The advent of large-scale quantum computing poses a fundamental threat to classical public-key cryptographic systems underpinning modern digital infrastructure.Widely deployed schemes such as RSA and elliptic curve cryptography rely on computational hardness assumptions-integer factorization and discrete logarithms-that are vulnerable to quantum algorithms such as Shor's algorithm.As critical infrastructure systems increasingly depend on secure communication, authentication, and data integrity mechanisms, the transition to quantum-resistant cryptography has become an urgent national and global priority.This paper examines the mathematical foundations of post-quantum cryptography (PQC) and their application to data protection in critical infrastructure environments, analyzes core hardness assumptions underlying leading PQC families, proposes a quantum-readiness framework for critical infrastructure sectors, and presents empirical benchmarking results across energy, healthcare, financial, and transportation systems.By integrating rigorous mathematical analysis with experimental performance data, this work provides a structured roadmap for transitioning mission-critical systems toward quantum-resilient data protection architectures.
The advent of large-scale quantum computing poses a fundamental threat to classical public-key cryptographic systems underpinning modern digital infrastructure.Widely deployed schemes such as RSA and elliptic curve cryptography rely on computational hardness assumptions-integer factorization and discrete logarithms-that are vulnerable to quantum algorithms such as Shor's algorithm.As critical infrastructure systems increasingly depend on secure communication, authentication, and data integrity mechanisms, the transition to quantum-resistant cryptography has become an urgent national and global priority.This paper examines the mathematical foundations of post-quantum cryptography (PQC) and their application to data protection in critical infrastructure environments, analyzes core hardness assumptions underlying leading PQC families, proposes a quantum-readiness framework for critical infrastructure sectors, and presents empirical benchmarking results across energy, healthcare, financial, and transportation systems.By integrating rigorous mathematical analysis with experimental performance data, this work provides a structured roadmap for transitioning mission-critical systems toward quantum-resilient data protection architectures.
The rapid development of quantum computing technologies poses a serious threat to modern public-key cryptographic systems. Classical cryptographic algorithms such as RSA and elliptic-curve cryptography rely on mathematical problems that can be efficiently solved using quantum algorithms. Post-quantum cryptography (PQC) aims to develop cryptographic schemes that remain secure even in the presence of quantum adversaries. This paper investigates the mathematical foundations of PQC, focusing on lattice-based, code-based, and hash-based cryptographic constructions. Security models based on computational complexity theory are analyzed, and illustrative examples using Learning With Errors (LWE) and decoding problems are presented. Experimental analysis demonstrates that PQC schemes provide strong resistance against both classical and quantum attacks when appropriate parameters are selected. The results highlight the importance of adopting new cryptographic standards to ensure long-term data security in quantum computing environments.
The accelerating development of quantum computing represents one of the most significant paradigm shifts in the history of information security. Cryptographic systems that currently underpin global digital infrastructure—including RSA, Diffie–Hellman, and Elliptic Curve Cryptography—rely on mathematical assumptions that collapse under quantum algorithms such as Shor’s and Grover’s. Post-Quantum Cryptography (PQC) emerges as the most viable and immediate solution to secure communications in the quantum era, offering cryptographic primitives that can be deployed on today’s classical hardware while resisting both classical and quantum attacks. This review provides a comprehensive, detailed examination of PQC, analyzing its mathematical foundations, algorithmic families, standardization progress, and deployment challenges. Special emphasis is placed on the NIST PQC standardization process, the risk posed by “harvest-now-decrypt-later” adversaries, the complexities of global cryptographic migration, and the implications for critical digital infrastructures such as cloud computing, blockchain systems, long-lifespan data archives, IoT ecosystems, and national cybersecurity. Through standalone equations, tables, and figures—including a conceptual visual provided by the user—this paper offers a complete, cohesive, and rigorous synthesis. The findings underscore that the transition to PQC is not optional but imperative, requiring coordinated scientific, governmental, and industrial effort to safeguard the digital future.
