Many practical security applications rely on inherently noisy data sources, such as biometric measurements, sensor-derived features, and physical unclonable functions (PUFs). This variability makes it difficult to develop reliable cryptographic primitives. Conventional solutions-like fuzzy commitment schemes, fuzzy vaults, secure sketches, and fuzzy extractors-enable key binding or generation from noisy data by combining cryptography with error-correcting codes to handle variations. However, using ECCs can cause information leakage. In this paper, we construct ISNR-PQC, an isometry noise resilient post-quantum cryptographic primitive designed for natural noisy sources, using secure biometric data as an application. ISNR-PQC specifically uses lattice-based cryptography based on the National Institute of Standards and Technology (NIST) standard FIPS 203. Our approach provides security guarantees against quantum adversaries under the Learning with Errors (LWE) assumption. We formalise correctness, robustness, and [Formula: see text]-restricted IND-CPA indistinguishability in a unified security model. Our ISNR-PQC is noise resilient because it accepts ancillary data that is close to the original encrypting data, as measured by an isometry-based threshold mapping. Our results demonstrate that ISNR-PQC addresses a major challenge in biometric authentication theory and is a promising base for future biometric and noisy-data security systems.
Many practical security applications rely on inherently noisy data sources, such as biometric measurements, sensor-derived features, and physical unclonable functions (PUFs). This variability makes it difficult to develop reliable cryptographic primitives. Conventional solutions-like fuzzy commitment schemes, fuzzy vaults, secure sketches, and fuzzy extractors-enable key binding or generation from noisy data by combining cryptography with error-correcting codes to handle variations. However, using ECCs can cause information leakage. In this paper, we construct ISNR-PQC, an isometry noise resilient post-quantum cryptographic primitive designed for natural noisy sources, using secure biometric data as an application. ISNR-PQC specifically uses lattice-based cryptography based on the National Institute of Standards and Technology (NIST) standard FIPS 203. Our approach provides security guarantees against quantum adversaries under the Learning with Errors (LWE) assumption. We formalise correctness, robustness, and [Formula: see text]-restricted IND-CPA indistinguishability in a unified security model. Our ISNR-PQC is noise resilient because it accepts ancillary data that is close to the original encrypting data, as measured by an isometry-based threshold mapping. Our results demonstrate that ISNR-PQC addresses a major challenge in biometric authentication theory and is a promising base for future biometric and noisy-data security systems.
The advent of quantum computing poses a significant existential threat to current public-key cryptographic standards, particularly RSA and Elliptic Curve Cryptography (ECC), which underpin global digital security. Shor's algorithm, if implemented on a sufficiently powerful quantum computer, can efficiently break these foundational schemes, rendering vast amounts of encrypted data vulnerable. This paper investigates lattice-based cryptography as a robust and promising candidate for post-quantum security. We provide a comprehensive analysis of its theoretical underpinnings, focusing on hard problems like the Shortest Vector Problem (SVP) and Learning With Errors (LWE), which are believed to be intractable even for quantum adversaries. Through a detailed literature review and methodological exposition, we examine the construction principles of prominent lattice-based Key Encapsulation Mechanisms (KEMs) and digital signature schemes, such as Kyber and Dilithium, highlighting their inherent security properties and performance characteristics. Our results demonstrate that lattice-based schemes offer competitive efficiency, compact key sizes, and strong security guarantees against both classical and quantum attacks, positioning them as essential building blocks for the post-RSA cryptographic landscape. The discussion elaborates on the practical implications, standardization efforts by NIST, and the challenges associated with the transition to quantum-resilient cryptographic infrastructure. We conclude that lattice-based cryptography is a cornerstone of quantum resilience, critical for securing future digital communications and data integrity.
