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Lecture notes in computer science

The Best of Both KEMs: Securely Combining KEMs in Post-quantum Hybrid Schemes

Gorjan Alagic, Fahran Bajaj, Aybars Kocoglu

Published Jul 21, 2026• 2 citations
Publisher
DOI
10.1007/978-3-032-32560-0_2

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Abstract The rapid progress of quantum computing threatens widely deployed public-key cryptosystems such as RSA and Diffie–Hellman, accelerating the transition toward post-quantum cryptography (PQC). During this migration, hybrid key encapsulation mechanisms (KEMs) that combine classical and post-quantum primitives are strongly recommended by standardization bodies and cybersecurity agencies. However, existing hybrid designs mainly focus on combining post-quantum KEMs with Diffie–Hellman–style constructions, while the systematic integration of standardized classical public-key encryption (PKE) schemes with post-quantum KEMs remains largely unexplored. In this work, we introduce two generic hybrid constructions, and , that combine a classical PKE scheme with a post-quantum KEM satisfying ciphertext second-preimage resistance (C2PRI). We prove that both constructions achieve IND-CCA security in the standard model. The refined construction additionally relies on a new security notion of the classical PKE scheme, termed partial ciphertext second-preimage resistance (PC2PRI), which captures second-preimage resistance when a designated ciphertext component is fixed. This new property enables shared-key derivation from only a designated PKE ciphertext component in . Finally, we provide a systematic analysis of the PC2PRI property for several standardized classical encryption schemes, including ECIES, PSEC, and SM2.
Traditional public-key cryptography algorithms, such as Elliptic Curve Diffie-Hellman (ECDH), are vulnerable to quantum computing attacks. More critically, security protocols based on these algorithms are exposed to the “Harvest Now, Decrypt Later” threat, an ongoing risk that emphasizes the urgency of transitioning to post-quantum cryptography. This transition presents a significant challenge for lightweight security protocols, such as Ephemeral Diffie-Hellman over COSE (EDHOC), which are designed for IoT environments. To address this, a PQ/T hybrid key exchange construction for EDHOC is proposed, combining post-quantum mechanisms alongside traditional algorithms to mitigate future quantum threats while remaining secure against current threats using well-established classical cryptography. The scheme is evaluated on a CortexM4 processor, demonstrating the best performance with ML-KEM-512, with a slight increase in processing time, limited RAM overhead, and a roughly sevenfold increase in message size. Despite these trade-offs, the hybrid construction remains practical and represents a viable option for enhancing EDHOC security in anticipation of the post-quantum era in constrained environments.
Hybrid key establishment runs a post-quantum key-encapsulation mechanism (KEM) alongside a classical Diffie-Hellman primitive, so that the session key stays secure while either component resists attack. This design is now standardized in the Transport Layer Security protocol, Secure Shell, and the Internet Key Exchange, with the standardized module-lattice KEM (ML-KEM) as the post-quantum component. A hybrid KEM secures the derived key, but not the integrity of the negotiation that selects which primitives are used. Full protocols authenticate that negotiation through a handshake transcript; a hybrid KEM deployed as a standalone drop-in primitive, or inside a minimal handshake without transcript authentication, inherits no such guarantee, and an active attacker can strip the post-quantum option. We ask what the key schedule alone must contain to make downgrade resilience a local property of the combiner. We give a game-based definition at the combiner layer and prove a two-sided separation: a combiner that ignores the transcript is downgraded with certainty, whereas one that binds the session key and the confirmation tag to a hash of the transcript blocks every such attempt, up to a term negligible for a 256-bit transcript hash. We also give an explicit strongest-link security bound. Using a calibrated cost model composed from published Cortex-M4 measurements, transcript binding adds one hash per party - about 11.8% of handshake computation but only 1.5% of radio-inclusive energy - and adds no messages or bytes on the wire. Every reported number is produced by a released harness that passes a 30-check validation gate.