A high-throughput fully digit-serial polynomial basis finite field $\text{GF}(2^{m})$ multiplier for IoT applications

Abstract

The performance of many data security and reliability applications depends on computations in finite fields $\text{GF} (2^{m})$ . In finite field arithmetic, field multiplication is a complex operation and is also used in other operations such as inversion and exponentiation. By considering the application domain needs, a variety of efficient algorithms and architectures are proposed in the literature for field $\text{GF} (2^{m})$ multiplier. With the rapid emergence of Internet of Things (IoT) and Wireless Sensor Networks (WSN), many resource-constrained devices such as IoT edge devices and WSN end nodes came into existence. The data bus width of these constrained devices is typically smaller. Digit-level architectures which can make use of the full data bus are suitable for these devices. In this paper, we propose a new fully digit-serial polynomial basis finite field $\text{GF} (2^{m})$ multiplier where both the operands enter the architecture concurrently at digit-level. Though there are many digit-level multipliers available for polynomial basis multiplication in the literature, it is for the first time to propose a fully digit-serial polynomial basis multiplier. The proposed multiplication scheme is based on the multiplication scheme presented in the literature for a redundant basis multiplication. The proposed polynomial basis multiplication results in a high-throughput architecture. This multiplier is applicable for a class of trinomials, and this class of irreducible polynomials is highly desirable for IoT edge devices since it allows the least area and time complexities. The proposed multiplier achieves better throughput when compared with previous digit-level architectures.