The advent of quantum computing poses a significant existential threat to current public-key cryptographic systems, most notably RSA and Elliptic Curve Cryptography (ECC), which rely on the presumed hardness of integer factorization and discrete logarithm problems. Shor's algorithm, a quantum algorithm, can efficiently solve these problems, rendering classical asymmetric primitives insecure. This paper addresses the imperative need for post-quantum cryptography (PQC) by exploring lattice-based constructs as robust alternatives for asymmetric primitives. We provide a comprehensive overview of the fundamental mathematical problems underlying lattice-based cryptography, such as the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), Learning With Errors (LWE), and Ring Learning With Errors (RLWE). The paper surveys prominent lattice-based schemes, including NTRU, CRYSTALS-Kyber, and CRYSTALS-Dilithium, analyzing their security foundations, performance characteristics, and the extent to which they offer a viable "post-quantum RSA." We delve into the methodology of constructing these primitives, discuss their resilience against both classical and quantum attacks, and evaluate their practical implications for key sizes, computational efficiency, and deployment challenges. Our analysis highlights that lattice-based cryptography, particularly the NIST-standardized schemes, presents a strong candidate for securing digital communications in the quantum era, offering provable security rooted in worst-case to average-case reductions for lattice problems.
The transition to post-quantum cryptography (PQC) based on the Learning with Errors (LWE) problem suffers from a critical epistemological gap: its security is predicated on transient computational bottlenecks, not information-theoretic permanence, making it vulnerable to mature quantum algorithms like Gottesman-Kitaev-Preskill (GKP) error correction. This critique argues that absolute quantum resilience requires a pivot to inherently hybrid architectures that systematically combine LWE's computational efficiency with the absolute, physics-bound security of Quantum Key Distribution (QKD) and Physical Random Oracles (PROs), such as Physical Unclonable Functions (PUFs). This volume details these hybrid primitives, addressing structural vulnerabilities in standard PQC and QKD. Key architectural syntheses include the Lattice PUF, which provably binds ML-modeling resistance to the LWE problem hardness using PAC theory, and Quantum-Locked Physical Mamun, SM (2026) …………………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Hybrid Info-Theoretic and Computational Primitives (Vol-II) K S C Primitives (HLPUF, HEPUF), which utilize conjugate coding and entanglement to provide authentication guarantees independent of algorithmic hardness. Also available on Academia.edu: https://www.academia.edu/attachments/132761055/download_file?s=portfolio
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.
The advent of quantum computing poses a significant threat to current cryptographic systems, particularly public-key algorithms such as RSA and ECC, which are vulnerable to quantum attacks like Shor's algorithm. Post-Quantum Cryptography (PQC) aims to develop and standardize quantum-resistant cryptographic algorithms to secure digital communications in the quantum era. This paper examines the current landscape of PQC, focusing on the evaluation and standardization efforts led by organizations such as the National Institute of Standards and Technology (NIST). We analyze the major families of quantum-resistant algorithms, including lattice-based, hash-based, code-based, multivariate, and isogeny-based cryptography, discussing their security guarantees, performance trade-offs, and implementation challenges. Furthermore, we review NIST's PQC standardization process, highlighting selected finalists and alternate candidates, and explore the ongoing transition challenges in adopting these algorithms across industries. Finally, we discuss future directions for PQC research, including hybrid cryptographic systems and the need for continued cryptanalysis to ensure long-term security. This work provides a comprehensive overview of the progress and challenges in deploying quantum-resistant cryptography to safeguard against emerging quantum threats.
This paper delves into lattice-based cryptography as a cornerstone of post-quantum cryptography (PQC), exploring its evolution, key principles, and applications. It examines how lattice-based schemes leverage the inherent hardness of problems such as the Shortest Vector Problem (SVP) and Learning With Errors (LWE) to provide quantum-resistant encryption, digital signatures, and homomorphic encryption. The paper also outlines the historical development of lattice-based cryptography, emphasizing its resilience to quantum attacks in contrast to traditional schemes like RSA and ECC, which are vulnerable to Shor's algorithm. Core concepts, including lattice trapdoors, parameter optimization, and real-world applications in blockchain, cryptocurrencies, and secure communication protocols, are explored in detail. Furthermore, the paper highlights ongoing standardization efforts led by NIST, ethical considerations, practical challenges, and future research directions aimed at improving efficiency, ensuring interoperability, and expanding lattice cryptography’s use in advanced security frameworks. Through comprehensive analysis, this research underscores the importance of lattice-based cryptography as a critical pillar for securing the digital ecosystem against the emerging threat of quantum computing.