NIST’s Module-Lattice-Based Key-Encapsulation Mechanism and its security
Year: 2025
Type: article
Abstract: This thesis is an in-depth introduction to NIST's post-quantum Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM). We begin by introducing the problem at the core of ML-KEM, known as the Module Learning With Errors (MLWE) problem. In this problem, an adversary attempts to distinguish between samples selected from a specific distribution and samples from uniformly random samples. We also discuss the hardness of the MLWE problem, under the conjecture that certain lattice problems over modules are hard. ML-KEM utilizes a variant of the Fujisaki-Okamoto transformation, which employs a weakly secure Public-Key Encryption (PKE) scheme to construct a strongly secure key-encapsulation mechanism in the Random Oracle Model (ROM). We explain the working principle of the MLWE-based public-key encryption scheme and demonstrate how ML-KEM is constructed from it. Finally, we analyze the security of ML-KEM. We provide a tight security bound for IND-CCA security of ML-KEM in ROM, under the assumption that the underlying PKE is IND-CPA secure. Additionally, we present two security theorems in the Quantum Random Oracle Model (QROM). The first theorem establishes non-tightly IND-CCA security of ML-KEM in QROM if the MLWE problem is hard to solve. The second theorem assumes that the deterministic PKE is ciphertext-indistinguishable. Under this assumption, we derive a tighter bound for the IND-CCA security of ML-KEM in QROM.
Source: Työväentutkimus Vuosikirja
Author: Jokiniemi, Anna
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7197479064