Secure Messaging Using Post-Quantum Key Sharing Based on CSIDH and Fujisaki-Okamoto Transform

Abstract

Preserving the confidentiality of information exchanges relies fundamentally on an end-to-end encryption system, involving the use of a secret key to secure the entire communication. However, with the imminent emergence of quantum computing, threats to traditional encryption systems are multiplying. This is where post-quantum key sharing, in particular the Commutative Super Isogenies Diffie Hellman (CSIDH) algorithm, comes in. The CSIDH uses the ideal of some class number to a morphism of elliptic curve for calculating the shared key. It offers an innovative solution for secure key generation between two users, while providing a robust defense against potential attacks from quantum computers, whose computing power is redefining the limits of cryptographic security, based on the mathematical foundations of elliptic curves and isogeny. This technological advance represents an essential pillar in preserving the confidentiality of communications, in a context where security challenges are constantly evolving. Combining with Fujisaki-Okamoto transform, socket, and Linux; a chat application over python could be created for transmitting secure messages.