This paper introduces an optimized policy on using polynomials sampling strategy in lattice-based key exchange protocols based on the hardness of Ring-LWE and Module-LWE. The suggested approach presents a discrete distribution that is refined and minimizes the rejection probability without loss of statistical indistinguishability and cryptographic security. The scheme combines inverse transform sampling with variable control bound that is constrained, and thus, it minimizes computation loads that are required by the conventional Gaussian sampling schemes. Compared to 148 µs sampling time and 7.8% rejection rate, experimental assessment shows that sampling time has been reduced by a factor of 32.6 (92 µs) and the rejection rate has decreased by 2.9 (2.9). The methodology retains the same degree of the polynomials and security assurances and enhances resource-constrained performance. When compared, improved performance is established at the expense of traditional sampling mechanisms without sacrificing the post-quantum resilience. The suggested optimization can be applied to real-time cryptographic implementations in IoT and embedded-systems that need low-latency secure communication.
This paper introduces an optimized policy on using polynomials sampling strategy in lattice-based key exchange protocols based on the hardness of Ring-LWE and Module-LWE. The suggested approach presents a discrete distribution that is refined and minimizes the rejection probability without loss of statistical indistinguishability and cryptographic security. The scheme combines inverse transform sampling with variable control bound that is constrained, and thus, it minimizes computation loads that are required by the conventional Gaussian sampling schemes. Compared to 148 µs sampling time and 7.8% rejection rate, experimental assessment shows that sampling time has been reduced by a factor of 32.6 (92 µs) and the rejection rate has decreased by 2.9 (2.9). The methodology retains the same degree of the polynomials and security assurances and enhances resource-constrained performance. When compared, improved performance is established at the expense of traditional sampling mechanisms without sacrificing the post-quantum resilience. The suggested optimization can be applied to real-time cryptographic implementations in IoT and embedded-systems that need low-latency secure communication.
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.
This paper offers a lattice-based digital signature construction, optimized for the provision of post-quantum security in resource-constrained environments, such as Internet of Things (IoT) devices. The offered scheme is built upon structured hardness assumptions, defined over polynomial rings that exhibit inherent algebraic symmetry. By exploiting the cyclic properties of these ring structures and implementing efficient Number Theoretic Transforms (NTTs), the construction achieves compact signatures that are under 3 KB and a runtime feasibility that uses less than 10 KB of RAM. The signature generation process incorporates balanced rejection sampling and carefully designed polynomial encodings that preserve structural regularity and computational efficiency. The security of the offered scheme is proven. The benchmark results generated from using the ARM Cortex-M4 platform demonstrate its practical usability. This study highlights how symmetric algebraic frameworks based on lattice-based cryptography can be leveraged to achieve both theoretical security and real-world performance in the post-quantum era.
Lattice-based cryptography offers some of the most attractive primitives believed to be resistant to quantum computers. Following increasing interest from both companies and government agencies in building quantum computers, a number of works have proposed instantiations of practical post-quantum key exchange protocols based on hard problems in ideal lattices, mainly based on the Ring Learning With Errors (R-LWE) problem. While ideal lattices facilitate major efficiency and storage benefits over their non-ideal counterparts, the additional ring structure that enables these advantages also raises concerns about the assumed difficulty of the underlying problems. Thus, a question of significant interest to cryptographers, and especially to those currently placing bets on primitives that will withstand quantum adversaries, is how much of an advantage the additional ring structure actually gives in practice. Despite conventional wisdom that generic lattices might be too slow and unwieldy, we demonstrate that LWE-based key exchange is quite practical: our constant time implementation requires around 1.3ms computation time for each party; compared to the recent NewHope R-LWE scheme, communication sizes increase by a factor of 4.7x, but remain under 12 KiB in each direction. Our protocol is competitive when used for serving web pages over TLS; when partnered with ECDSA signatures, latencies increase by less than a factor of 1.6x, and (even under heavy load) server throughput only decreases by factors of 1.5x and 1.2x when serving typical 1 KiB and 100 KiB pages, respectively. To achieve these practical results, our protocol takes advantage of several innovations. These include techniques to optimize communication bandwidth, dynamic generation of public parameters (which also offers additional security against backdoors), carefully chosen error distributions, and tight security parameters.
The advancement of quantum computing poses a significant threat to classical cryptographic algorithms, particularly those based on factorization and discrete logarithm problems. In this paper, we propose a secure and quantum-resistant key exchange scheme leveraging the FrodoKEM algorithm, a lattice-based post-quantum key encapsulation mechanism designed to resist attacks from quantum adversaries. FrodoKEM, being based on the Learning with Errors (LWE) problem, offers a conservative and standard approach to post-quantum cryptography without relying on structured lattices. We compare the performance and security of the proposed scheme against traditional key exchange mechanisms such as RSA and Elliptic Curve Diffie-Hellman (ECDH), as well as other post-quantum algorithms like Kyber and NTRU. Our analysis demonstrates that FrodoKEM offers improved security assurances and competitive performance metrics, especially in environments where long-term confidentiality and forward secrecy are critical. The experimental results affirm FrodoKEM's suitability for real-world deployment in post-quantum secure communications.
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.
The rapid advancement of quantum computing poses a significant threat to modern cryptographic systems, with algorithms such as Shor's, which can break RSA and ECC, and Grover's, which can weaken symmetric-key systems. In response, post-quantum cryptography aims to develop secure protocols resilient to quantum attacks. This paper introduces a lattice-based key generation mechanism that combines the Ring Learning With Errors (RLWE) problem with ECC. Using the secp256r1 curve, ECC keys are transformed into polynomials suitable for RLWE-based cryptographic schemes via KECCAK hash functions. The performance of this hybrid approach is assessed through key generation time and CPU cycle analysis, demonstrating its efficiency and potential for post-quantum cryptography.