Optimization of Supersingular Isogeny Cryptography for Deeply Embedded Systems

Public-key cryptography in use today can be broken by a quantum computer with sufficient resources. Microsoft Research has published an open-source library of quantum-secure supersingular isogeny (SI) algorithms including Diffie-Hellman key agreement and key encapsulation in portable C and optimized x86 and x64 implementations. For our research, we modified this library to target a deeply-embedded processor with instruction set extensions and a finite-field coprocessor originally designed to accelerate traditional elliptic curve cryptography (ECC). We observed a 6.3-7.5x improvement over a portable C implementation using instruction set extensions and a further 6.0-6.1x improvement with the addition of the coprocessor. Modification of the coprocessor to a wider datapath further increased performance 2.6-2.9x. Our results show that current traditional ECC implementations can be easily refactored to use supersingular elliptic curve arithmetic and achieve post-quantum security