Efficient Elliptic Curve Cryptography for Embedded Devices

Zhe Liu, Jian Weng, Zhi Hu, Hwajeong Seo

Abstract: Many resource-constrained embedded devices, such as wireless sensor nodes, require public key encryption or a digital signature, which has induced plenty of research on efficient and secure implementation of elliptic curve cryptography (ECC) on 8-bit processors. In this work, we study the suitability of a special class of finite fields, called optimal prime fields (OPFs), for a “lightweight” ECC implementation with a view toward high performance and security. First, we introduce a highly optimized arithmetic library for OPFs that includes two implementations for each finite field arithmetic operation, namely a performance-optimized version and a security-optimized variant. The latter is resistant against simple power analysis attacks in the sense that it always executes the same sequence of instructions, independent of the operands. Based on this OPF library, we then describe a performance-optimized and a security-optimized implementation of scalar multiplication on the elliptic curve over OPFs at several security levels. The former uses the Gallant-Lambert-Vanstone method on twisted Edwards curves and reaches an execution time of 3.14M cycles (over a 160-bit OPF) on an 8-bit ATmega128 processor, whereas the latter is based on a Montgomery curve and executes in 5.53M cycles.