High-Throughput Low-Complexity Unified Multipliers Over $GF(2^{m})$ in Dual and Triangular Bases

Abstract

Multiplication is an essential operation in cryptographic computations. One of the important finite fields for such computations is the binary extension field. High-throughput low-complexity multiplication architectures lead to more efficient cryptosystems. In this paper, a high-throughput low-complexity unified multiplier for triangular and dual bases is presented, and is referred to as basic architecture. This multiplier enjoys slightly simpler and more regular structure due to use of the mentioned bases. Additionally, structurally improved architectures have been proposed, which have smaller time complexity than basic ones. This is achieved by the use of parallel processing method. Experimental results show that the proposed basic multipliers implemented using trinomials and pentanomials have, respectively, 37.51% and 68.54% reduction in AT (area $\times$ time). Furthermore, the proposed structurally improved multipliers implemented using trinomials and pentanomials have 94.86% and 34.22% reduction in AT, respectively.