Quantum Resistant Public Key Exchange-The Supersingular Isogenous Diffie-Hellman Protocol

Chukhu Chunka, Subhasish Banerjee, Soumyajit Nag +1 more

Markus Alvila

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.

Mao Mao, Shaowu, Zhang +9 more

Veera Reddy Dasari, Padmaja Madugula

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.

Mohammed Abdul Nayeem

Yang Li, Rui-Rui Zhou