operations, including inversion and exponentiation, can be implemented. Moreover, the needs for fast algorithms to compute multiplication is specially important in the case of asymmetric cryptography, since the key length is much longer than that of symmetric cryptography.There are a number of implementations of the binary extension field, GF (2 m ), multipliers based on various algorithms such as Montgomery and Karatsuba-Ofman [1], [2]. These implementations can also be structurally categorized, as examples, into bit-serial, bit-parallel, digit-serial, LFSR based, systolic and etc [3], [4]. For large binary extension fields, systolic array techniques can result in high throughput and regular very large scale integration (VLSI) implementations. A number of recent systolic or semi-systolic architectures have been proposed to implement multiplication [5]-[13].In this work, we have proposed a low-complexity systolic Montgomery multiplication using trinomials which appears to have lower space complexity compared to previous work while its throughput is similar or even higher. Our ASIC implementation results show that our work has 12.83% and 4.74% reductions in the area and latency, respectively, compared to mentioned previous work. This paper is organized as follows. Section II presents the preliminaries regarding the Montgomery multiplication over
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.