An Internet Messenger Using Post-Quantum Cryptography Algorithms Based on Isogenies of Elliptic Curves

Abstract

This paper presents the design and implementation of an Internet-based instant messaging application that leverages post-quantum cryptographic algorithms founded on isogenies of elliptic curves. The system employs the CSIDH cryptosystem for key exchange and SeaSign for digital signatures, integrating these with the X3DH and Double-Ratchet protocols to enable end-to-end encryption for both text messages and binary file transfers. Key generation is supported for new users upon registration, ensuring robust cryptographic foundations from the outset. The performance of the CSIDH and SeaSign algorithms is evaluated at various security levels using a Python-based prototype, providing practical benchmarks. By combining isogeny-based cryptographic schemes with widely adopted secure messaging protocols, this work presents an illustration of a selected quantum-resistant communication solution and offers insights into the feasibility and practicality of deploying such protocols in real-world applications.