In recent years, the advancement of quantum computing technology has posed potential security threats to RSA cryptography and elliptic curve cryptography. In response, the National Institute of Standards and Technology (NIST) published several Federal Information Processing Standards (FIPS) of post-quantum cryptography (PQC) in August 2024, including the Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM), Module-Lattice-Based Digital Signature Algorithm (ML-DSA), and Stateless Hash-Based Digital Signature Algorithm (SLH-DSA). Although these PQC algorithms are designed to resist quantum computing attacks, they may not provide adequate security in certain specialized application scenarios. To address this issue, this study proposes quantum random number generator (QRNG)-based PQC algorithms. These algorithms leverage quantum computing to generate random numbers, which serve as the foundation for key pair generation, key encapsulation, and digital signature generation. A generalized architecture of QRNG is proposed, along with the design of six QRNGs. Each generator is evaluated according to the statistical validation procedures outlined in NIST SP 800-90B, including tests for verification of entropy sources and independent and identically distributed (IID) outputs. Experimental results assess the computation time of the six QRNGs, as well as the performance of QRNG-based ML-KEM, QRNG-based ML-DSA, and QRNG-based SLH-DSA. These findings provide valuable reference data for future deployment of PQC-based Transport Layer Security in web systems.
In recent years, the advancement of quantum computing technology has posed potential security threats to RSA cryptography and elliptic curve cryptography. In response, the National Institute of Standards and Technology (NIST) published several Federal Information Processing Standards (FIPS) of post-quantum cryptography (PQC) in August 2024, including the Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM), Module-Lattice-Based Digital Signature Algorithm (ML-DSA), and Stateless Hash-Based Digital Signature Algorithm (SLH-DSA). Although these PQC algorithms are designed to resist quantum computing attacks, they may not provide adequate security in certain specialized application scenarios. To address this issue, this study proposes quantum random number generator (QRNG)-based PQC algorithms. These algorithms leverage quantum computing to generate random numbers, which serve as the foundation for key pair generation, key encapsulation, and digital signature generation. A generalized architecture of QRNG is proposed, along with the design of six QRNGs. Each generator is evaluated according to the statistical validation procedures outlined in NIST SP 800-90B, including tests for verification of entropy sources and independent and identically distributed (IID) outputs. Experimental results assess the computation time of the six QRNGs, as well as the performance of QRNG-based ML-KEM, QRNG-based ML-DSA, and QRNG-based SLH-DSA. These findings provide valuable reference data for future deployment of PQC-based Transport Layer Security in web systems.
Since the security of post-quantum cryptography (PQC) algorithms is based on the hardness of mathematical problems, while the security of quantum key distribution (QKD) relies on the fundamental principles of quantum physics, each approach possesses distinct advantages and limitations that can complement one another. Consequently, recent studies have proposed hybrid schemes that combine QKD and PQC to establish a dual-layered security model. In response to this trend, this study proposes hybrid schemes that integrate QKD with the National Institute of Standards and Technology (NIST) standardized PQC algorithms. These hybrid schemes include two core components: a hybrid QKD-PQC key exchange protocol and a hybrid QKD-PQC digital signature scheme. For the hybrid key exchange protocol, this study combines Module-Lattice-based Key Encapsulation Mechanisms (ML-KEM) with QKD protocols, specifically BB84 and E91, to construct a secure key exchange protocol. In the design of the hybrid digital signature scheme, this study utilizes Module-Lattice-based Digital Signature Algorithms (ML-DSA) and Stateless Hash-based Digital Signature Algorithms (SLH-DSA) to generate signature reconstruction values. These values are verified using confirmation codes transmitted via the BB84 and E91 protocols. The proposed hybrid key exchange protocol is evaluated by examining the shared secret key it produces, particularly with respect to entropy and whether the output is independent and identically distributed (IID). Furthermore, the computation time and message lengths of the proposed hybrid schemes are evaluated.
