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.
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.
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.
Due to development in quantum computing, we need to create and implement new cryptographic protocols, which are resistant to attacks using a quantum computer, in all practical cases. Last years humans became using messengers to transfer far more important information than earlier, so it is necessary to create new post-quantum secure messaging protocols for peer-to-peer and group communications. In this article, we describe needed security properties, existing ways for the creation of group chats, and our suggestions. We described ways and needed primitives for the creation of a group key establishment scheme based on isogenies of elliptic curves. We describe such protocol as an extended Double Ratchet protocol.
We propose and develop new schemes for post-quantum cryptography based on isogenies over elliptic curves. First we show that ordinary elliptic curves are have less than exponential security against quantum computers. These results were used as the motivation for De Feo, Jao and Pl\\^ut's construction of public key cryptosystems using supersingular elliptic curve isogenies. We extend their construction and show that isogenies between supersingular elliptic curves can be used as the underlying hard mathematical problem for other quantum-resistant schemes. For our second contribution, we propose is an undeniable signature scheme based on elliptic curve isogenies. We prove its security under certain reasonable number-theoretic computational assumptions for which no efficient quantum algorithms are known. This proposal represents only the second known quantum-resistant undeniable signature scheme, and the first such scheme secure under a number-theoretic complexity assumption. Finally, we also propose a security model for evaluating the security of authenticated encryption schemes in the post-quantum setting. Our model is based on a combination of the classical Bellare-Namprempre security model for authenticated encryption together with modifications from Boneh and Zhandry to handle message authentication against quantum adversaries. We give a generic construction based on Bellare-Namprempre for producing an authenticated encryption protocol from any quantum-resistant symmetric-key encryption scheme together with any digital signature scheme or MAC admitting any classical security reduction to a quantum-computationally hard problem. We apply the results and show how we can explicitly construct authenticated encryption schemes based on isogenies.
Widely used communication and messaging protocols, e.g., TLS 1.3 and Signal, are insecure against an adversary with a quantum computer. We expect that post-quantum security will become mandatory for a new generation of cryptographic protocols in the nearest 10-15 years. The analysis of existing post-quantum secure cryptographic tools for key exchange, encryption and message authentication based on hard problems in codes, lattices, ring learning with errors and elliptic curve isogenies revealed their advantages and drawbacks. In particular, we conclude, that the main threat to communication and messaging protocols is only pre-quantum security of currently used Diffie-Hellman key exchange protocols. We summarize efficiency and safety results for each class of post-quantum cryptographic schemes and present an experimental implementation of isogeny-based Diffie-Hellman-like key exchange protocol as an illustration of their applicability.
The Signal protocol can be considered state-of-the-art when it comes to secure messaging, but advances in quantum computing stress the importance of finding post-quantum resistant alternatives to its asymmetric cryptographic primitives. The aim is to determine whether existing post-quantum cryptography can be used as a drop-in replacement for the public-key cryptography currently used in the Signal protocol and what the performance trade-offs may be. An implementation of the Signal protocol using commutative supersingular isogeny Diffie-Hellman (CSIDH) key exchange operations in place of elliptic-curve Diffie-Hellman (ECDH) is proposed. The benchmark results on a Samsung Galaxy Note 8 mobile device equipped with a 64-bit Samsung Exynos 9 (8895) octa-core CPU shows that it takes roughly 8 seconds to initialize a session using CSIDH-512 and over 40 seconds using CSIDH-1024, without platform specific optimization. To the best of our knowledge, the proposed implementation is the first post-quantum resistant Signal protocol implementation and the first evaluation of using CSIDH as a drop-in replacement for ECDH in a communication protocol.
The rapid development of quantum computing presents a substantial threat to traditional cryptographic algorithms, particularly those relying on mathematical problems such as integer factorization and elliptic curve operations. As a response, the cryptographic community has accelerated the design of post-quantum cryptographic schemes that can withstand attacks from both classical and quantum computers. However, many of these new schemes exhibit inherent trade-offs between performance, key sizes, and implementation complexity. To address this, we propose a novel hybrid cryptographic framework tailored for secure and efficient data transmission in future quantum-aware environments. The proposed system combines three algorithmic paradigms: a lattice-based encryption method for fast and lightweight data protection, a hash-based signature mechanism for authenticity, and a code-based key exchange method to ensure session confidentiality. This layered integration is designed to capitalize on each algorithm’s strengths while mitigating individual limitations. The system is implemented using modular components in a testbed simulating real-world deployments, and its performance is benchmarked across multiple metrics including encryption latency, signature generation time, key sizes, and throughput. Comparative results indicate that the hybrid approach outperforms monolithic schemes in critical areas such as execution time and cryptographic strength under quantum adversary models. The findings support the practicality of using multiple post-quantum primitives in tandem to build robust communication systems. This research contributes a realistic implementation and evaluation of post-quantum security models and highlights key directions for future research and standardization efforts as the global transition to quantum-safe infrastructure begins.