Optimization of Ristretto255 Group Implementation for Cortex-M4 based Cryptographic Applications

This article focuses on specifying and optimizing one primary order group, Ristretto255, which is suitable for securely implementing higher and more complex modern cryptographic protocols. The Ristretto255 Group is employed across a spectrum of modern cryptographic applications, spanning zero-knowledge protocols, elliptic curve cryptography, key exchange protocols, etc. In this article, we present the principles and optimization of Ristretto255 Group implementation for embedded cryptographic applications based on the Bernstein elliptic curve Curve25519. In our implementation, with a combination of the C programming language and Assembler, we achieved a faster and more compact result on a microcontroller built on 32-bit ARM Cortex-M4 core. We have prepared our Ristretto255 Group transformation implementation that serves as a compliant building block for cryptographic protocols operating at the 128-bit security level.