The impressively fast development of quantum computing is a serious threat to classical public-key cryptography, and algorithms such as Shor's and Grover's will render RSA and elliptic curve systems essentially useless as soon as a cryptanalytically relevant quantum computer becomes available. Although it is still some way off before such machines are available, the harvest-now-encrypt-later threat highlights the need for proactive defense. In response, the National Institute of Standards and Technology (NIST) published the first post-quantum cryptography standards in 2024, including ML-KEM (Kyber) for key establishment, ML-DSA (Dilithium) for digital signatures and SLH-DSA (SPHINCS+) as a stateless hash-based alternative. This paper is a summary of the evolving post-quantum landscape, starting with the standards and their underlying security and then moving on to migration policies such as CNSA 2.0 and CISA, NSA and NIST guidance. It also looks at integration patterns for important protocols such as TLS, IPsec, SSH, and code signing. A performance, interoperability and overhead evaluation methodology is presented with results showing that hybrid deployment and crypto-agile architectures make PQC adoption a viable option. The paper concludes by providing a governance-oriented roadmap, where inventory, prioritization and pilot deployments are identified as near-term actions, with open questions remaining on performance optimization, implementation security and algorithm resilience over time.
The transition to post-quantum cryptography (PQC) marks a pivotal shift in ensuring digital security, prompted by the potential of quantum computers to compromise classical systems such as Rivest-Shamir-Adlema and elliptic-curve cryptography. In response, NIST has standardized three foundational PQC algorithms: Module-lattice-based Key-encapsulation Mechanism for key establishment; Module-lattice-based Digital Signature, and Stateless Hash-based Digital Signature algorithms for digital signatures. Meanwhile, FALCON and Hamming Quasi-cyclic (HQC) schemes, both selected as finalists, are expected to join the standards soon. This paper presents a comprehensive survey of these NIST-selected PQC standards, with a dual focus on software implementations and hardware architecture designs. We analyze their mathematical frameworks, distinctive features, and optimization strategies related to performance, security, and resource efficiency. The software review examines algorithmic complexity, memory usage, and programming considerations, while the hardware review discusses FPGA and ASIC implementations, emphasizing modular arithmetic, polynomial operations, and resource efficiency challenges. A comparative analysis highlights the strengths and trade-offs of each algorithm, offering insights into their applicability across various platforms-from resource-constrained internet of things devices to high-performance computing environments. This study provides a foundational understanding of NIST’s selected PQC standards and their practical deployment in securing the post-quantum era.
Background: The imminent threat posed by cryptographically relevant quantum computers to classical public-key infrastructure specifically RSA and Elliptic-Curve Cryptography (ECC), whose security rests on the conjectured computational intractability of integer factorisation and the discrete logarithm problem respectively has propelled lattice-based cryptography to the centre of global post-quantum standardisation efforts. On 13 August 2024, the United States National Institute of Standards and Technology (NIST) published three landmark Federal Information Processing Standards (FIPS): FIPS 203 (ML-KEM, derived from CRYSTALS-Kyber), FIPS 204 (ML-DSA, derived from CRYSTALS-Dilithium), and FIPS 205 (SLH-DSA, derived from SPHINCS+), with FIPS 206 (FN-DSA, derived from FALCON) in advanced draft. The first three of these standards rest on algebraic structures intimately connected to classical number theory: polynomial rings over integer quotients, cyclotomic fields, and the algebraic geometry of ideal lattices in rings of integers of number fields. Objectives: This article provides: (1) a rigorous mathematical exposition of the lattice problems underpinning NIST’s post-quantum standards, specifically the Learning With Errors (LWE), Ring-LWE (RLWE), Module-LWE (MLWE), Short Integer Solution (SIS), and NTRU problems, and their connections to algebraic number theory; (2) a comparative performance analysis of NIST-standardised lattice-based algorithms against classical RSA and ECC benchmarks; (3) a security analysis examining known classical and quantum attacks on each hard problem; (4) a comparative evaluation of the four NIST-selected algorithms across key size, signature size, and computational benchmarks; and (5) a strategic assessment of the migration challenges facing deployed cryptographic infrastructure. Methods: The study synthesises peer-reviewed literature, NIST official standards documentation (FIPS 203, 204, 205, and draft FIPS 206), and independently published performance benchmarks published between June 2024 and June 2026. Mathematical security analysis is grounded in the worst-case