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 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 goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented.
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.
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 present thesis focus on one of the post-quantum cryptosystems, in particular, the isogenybased cryptography. Because of its certain properties like the hard problem of computing isogenies between two elliptic curves, it makes it to be one of the few candidates for post-quantum cryptography. We will study the algorithms based on this isogeny-based cryptography and why they are useful against quantum computers. One of these algorithms is the Supersingular Isogeny Diffie Hellman (SIDH), a candidate for substituing ECDH in the Signal protocol to make it quantum safe.
Quantum computing threatens classical key exchange protocols such as Elliptic Curve Diffie–Hellman (ECDH). Post-quantum schemes like Supersingular Isogeny Diffie–Hellman (SIDH) offer quantum resistance but at notable computational and communication costs. We propose DualSecure Key Exchange (DSKE), a hybrid protocol that integrates the classical security of ECDH with the quantum resistance of SIDH. Methodology: DSKE jointly derives two shared secrets -KECDH via elliptic-curve scalar multiplication over a 256-bit prime field and KSIDHvia supersingular isogeny mappings—then fuses them using a secure KDF (e.g., SHA-3): K=KDF(KECDH || KSIDH). We formalize core operations and asymptotics (ECDH O(n3); SIDH O(mlog m)), specify key materials, and fix parameter choices aligned with established baselines (e.g., Curve25519 for ECDH and standard SIKE/SIDH parameter sets) to ensure reproducibility. Experimental settings: Evaluations were conducted on an Intel Core i7 with 16 GB RAM using Python-based cryptographic libraries, with repeated trials for timing stability. Results: DSKE achieves runtime = 6.6 ms versus ECDH = 1.2 ms and SIDH = 5.4 ms; communication = 512 bytes versus ECDH = 128 bytes and SIDH = 384 bytes; and key size 1024 bits (hybrid) versus 256 bits (ECDH) and 768 bits (SIDH). Comparative analysis against SIKE further contextualizes DSKE’s efficiency–security trade-off. Security strength follows the minimum of the constituent levels; with a 256-bit prime for ECDH (=128-bit classical) and standard SIDH/SIKE parameters (targeting =128-bit quantum), the fused key maintains an effective 128-bit level under the stated assumptions and KDF construction. These results indicate that DSKE offers a balanced pathway toward post-quantum readiness, particularly for long-lived, security-critical deployments that can tolerate modest overheads for dual-layer protection.
In this paper, a technique to develop a secure messaging service utilizing a new post-quantum cryptosystem, termed CryptoMess, is proposed. Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) is utilized to secure key exchange paired with the AES algorithm to protect message content in communication. At the same time, the Rainbow post-quantum digital signature technology is incorporated to assure the integrity and authenticity of communications between the sender and the recipient. As a consequence, the messaging program is able to exchange messages between users, assuring safety, security, integrity, and authenticity. The performance of the program has a transmitting rate of approximately 0.26 s and a receiving rate of approximately 0.22 s. The message signing time is approximately 0.027 s, the message verification speed is approximately 0.22 s, and the key exchange time is approximately 0.0017s.