The rapid advancement of quantum computing introduces unprecedented security threats to modern cloud and edge computing infrastructures. Classical public-key cryptographic algorithms such as RSA, Diffie–Hellman, and Elliptic Curve Cryptography (ECC) are fundamentally vulnerable to quantum attacks enabled by Shor’s algorithm. As a result, the confidentiality, integrity, and authenticity of data stored and processed in distributed systems are at serious risk.Post-quantum cryptography (PQC) aims to develop cryptographic algorithms that are resistant to both classical and quantum adversaries. This paper presents a comprehensive quantum-resilient cryptographic framework designed specifically for post-quantum cloud and edge computing environments. The framework integrates post-quantum cryptographic primitives, hybrid cryptographic approaches, crypto-agile architectures, and secure key management mechanisms. The proposed framework addresses performance constraints, scalability requirements, and deployment challenges in heterogeneous environments. A detailed discussion of security threats, architectural components, performance considerations, and future research directions is provided. The proposed approach enables longterm security and supports a smooth transition toward quantum-safe distributed computing systems.
The rapid advancement of quantum computing presents a significant challenge to classical cryptographic systems that underpin modern digital security infrastructures. In particular, RSA-2048 encryption, widely deployed in banking and financial institutions for secure transactions, relies on the computational hardness of integer factorization. However, the emergence of quantum algorithms—especially Shor’s algorithm—poses a fundamental threat to RSA security by enabling polynomial-time factorization of large integers on sufficiently powerful quantum computers. This case study investigates the vulnerability of RSA-2048 within a banking environment, analyzing the mathematical foundations of the threat, potential timelines for quantum feasibility, and associated cybersecurity risks. The study further examines the implications for financial data protection, digital signatures, and secure communication channels. In response to these emerging risks, the paper explores post-quantum cryptographic alternatives, including lattice-based, hash-based, and code-based schemes, and evaluates their suitability for banking applications. The findings emphasize the urgency of transitioning toward quantum-resistant cryptographic frameworks and propose strategic recommendations for proactive cryptographic migration to ensure long-term data confidentiality and system resilience.
The advent of quantum computing poses a significant threat to contemporary cryptographic systems underpinning national security infrastructures globally. Classical public-key cryptographic algorithms such as RSA and ECC, which secure communications, data storage, and critical infrastructure, are vulnerable to quantum attacks, particularly through Shor’s algorithm. Post-Quantum Cryptography (PQC) aims to develop quantum-resistant cryptographic primitives to ensure confidentiality, integrity, and authentication in the quantum era. This article explores the implications of PQC adoption for national security, including the challenges of transitioning legacy systems, potential vulnerabilities during migration, and the strategic importance of standardizing PQC protocols to safeguard military, governmental, and critical infrastructure communications. The article also discusses policy recommendations for governments to mitigate emerging quantum risks.
The advent of large-scale quantum computers poses a profound and imminent threat to the foundational public-key cryptographic systems that secure modern digital communication, including RSA and Elliptic Curve Cryptography (ECC). These widely deployed algorithms rely on the computational intractability of factoring large integers and solving discrete logarithm problems, which are known to be efficiently solvable by Shor's algorithm on a sufficiently powerful quantum computer. This paper explores the transition to a post-quantum cryptographic (PQC) era, with a particular focus on lattice-based cryptography as a leading candidate for quantum-resistant solutions. We provide a comprehensive overview of the quantum threat, delve into the mathematical underpinnings of lattice problems, and examine prominent lattice-based schemes such as Kyber, Dilithium, and NTRU. Through a detailed literature review, theoretical analysis, and comparison with other PQC families, we highlight the security properties, efficiency considerations, and implementation challenges of lattice-based cryptography. The paper discusses the ongoing standardization efforts, particularly by the US National Institute of Standards and Technology (NIST), and evaluates the suitability of lattice-based schemes for securing critical infrastructure in the face of quantum adversaries. We conclude by emphasizing the urgency of cryptographic migration and the pivotal role lattice-based solutions are poised to play in safeguarding digital security in the post-RSA era.