to average-case reductions established by Regev (2005) for LWE and by Lyubashevsky, Peikert, and Regev (2013) [11, 18] for Ring-LWE. Performance data are drawn from Garani (2024) [8], the ARM Cortex-M0+ benchmarking study of Ratnayaka and Fischer (2026) [4], and the cross-platform evaluation by Alzahrani et al. (2025) [2]. Results: NIST’s three August 2024 standards establish a comprehensive lattice-based post-quantum portfolio. ML-KEM-768 produces a 1,184-byte public key and 1,088-byte ciphertext, achieving IND-CCA2 security under the MLWE assumption at NIST Level 3 (AES-192 equivalent). ML-DSA-65 produces 1,952-byte public keys and 3,309-byte signatures under the Module-LWE and Module-SIS assumptions at Level 3. FN-DSA-512 (FALCON, draft FIPS 206) produces 897-byte public keys and 666-byte signatures under the NTRU assumption, offering the most compact lattice-based signatures. Performance benchmarks on an Intel Core i7-12700K (3.6 GHz) confirm that ML-KEM key generation is orders of magnitude faster than RSA-3072 key generation. The algebraic structure of cyclotomic polynomial rings ∑₂ⁿ = Z[x]/(x^n + 1) is central to the efficiency of all three lattice-based NIST standards. Conclusion: Lattice-based cryptography, grounded in the algebraic number theory of ideal lattices over cyclotomic fields, provides the most comprehensive and mathematically well-founded response to the quantum computational threat. The August 2024 NIST standardisation of ML-KEM, ML-DSA, and SLH-DSA represents a landmark in cryptographic history, and the imminent finalisation of FN-DSA will complete the post-quantum toolbox. Organisations should prioritise immediate migration planning, leveraging hybrid classical-quantum schemes during transition, with full transition to NIST post-quantum standards recommended by 2030 per NSA and CISA guidance.
The prospect of cryptographically relevant quantum computers threatens public-key primitives underpinning modern digital infrastructure, including RSA, Diffie-Hellman, and elliptic-curve cryptography. Post-quantum cryptography (PQC) responds with algorithms believed to be hard for both classical and quantum adversaries. In August 2024, the U.S. National Institute of Standards and Technology (NIST) finalised the first three PQC standards: FIPS 203 (ML-KEM, based on Kyber), FIPS 204 (ML-DSA, based on Dilithium), and FIPS 205 (SLH-DSA, based on SPHINCS+). This paper surveys the algorithmic families behind these standards, the harvest-now-decrypt-later threat model, hybrid migration strategies, performance trade-offs, and the engineering challenges of transitioning the global cryptographic stack. We examine deployment progress in TLS, SSH, X.509, and constrained devices, and outline open research questions on side-channel security, falcon-style signatures, and the long-term replacement schedule for classical asymmetric cryptography.
Purpose: The purpose of this paper is to examine the emerging threat that large-scale quantum computing poses to classical public-key cryptographic systems, particularly RSA and Elliptic Curve Cryptography (ECC), which form the backbone of contemporary digital security infrastructures. In response to this threat, the study aims to analyze post-quantum cryptography (PQC) as a viable long-term solution capable of resisting both classical and quantum adversaries. The paper further seeks to assess the urgency of PQC adoption in light of the “harvest now, decrypt later” threat model and to evaluate the practical readiness of quantum-safe cryptographic algorithms currently under consideration by the National Institute of Standards and Technology (NIST). Materials and Methods: This study employs a qualitative and analytical research methodology grounded in an extensive review of authoritative sources, including NIST’s post-quantum cryptography standardization documents, recent academic literature, industry white papers, and policy reports from organizations such as RAND Corporation and Cloudflare. The analysis systematically surveys major families of post-quantum cryptographic algorithms namely lattice-based, code-based, and hash-based schemes and evaluates them based on security assumptions, computational efficiency, implementation complexity, and standardization maturity. Findings: The analysis indicates that Lattice-based cryptographic schemes demonstrate the highest maturity and practical readiness, evidenced by their selection in NIST’s PQC process. Code- and hash-based methods provide strong security but face key size and performance challenges. The lack of scalable quantum computers does not reduce urgency, as data harvesting persists. Artificial intelligence emerges as a key enabler for accelerating PQC adoption. Unique Contribution to Theory, Practice and Policy: The paper recommends a proactive, phased post-quantum migration using hybrid cryptographic architectures. Organizations should conduct inventories, benchmarking, and pilot deployments aligned with NIST standards. AI-driven tools are advised to improve key management and reduce complexity. Continued interdisciplinary research and policy support are encouraged to ensure a secure, scalable transition to quantum-resistant security systems.