Energy/Area-Efficient Scalar Multiplication with Binary Edwards Curves for the IoT

Abstract

Making Elliptic Curve Cryptography (ECC) available for the Internet of Things (IoT) and related technologies is a recent topic of interest. Modern IoT applications transfer sensitive information which needs to be protected. This is a difficult task due to the processing power and memory availability constraints of the physical devices. ECC mainly relies on scalar multiplication (kP)—which is an operation-intensive procedure. The broad majority of kP proposals in the literature focus on performance improvements and often overlook the energy footprint of the solution. Some IoT technologies—Wireless Sensor Networks (WSN) in particular—are critically sensitive in that regard. In this paper we explore energy-oriented improvements applied to a low-area scalar multiplication architecture for Binary Edwards Curves (BEC)—selected given their efficiency. The design and implementation costs for each of these energy-oriented techniques—in hardware—are reported. We propose an evaluation method for measuring the effectiveness of these optimizations. Under this novel approach, the energy-reducing techniques explored in this work contribute to achieving the scalar multiplication architecture with the most efficient area/energy trade-offs in the literature, to the best of our knowledge.

Keywords

• elliptic curve cryptography
• low-power
• low-energy
• binary Edwards curves
• scalar multiplication
• internet of things
• wireless sensor networks
• lightweight cryptography