A Post-Quantum Key Encapsulation Mechanism Based on Structured Lattice Decoding

This paper introduces a high-performance post-quantum Key EncapsulationMechanism (KEM) leveraging structured lattice decoding primitives. The proposedscheme is grounded in a rigorous theoretical framework, providing explicit security reductions to the Module Ring Learning With Errors (Module-RLWE) assumption anda separate Pseudo-Random Generator (PRG) assumption for deterministic sampling.Key technical contributions include: (i) a canonical IND-CPA KEM constructionwhere key encapsulation is cryptographically decoupled from the underlying RLWErandomness; (ii) a formalized deterministic sampler (Expand) utilizing rejectionsampling with explicit smoothing parameter bounds; and (iii) a rigorous applicationof the Leftover Hash Lemma (LHL) supported by detailed min-entropy accounting.To ensure practical reliability, we replace traditional variance heuristics withhigh-probability norm conditioning for precise parameter selection. Furthermore,we provide a comprehensive hybrid reduction sequence with exact loss accounting and define the necessary conditions for an IND-CCA secure variant via theFujisaki-Okamoto transform. The mechanism is optimized for Number TheoreticTransform (NTT) implementations, achieving a balance between provable securityand computational efficiency on modern hardware.