In 2015, NIST held a workshop calling for new candidates for the next generation of elliptic curves to replace the almost two-decade old NIST curves. Nothing Upon My Sleeves (NUMS) curves are among the potential candidates presented in the workshop. Here, we present the first implementation of the NUMS256, NUMS379, and NUMS384 curves on two types of embedded devices. The implementations, which exhibit regular, constant-time execution to protect against timing and simple side-channel attacks, set new speed records and advance the state-of-the-art of curve-based (without endomorphism) scalar multiplication on 8-bit AVR and 32-bit ARM11 microcontrollers. For example, our NUMS256 implementation computes a scalar multiplication in ~1.4 million cycles on a low-power 32-bit ARM11 microcontroller using mixed C and assembly language. These results demonstrate the potential of deploying IoT-NUMS on constrained and low-power applications such as protocols for the Internet of Things.
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