This paper introduces a novel Distributed Key Generation (DKG) protocol based on the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) framework for secure multi-party cryptography. Our proposed protocol is designed to address scalability and security concerns, particularly in post-quantum cryptographic systems. The main contributions include the introduction of Piecewise Verifiable Proofs (PVPs) for non-interactive zero-knowledge verification of secret shares, and the provision of rigorous security analysis, including resistance to quantum adversaries via Shor’s and Grover’s algorithms. We analyze the protocol’s efficiency, ensuring low computational overhead even in large-scale systems, and compare it with other distributed cryptographic protocols such as RSA-based and lattice-based schemes. Through mathematical proofs and complexity analysis, we demonstrate that our protocol offers enhanced security, efficiency, and scalability in a post-quantum environment. The results presented in this paper provide a strong foundation for implementing secure multi-party computations in quantum-resistant systems.
This paper introduces a novel Distributed Key Generation (DKG) protocol based on the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) framework for secure multi-party cryptography. Our proposed protocol is designed to address scalability and security concerns, particularly in post-quantum cryptographic systems. The main contributions include the introduction of Piecewise Verifiable Proofs (PVPs) for non-interactive zero-knowledge verification of secret shares, and the provision of rigorous security analysis, including resistance to quantum adversaries via Shor’s and Grover’s algorithms. We analyze the protocol’s efficiency, ensuring low computational overhead even in large-scale systems, and compare it with other distributed cryptographic protocols such as RSA-based and lattice-based schemes. Through mathematical proofs and complexity analysis, we demonstrate that our protocol offers enhanced security, efficiency, and scalability in a post-quantum environment. The results presented in this paper provide a strong foundation for implementing secure multi-party computations in quantum-resistant systems.
The advent of quantum computing presents a paradigm shift in modern cybersecurity, threatening the foundations of classical cryptographic systems such as RSA, ECC, and Diffie–Hellman key exchange. Quantum algorithms like Shor’s and Grover’s can efficiently break these schemes, rendering existing encryption mechanisms vulnerable and obsolete. This growing risk necessitates the development of quantum-resilient or post-quantum cryptographic (PQC) solutions that can safeguard data and computation in the era of quantum networks. Secure Multi-Party Computation (SMPC), a cornerstone of privacy-preserving computation, enables multiple entities to jointly compute a function over their private inputs without revealing them. However, its traditional security assumptions are also undermined by quantum threats. This research aims to explore and evaluate quantum-safe cryptographic protocols for integrating PQC into SMPC frameworks, thereby ensuring both confidentiality and correctness even in the presence of quantum-capable adversaries. The study focuses on lattice-based, hash-based, and code-based cryptographic primitives, analyzing their resilience, efficiency, and scalability when applied to distributed systems. A comparative framework is proposed to assess the performance and security trade-offs of different post-quantum SMPC implementations under realistic network conditions. The findings are expected to contribute to the design of a new class of cryptographic protocols capable of resisting quantum attacks, supporting the secure functioning of next-generation networks, and guiding policymakers and technologists toward practical post-quantum standardization. Ultimately, this research strengthens the bridge between theoretical cryptography and real-world cybersecurity readiness in the post-quantum era.
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.
