Memory-Efficient Implementation of Elliptic Curve Cryptography for the Internet-of-Things

In this paper, we present memory-efficient and scalable implementations of NIST standardized elliptic curves P-256, P-384 and P-521 on three ARMv6-M processors (i.e. Cortex-M0, M0+, and M1). Specifically, we propose a refined approach to perform the Multiply-ACcumulate (MAC) operation using hardware multiplier provided by ARMv6-M processor, and a compact doubling routine for multi-precision squaring that executes both doubling and partial product operations in an efficient way. We demonstrate that the proposed squaring implementation achieves a speed up of 28 percent compared to the same operation employed in Micro-ECC. Then, we reduce one modular reduction in co-Z conjugate point addition by using lazy reduction and special form representation (CD-AB, EF-AB), which further reduces the execution time of both P-256 and P-384 implementations. Finally, we propose scalable implementations of ECC scalar multiplication on ARMv6-M processors that are widely used for Internet of Things applications.