Evaluation of modular multiplication techniques for Supersingular Isogeny Schemes on ARMv8 cores

This paper focuses on the evaluation of different modular multiplication implementation techniques on 64-bit ARMv8 systems for the third-round NIST alternate candidate SIKE. The benchmarks were performed on four devices: an Orange Pi WinPlus featuring the Cortex-A53 processor, an NVIDIA Jetson Nano with a Cortex-A57, a Raspberry Pi 4 with a Cortex-A72 and a Macbook Air based on an Apple M1 chip. Throughout these platforms we observed that the two-level Karatsuba Comba method performs better on most Cortex-A processors but the Operand Scanning method presented a performance improvement ranging from 10% to 43% for the multiplication procedure and a 7% to 25% improvement for the modular reduction on the Apple M1 for all SIKE security levels, resulting in an overall improvement ranging from 8% to 28% for the SIKE KEM operations on this architecture.