With the growing need for long-term secure communications in Internet-of-Things (IoT) and sensor-network environments, practical and robust post-quantum key-establishment mechanisms have become increasingly important. In this work, we revisit the ephemeral-only Ding key exchange (DKE) proposed at ACNS 2019, which is based on one-sample Ring Learning With Errors (Ring-LWE) with rounding, and the original analysis of which covers only passive security. Building on the DKE framework, we propose MoRo-KEM, a Module Learning With Errors (Module-LWE)-based key-encapsulation mechanism using rounding. First, we lift the construction from the Ring-LWE setting to the Module-LWE setting, retaining ring-level efficiency while enabling more flexible parameter choices and reducing reliance on rigid algebraic structure. Second, we replace discrete Gaussian sampling for secrets and errors with centered binomial sampling, thereby simplifying constant-time vectorized implementations while preserving the required noise behavior. Third, we extend the resulting key-exchange core to an IND-CPA-secure public-key encryption scheme and further obtain an IND-CCA-secure KEM via the Fujisaki-Okamoto transform. Finally, at security level I, MoRo-KEM achieves a decryption failure rate of 2-166, lower than the 2-139 reported for CRYSTALS-Kyber, thus improving robustness against decryption-failure attacks. These properties make the proposed design attractive for secure key establishment among sensor nodes, edge devices, and gateways operating under constrained computation, memory, and communication budgets. Overall, our construction provides a concrete path from ephemeral key exchange to a practical IND-CCA-secure KEM instantiated over Module-LWE.
With the growing need for long-term secure communications in Internet-of-Things (IoT) and sensor-network environments, practical and robust post-quantum key-establishment mechanisms have become increasingly important. In this work, we revisit the ephemeral-only Ding key exchange (DKE) proposed at ACNS 2019, which is based on one-sample Ring Learning With Errors (Ring-LWE) with rounding, and the original analysis of which covers only passive security. Building on the DKE framework, we propose MoRo-KEM, a Module Learning With Errors (Module-LWE)-based key-encapsulation mechanism using rounding. First, we lift the construction from the Ring-LWE setting to the Module-LWE setting, retaining ring-level efficiency while enabling more flexible parameter choices and reducing reliance on rigid algebraic structure. Second, we replace discrete Gaussian sampling for secrets and errors with centered binomial sampling, thereby simplifying constant-time vectorized implementations while preserving the required noise behavior. Third, we extend the resulting key-exchange core to an IND-CPA-secure public-key encryption scheme and further obtain an IND-CCA-secure KEM via the Fujisaki-Okamoto transform. Finally, at security level I, MoRo-KEM achieves a decryption failure rate of 2-166, lower than the 2-139 reported for CRYSTALS-Kyber, thus improving robustness against decryption-failure attacks. These properties make the proposed design attractive for secure key establishment among sensor nodes, edge devices, and gateways operating under constrained computation, memory, and communication budgets. Overall, our construction provides a concrete path from ephemeral key exchange to a practical IND-CCA-secure KEM instantiated over Module-LWE.
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.
The ongoing transition to Post-Quantum Cryptography (PQC) has highlighted the need for cryptographic schemes that offer high security, strong performance, and fine-grained parameter selection. In lattice-based cryptography, particularly for the popular module variants of learning with errors (Module-LWE) and learning with rounding (Module-LWR) schemes based on power-of-two cyclotomics, existing constructions often force parameter choices that either overshoot or undershoot desired security levels due to structural constraints. In this work, we introduce a new class of techniques that are the advantages of both worlds: structured Module-LWE (or LWR) embeds more algebraic structure than a module such that it significantly improves performance, yet less structure than a power-of-two cyclotomic ring such that it still enables more flexible and efficient parameter selection. We present two concrete instances: a construction based on a radical extension of a two-power cyclotomic field denoted radical Ring-LWE (RR-LWE) or Ring-LWR (RR-LWR), and a cyclotomic block-ring module lattice approach (BRM-LWE or BRM-LWR). These new structured Module-LWE and LWR reduce the required number of uniformly random bytes in its matrix by a factor up to the module rank and allow efficient NTT implementations while enabling more granular security-performance trade-offs. We analyze the security of these constructions, provide practical parameter sets, and present implementation results demonstrating a performance improvement of up to 37% compared to an optimized implementation of ML-KEM. Our techniques apply to both key encapsulation mechanisms and digital signature schemes, offering a pathway to more adaptable and performant PQC standards.
