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DualSecure Key Exchange (DSKE): A Hybrid ECDH-SIDH Protocol for Post-Quantum Cryptography

Veera Reddy Dasari, Padmaja Madugula

Published Feb 2, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.31449/inf.v50i5.8214

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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.
The emergence of quantum computing poses a significant threat to the security of currently deployed public-key cryptosystems, including those based on elliptic curves (ECC). Shor's algorithm can solve the underlying integer factorization and discrete logarithm problems in polynomial time, rendering established cryptographic standards obsolete. This has catalyzed the development of post-quantum cryptography (PQC), a new generation of algorithms resistant to attacks by both classical and quantum computers. Among the most promising PQC candidates are systems based on supersingular isogeny graphs. This paper provides a comprehensive analysis of the supersingular isogeny paradigm as a quantum-secure evolution of elliptic curve cryptography. It begins by introducing the mathematical foundations of elliptic curves and isogenies, which are structure-preserving maps between them. The core of isogeny-based cryptography lies in the conjectured hardness of finding an isogeny path between two given supersingular elliptic curves in the vast isogeny graph. This is fundamentally different from the discrete logarithm problem that underpins traditional ECC. We review the foundational Supersingular Isogeny Diffie-Hellman (SIDH) key exchange protocol and its subsequent realization as the Supersingular Isogeny Key Encapsulation (SIKE) mechanism, which was a candidate in the NIST PQC standardization process. We discuss its advantages, such as small key sizes and perfect forward secrecy, which made it an attractive alternative. However, the paper also presents a balanced view by thoroughly examining the devastating cryptanalytic breakthroughs of 2022 that rendered the original SIDH/SIKE schemes insecure. These attacks, which exploit auxiliary point information, underscore the dynamic nature of PQC research. Despite this setback, the isogeny-based field remains active, with ongoing research into alternative constructions like CSIDH and other variants that are not vulnerable to the known attacks. We conclude that while the initial promise of SIDH/SIKE was broken, the underlying mathematical problem of finding isogenies remains a compelling basis for quantum-secure cryptography, representing a paradigm of active research rather than a discarded concept.
The rise of quantum computing poses a significant threat to contemporary public-key cryptography, which relies on problems like integer factorization and the discrete logarithm, both of which are solvable in polynomial time by Shor's algorithm. This has prompted a global effort to develop and standardize post-quantum cryptographic primitives that are resistant to attacks by both classical and quantum computers. Among the various families of post-quantum candidates, isogeny-based cryptography has emerged as a particularly compelling, albeit challenging, alternative. This paper explores the mathematical foundations of elliptic curve isogenies and their application as a basis for quantum-resistant cryptographic protocols. We delve into the structure of supersingular elliptic curves and the associated isogeny graphs, which form the basis for the conjectured hardness of the underlying computational problems. The Supersingular Isogeny Diffie-Hellman (SIDH) protocol and its derivative, Supersingular Isogeny Key Encapsulation (SIKE), are examined in detail as principal examples of this cryptographic paradigm. We analyze their key advantages, most notably their exceptionally small key sizes, which offer significant benefits for constrained environments. However, the security landscape of isogeny-based cryptography has been dramatically reshaped by recent cryptanalytic breakthroughs that completely broke the SIKE protocol. This paper analyzes the nature of these attacks, discussing the vulnerabilities they exploited and the profound implications for the field. We conclude by surveying the current state of isogeny-based cryptography in the aftermath of these developments, outlining the proposed countermeasures, alternative designs, and the open research questions that define the new frontier for this promising area of post-quantum cryptography.
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.
Quantum key cryptography is the cryptography that has capability to overcome the threat of quantum computing in future when exploited by adversaries. With quantum computers in the hands of adversaries in future, the existing security schemes might be broken due to massive computing power. As security is not one-time effort, it is a continuous process that needs development of stronger security schemes. Existing PQC schemes focused on either data security or key exchange. Besides, there is need for further improvement towards enhanced PQC primitives. In this paper, we proposed an integrated cloud data security framework with novel schemes towards PQC. For data security with encryption and decryption, we proposed Hybrid Encoding and Data Transformation (HEDT) algorithm. Another key exchange security scheme called Elliptic Curve Super singular Isogeny Diffie–Hellman (ECSIDH) was developed. The key agreement scheme consists of Elliptic-Curve Diffie–Hellman (ECDH) and Super singular Isogeny Diffie–Hellman (SIDH). ECDH combined with SIDH candidate in PQC which enhances the security of the proposed scheme since they strengthen the ECDH with PQC candidate SIDH. The ECSIDH is found more secure than individual key exchange scheme such as SIDH. Security analysis of HEDT revealed that it is more secure than existing algorithms and ECSIDH is more secure PQC candidate.
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 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.