Quantum computing endangers classical cryptography via two main avenues: Shor’s al-gorithm reduces integer factorization to polynomial time, and Grover’s algorithm yields a quadratic speed-up for unstructured key search. We develop rigorous mathematical treatment of both algorithms, enrich the literature survey with detailed complexity and resource analyses, and extend the development section to include quantum er-ror-correction overhead, resource estimates for breaking 2048-bit RSA, and advanced as-ymptotic bounds. In Discussion, we propose lattice-, code-, multivariate-, and hash-based post-quantum schemes, analyze their security margins against quantum attacks, and out-line standardized migration strategies. We include three illustrative figures and 35+ se-quential IEEE citations.
Quantum computing endangers classical cryptography via two main avenues: Shor’s al-gorithm reduces integer factorization to polynomial time, and Grover’s algorithm yields a quadratic speed-up for unstructured key search. We develop rigorous mathematical treatment of both algorithms, enrich the literature survey with detailed complexity and resource analyses, and extend the development section to include quantum er-ror-correction overhead, resource estimates for breaking 2048-bit RSA, and advanced as-ymptotic bounds. In Discussion, we propose lattice-, code-, multivariate-, and hash-based post-quantum schemes, analyze their security margins against quantum attacks, and out-line standardized migration strategies. We include three illustrative figures and 35+ se-quential IEEE citations.
The advent of large-scale quantum computers poses an existential threat to the cryptographic algorithms that underpin modern digital security. Shor's algorithm enables quantum computers to factor large integers and compute discrete logarithms in polynomial time, rendering RSA, Elliptic Curve Cryptography (ECC), and Diffie-Hellman key exchange fundamentally insecure. Meanwhile, Grover's algorithm provides a quadratic speedup for brute-force search, effectively halving the security strength of symmetric ciphers and hash functions. This paper presents a comprehensive investigation into the impact of quantum computing on both asymmetric and symmetric cryptographic algorithms. We analyze the computational resources required by quantum attacks on current standards, evaluate the timeline of quantum threats based on hardware roadmaps from leading quantum computing companies, and conduct a systematic performance comparison of NIST-standardized post-quantum cryptographic (PQC) algorithms. Our experimental evaluation covers key generation time, encapsulation/decapsulation latency, signature generation/verification speed, key sizes, and bandwidth overhead across lattice-based, code-based, hash-based, and multivariate cryptographic schemes. Results indicate that lattice-based schemes, particularly CRYSTALS-Kyber and CRYSTALS-Dilithium, offer the most favorable balance of security and performance for practical deployment. We also propose a phased migration framework for transitioning existing cryptographic infrastructure to quantum-resistant alternatives, addressing compatibility, performance, and operational challenges.
The rapid advancement of quantum computing threatens to undermine the security foundations of modern cryptographic systems, particularly those based on integer factorization and discrete logarithm problems. Algorithms such as Shor’s and Grover’s promise exponential or quadratic speedups, rendering RSA, ECC, and certain symmetric schemes vulnerable within the next decade. This paper presents a simulated evaluation of classical cryptographic algorithms against quantum attacks, followed by a performance assessment of post-quantum cryptographic (PQC) schemes—specifically lattice-based, hash-based, and code-based algorithms. A testing framework was developed using a quantum simulator (Qiskit) and a classical benchmarking environment to model potential attack timelines and measure computational efficiency. Results demonstrate that RSA-2048 can be theoretically broken within 8 hours on a 4000-qubit fault-tolerant quantum processor, while ECC-P256 succumbs in less than 4 hours. In contrast, lattice-based schemes such as CRYSTALS-Kyber resisted quantum simulation attacks, maintaining equivalent classical security levels with only a 27% performance overhead. The study also analyzes the trade-offs between key size, encryption/decryption speed, and resistance to quantum attacks. Our findings emphasize the urgent need for migration to NIST-recommended PQC algorithms and provide a decision-support matrix for selecting suitable replacements in government and enterprise systems.
The advent of quantum computing poses an existential threat to classical cryptographic systems. Shor’s algorithm (1994) can factor large integers and compute discrete logarithms in polynomial time, breaking widely used schemes like RSA, ECC, and Diffie-Hellman. This paper surveys the state-of-the-art in quantum cryptanalysis, examining its impact on symmetric and asymmetric cryptography, recent progress in quantum attacks, and defenses via post-quantum cryptography (PQC). We analyze key quantum algorithms (Shor’s, Grover’s), their real-world feasibility given current hardware (NISQ-era limitations), and emerging PQC standards (NIST’s CRYSTALS-Kyber, Dilithium). We also discuss novel attack vectors (e.g., hybrid quantum-classical cryptanalysis) and future research directions.
The rapid growth of quantum computing poses a critical threat to classical cryptographic systems. That is due in large part to the fact that they represent efficient solutions for some of the most challenging mathematical problems such as integer factoring or finding discrete logarithms. Schemes currently in wide use including RSA, Diffie–Hellman, and elliptic curve cryptography are particularly susceptible to being attacked by quantum computers, using algorithms like Shor's Algorithm and Grover's Algorithm. The advent of post-quantum cryptography (PQC) provides a promising potential answer to providing longterm security from adversaries using quantum computing capabilities. This paper presents a comprehensive state-of-the-art review of various PQC techniques currently being researched, including lattice-based methods, code-based methods, multivariate methods, hash-based methods, and isogeny-based methods. key challenges that will need to be addressed include computational overhead, large key sizes and implementation complexity. Furthermore the study reviews the current standardization efforts by the National Institute of Standards and Technology related to PQC and discusses some of the very specific practical considerations that need to be considered before widely deploying these techniques. The paper concludes by a complete list of existing research challenges and proposed future work that will assist in the development of efficient and scalable systems that will resist attacks from quantum computers.
Quantum computing offers transformative computational power by harnessing phenomena such as superposition and entanglement. Yet, this potential simultaneously poses severe risks to classical cryptographic systems. In this paper, we explore how quantum algorithms, most notably Shor’s algorithm for integer factorization and Grover’s algorithm for unstructured search, could break widely deployed cryptographic schemes. We present a rigorous mathematical analysis of these quantum algorithms, compare their complexity with classical methods, and examine their impact on public-key and symmetric cryptography. Finally, we discuss potential countermeasures, including post-quantum cryptographic solutions, to safeguard data in the quantum era.
This preprint presents a systematic review of how quantum computing impacts the security of classical cryptography and what mitigation strategies are available. The review synthesises key survey papers, standards reports and transition guidelines on post-quantum cryptography (PQC) and quantum-safe security published between 2015 and 2025. First, the paper summarises the impact of Shor’s and Grover’s algorithms on widely deployed public-key schemes, symmetric ciphers and hash functions, highlighting in particular the existential break of RSA, Diffie–Hellman and elliptic-curve cryptography, and the reduced security margins for symmetric and hash-based constructions. It then examines major quantum-resilient responses, including lattice-, code-, multivariate- and hash-based PQC, quantum key distribution (QKD), hybrid classical–PQC schemes and crypto-agile architectures. Building on Mosca’s x, y, z risk-timing model, the review discusses cross-cutting themes such as harvest-now-decrypt-later threats and sector-specific implications for government and defence, finance and blockchain, healthcare, cloud providers and critical infrastructure. It identifies several research gaps, including the lack of quantitative migration-cost data, limited coverage of small and resource-constrained organisations, and few system-scale evaluations comparing PQC-only, hybrid and QKD-based designs. The paper concludes by arguing that planning and investment in quantum-resilient cryptography need to start now, before migration time and data shelf-life push critical systems into the risky regime.