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.
public-key cryptography, elliptic curve, isogeny, hardware acceleration, finite-field arithmetic
Level of Degree
Electrical and Computer Engineering
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Calhoun, Jeffrey Denton. "Optimization of Supersingular Isogeny Cryptography for Deeply Embedded Systems." (2018). https://digitalrepository.unm.edu/ece_etds/420