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Quantum Computing in Cryptography: Challenges and Post-Quantum Solutions

Ritesh K. Malhotra1 Shalini P. Deshmukh2, Pranav R. Chatterjee3

Published Jun 20, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.17657455

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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 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 advent of quantum computing presents a significant threat to classical public-key cryptographic systems, including RSA and Elliptic Curve Cryptography (ECC), thereby accelerating the development and standardization of post-quantum cryptography (PQC). This study evaluates the performance and implementation challenges of leading PQC algorithms across three major categories: lattice-based, hash-based, and multivariate cryptographic schemes. Utilizing empirical benchmark data from NIST candidate algorithms, the analysis focuses on key generation time, encryption latency, and memory consumption. Simulations and regression modeling reveal that lattice-based algorithms, particularly Kyber, demonstrate favorable trade-offs between computational efficiency and cryptographic strength. However, these schemes also present integration difficulties, especially in resource-constrained or legacy systems. Hash-based schemes like SPHINCS+ exhibit strong security guarantees but suffer from high latency and memory overhead, while multivariate algorithms such as Rainbow offer compact key sizes with moderate performance. The findings highlight the need for application-specific evaluation in selecting PQC solutions and provide actionable insights for guiding secure and efficient cryptographic transitions in the post-quantum era. Keywords: Post-Quantum Cryptography, Lattice-Based Cryptography, Hash-Based Cryptography, Multivariate Cryptography, Quantum Computing, Cryptographic Algorithms, Key Generation, Encryption Latency, Implementation Challenges, NIST PQC Standardization
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 presents computational powers previously thought unattainable. This brings severe threats to classical cryptographic methods, especially RSA and ECC. This paper addresses these risks through a detailed investigation of quantum-resistant algorithms, focusing on lattice- based (CRYSTALS-Kyber), hash-based (SPHINCS+), and code-based (McEliece) systems. Research questions guiding this study include: How vulnerable are traditional algorithms under quantum attack, and which quantum-resistant alternatives offer viable performance and security trade-offs? Through simulations, we analyzed key metrics like encryption speeds, key sizes, and efficiency under quantum threats. Additionally, we demonstrated vulnerabilities in RSA-2048 and ECC-256 under Shor’s algorithm, emphasizing the necessity for quantum-resistant cryptography. Our results highlighted CRYSTALS-Kyber as a balanced candidate, aligning with the NIST PQC Standardization, while Quantum Key Distribution (QKD) is reviewed for high-sensitivity contexts. Given the forecasted advancements in quantum hardware, we propose a transitional approach using hybrid cryptographic systems to ensure immediate security and ease the shift to quantum-safe protocols. This study also explores industry applications, particularly in finance, healthcare, and IoT, recommending a phased adoption strategy utilizing hybrid cryptographic systems for a secure, gradual transition.
The rapid advancement of quantum computing poses a fundamental threat to classical cryptographic mechanisms that underpin modern digital security. Shor’s algorithm can efficiently solve integer factorization and discrete logarithm problems, thereby breaking widely used public-key cryptosystems such as RSA, ECC, and Diffie–Hellman. Grover’s algorithm also reduces the effective security of symmetric encryption and hash functions by half. This paper provides a systematic analysis of the impact of quantum attacks on current cryptographic infrastructures, including TLS, digital signatures, and blockchain. We then review the state of post-quantum cryptography (PQC) as standardized by NIST, focusing on three leading candidates: CRYSTALS-Kyber for key encapsulation, and CRYSTALS-Dilithium and FALCON for digital signatures. Through simulation using the Open Quantum Safe (liboqs) library on a standard x86_64 platform, we measure key generation time, encryption/signing speed, decryption/verification latency, and key/signature sizes. Our results show that Kyber-768 achieves key generation in <0.1 ms and produces public keys of about 1.2 KB, while Dilithium-3 generates signatures of ~2.7 KB with verification times under 0.3 ms. Compared to RSA-2048 and ECDSA-P256, PQC algorithms offer competitive performance at the cost of larger key and signature sizes. Based on these findings, we propose a hybrid transition roadmap that combines classical and PQC algorithms in parallel, minimizing risk while maintaining backward compatibility. The paper concludes that organizations should begin immediate preparations for the post-quantum era, especially for data requiring long-term confidentiality.
The advent of quantum computing poses a paradigm-shifting threat to classical cryptographic systems that underpin global digital security. As quantum processors advance towards practical scalability, previously secure encryption schemesparticularly those based on integer factorization (e.g., RSA) and discrete logarithm problems (e.g., ECC and DH)-are rendered vulnerable due to quantum algorithms like Shor's and Grover's. This paper critically examines the implications of quantum computing for contemporary cryptographic frameworks and explores the urgent need to transition toward quantum-resistant alternatives. We begin by analyzing the computational capabilities of quantum systems and their impact on symmetric and asymmetric cryptographic algorithms. The study delves into the principles of postquantum cryptography (PQC), including lattice-based, hash-based, code-based, multivariate polynomial, and supersingular isogeny cryptography, evaluating their strengths, implementation challenges, and resistance to quantum attacks. Additionally, we assess ongoing global initiatives such as NIST's post-quantum cryptography standardization project, highlighting their role in shaping future security infrastructures. The paper also considers hybrid cryptographic models and quantum key distribution (QKD) as transitional and long-term security strategies. By rethinking security from both theoretical and practical standpoints, this study emphasizes the need for immediate and collaborative action across academia, industry, and government sectors to future-proof digital communication systems against the looming quantum threat.