Following the completion of the NIST post-quantum cryptography standardization, Kyber has been adopted as a key encapsulation mechanism (KEM) for quantum-resistant communication. Although lattice-based KEMs provide strong security and efficiency, most existing designs restrict the cyclotomic ring dimension to powers of two, which limits parameter flexibility for heterogeneous and resource-constrained Internet of Things (IoT) devices. In this paper, we propose Fyber, a post-quantum KEM based on the Module Learning With Errors (M-LWE) problem over a module ring defined by the cyclotomic polynomial f(x)=xn−xn/2+1, where n is a product of powers of 2 and 3. This construction enables mixed-radix parameter selection and allows finer-grained trade-offs between security and efficiency. To further improve performance on constrained platforms, we introduce an efficient non-Gaussian sampling method. The proposed KEM supports flexible security-level stratification for IoT applications, achieving reduced public key and ciphertext sizes for selected parameter sets at the cost of moderately increased computational overhead compared to Kyber, and fills intermediate security gaps between existing standardized parameter sets.
The widespread use of Internet of Things devices alongside advances in quantum computing presents urgent challenges for secure communication. RSA and ECC have become inadequate, prompting the need for Post-quantum Cryptography (PQC). This work introduces a novel reconciliation-based Module-LWE key exchange protocol that eliminates the traditional encapsulation-decapsulation structure in schemes like Kyber.KE, thereby reducing computational cycles, communication size, and memory footprint. Unlike Kyber and NewHope, the proposed design employs modular rounding with Peikert reconciliation, optimizing the entire key exchange process without requiring additional randomness or ciphertext transmission. By leveraging Peikert’s error reconciliation technique and modular rounding, the proposed protocol achieves a 15% reduction in computational cycles, a 78-byte reduction in communication size, and a 10% decrease in memory usage. Using Open Quantum Safe (OQS) benchmark data, we evaluate performance across Kyber512, Kyber768, and Kyber1024 levels, demonstrating the protocol’s superior energy efficiency and lightweight design. These improvements position our protocol as a secure, efficient, and scalable solution for post-quantum key exchange in resource-constrained environments such as embedded systems and IoT networks.
Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digitalsignature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of postquantum security.
Lattice-based cryptography has emerged as a leading approach for post-quantum secure communication, particularly in key exchange mechanisms such as Key Encapsulation Mechanisms (KEMs). Prominent schemes based on Learning with Errors (LWE), Ring-LWE, Module-LWE, and NTRU lattices provide strong resistance to quantum attacks while maintaining practical efficiency. A key factor influencing their performance and security is polynomial sampling, which controls noise generation, randomness, and key distribution. This systematic review examines advancements in lattice-based key exchange mechanisms with a focus on optimized polynomial sampling techniques, based on 30 peer-reviewed studies. The approaches are categorized into algorithmic improvements, hardware acceleration, side-channel resistant sampling, and emerging intelligent optimization methods. Efficient polynomial arithmetic, Number Theoretic Transform (NTT)-based multiplication, and structured lattices significantly enhance performance. Optimized sampling techniques reduce computational cost and energy consumption while preserving statistical accuracy. However, polynomial sampling remains vulnerable to side-channel attacks such as timing and power analysis, prompting the use of countermeasures like constant-time and masked sampling. Hardware implementations further improve efficiency, though challenges persist in balancing scalability, security, and performance, highlighting the need for adaptive and robust solutions.