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ARMv8-CSIDH v1.0

Optimized and Constant-time implementation of Post-Quantum Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) key exchange on ARMv8 Processors.

This repository contains an highly-optimized implementation of CSIDH on ARMv8 processors. The finite field arithmetic is designed and engineered for the p511 prime proposed in the original CSIDH scheme by Castryck et al.

This library implements CSIDH in both constant-time and variable-time. The constant-time implementation is designed and developed by Amir Jalali. The variable-time implementation is developed based on the proof-of-concept implementation of CSIDH authors.

Building Binaries

Cross Compliation for ARMv8 on Ubuntu

ARMv8 executables can be generated using cross-compilation on Linux. There are different methods for cross-compilation. An easy approach is to install gcc-aarch64-linux-gnu package by executing:

$  sudo apt-get install gcc-aarch64-linux-gnu

After installation, use the following command to generate the ARMv8 executables:

Variable-time Executable

Simply use make in the terminal:

$ make

Constant-time Executable

Use the following command in the terminal:

$ make CONSTANT=TRUE

Constant-time with uniform variable-time ladder

In order to improve the constant-time CSIDH performance, we can replace the constant-time Montgomery ladder inside the scheme with the uniform variable-time ladder. This rises some security concerns regarding side-channel attacks, however the performance improvement is significant. To generate a constant-time with uniform (variable-time) ladder, use the following command in the terminal:

$ make CONSTANT=TRUE FASTLADDER=TRUE

The generated executable is CSIDH_TEST and can be run on ARMv8 cores.

Contributors

The constant-time implementation as well as optimized finite field arithmetic are designed and developed by Amir Jalali ([email protected]) and Reza Azarderakhsh ([email protected]). The variable-time implementation and key validation is designed with minor modifications based on the CSIDH proof-of-concept implementation by Castryck et al. The field arithmetic implementation is designed for ARMv8 processors.