Low-Space Bit-Parallel Systolic Structure for AOP-Based Multiplier Suitable for Resource-Constrained IoT Edge Devices

Abstract

Security and privacy issues with IoT edge devices hinder the application of IoT technology in many applications. Applying cryptographic protocols to edge devices is the perfect solution to security issues. Implementing these protocols on edge devices represents a significant challenge due to their limited resources. Finite-field multiplication is the core operation for most cryptographic protocols, and its efficient implementation has a remarkable impact on their performance. This article offers an efficient low-area and low-power one-dimensional bit-parallel systolic implementation for field multiplication in GF(2n) based on an irreducible all-one polynomial (AOP). We represented the adopted multiplication algorithm in the bit-level form to be able to extract its dependency graph (DG). We choose to apply specific scheduling and projection vectors to the DG to extract the bit-parallel systolic multiplier structure. In contrast with most of the previously published parallel structures, the proposed one has an area complexity of the order O(n) compared to the area complexity of the order of O(n2) for most parallel multiplier structures. The complexity analysis of the proposed multiplier structure shows that it exhibits a meaningful reduction in area compared to most of the compared parallel multipliers. To confirm the results of the complexity analysis, we performed an ASIC implementation of the proposed and the existing efficient multiplier structures using an ASIC CMOS library. The obtained ASIC synthesis report shows that the proposed multiplier structure displays significant savings in terms of its area, power consumption, area-delay product (ADP), and power-delay product (PDP). It offers average savings in space of nearly 33.7%, average savings in power consumption of 39.3%, average savings in ADP of 24.8%, and savings in PDP of 31.2% compared to the competitive existing multiplier structures. The achieved results make the proposed multiplier structure more suitable for utilization in resource-constrained devices such as IoT edge devices, smart cards, and other compact embedded devices.