We analyze the Commutative Supersingular Isogeny Diffie-Hellman protocol (CSIDH), a novel supersingular isogeny-based key establishment protocol. Our analysis is from three perspectives: \n \nQuantum Cryptanalysis. Building upon quantum attacks on ordinary isogeny-based cryptography, we propose a subexponential-time quantum algorithm for inverting the complex multiplication group action for supersingular elliptic curves, which uses only polynomial quantum space. This improves upon previously-known algorithms which required subexponential quantum space. \n \nOptimization. We develop more efficient algorithms for evaluating the class group action in the context of CSIDH. We consider "strategies"—formerly only considered for Supersingular Isogeny Diffie-Hellman (SIDH)—in the context of CSIDH, and develop systematic methods for optimizing "permutations" of the small primes used in CSIDH, which previously had been treated only in an ad hoc fashion. We also develop a systematic technique to optimize the CSIDH keyspace. These optimizations are complementary to prior work on optimizing CSIDH, including improved field arithmetic, Splitting Isogenies into Multiple Batches (SIMBA), and the two-point method. We apply our optimizations to the CSIDH-512 parameter set and give experimental results. \n \nFault Attacks. We consider physical attacks on static/ephemeral CSIDH in which limited information about which isogenies are "real" and which are "dummy" is revealed. We determine bounds on the number of fault injections required to recover the static secret key, and show that simply reordering the real and dummy isogenies from the ubiquitous "real-then-dummy" ordering to a dynamic random ordering dramatically increases the number of faults required, with negligible impact on the running time of the key exchange protocol (in contrast with prior fault attack countermeasures, which prevent fault attacks entirely at the cost of doubling the running time for key exchange).
In this paper, we have discussed isogeny-based cryptography as a rather appealing option for post-quantum security. We provide analysis of current protocols like SIDH (Supersingular Isogeny Diffie-Hellman) and SIKE (Supersingular Isogeny Key Encapsulation) setting up fundamental issues with their security and performance. In this work we introduce a novel isogeny pathfinding algorithm that employs graph theory as well as probabilistic models in order to lower its computational complexity. The results show significant improvement in both efficiency and security, strengthening the case for the use of isogeny based systems in a quantum-resilient cryptographic space.
The development of quantum computing poses a very real threat to traditional cryptography, especially these, which are number-theoretic like RSA and ECC. With the more and more development of quantum algorithms such as Shor and Grover, there is an immediate necessity to come up with cryptographic protocols that are resistant to quantum attacks. This paper reviews and discusses different quantum-resistant (post-quantum) cryptographic schemes, such as lattice-based, code-based, multivariate, hash-based, and isogeny-based cryptography. It compares these protocols on the assumptions of their security and their efficiency in their computation and the size of their keys as well as their possible integrations into the existing communication infrastructure. Moreover, we also evaluate the standardization process by NIST and the difficulties of moving towards post-quantum security in practical use. This paper proposes a scalable comparison system, which correlates the hypothetical security basis of postquantum cryptography with the ability to effectively operate in the real world. It has emphasized protocol interoperability, migration compatibility and trade-offs in performance that gives a viable roadmap towards quantum-resistant cryptographic protocols implementation into current communication infrastructures whilst also providing scalable and future secure communication systems. This study, by emphasizing the potential and the drawbacks of the existing post-quantum cryptography schemes, helps in a more precise idea of the directions to follow on the way to a secure, future-proof communications scheme.
The development of quantum computing poses a very real threat to traditional cryptography, especially these, which are number-theoretic like RSA and ECC.With the more and more development of quantum algorithms such as Shor and Grover, there is an immediate necessity to come up with cryptographic protocols that are resistant to quantum attacks.This paper reviews and discusses different quantum-resistant (post-quantum) cryptographic schemes, such as latticebased, code-based, multivariate, hash-based, and isogeny-based cryptography.It compares these protocols on the assumptions of their security and their efficiency in their computation and the size of their keys as well as their possible integrations into the existing communication infrastructure.Moreover, we also evaluate the standardization process by NIST and the difficulties of moving towards post-quantum security in practical use.This paper proposes a scalable comparison system, which correlates the hypothetical security basis of post-quantum cryptography with the ability to effectively operate in the real world.It has emphasized protocol interoperability, migration compatibility and trade-offs in performance that gives a viable roadmap towards quantum-resistant cryptographic protocols implementation into current communication infrastructures whilst also providing scalable and future secure communication systems.This study, by emphasizing the potential and the drawbacks of the existing post-quantum cryptography schemes, helps in a more precise idea of the directions to follow on the way to a secure, future-proof communications scheme.