The advent of quantum computing poses a fundamental threat to classical cryptographic systems, particularly RSA encryption, which relies on the computational limit of prime factorization. This paper presents a comparative analysis of four integer factorization approaches-a selfcurated brute-force classical implementation, optimized Trial Division, Pollard's Rho algorithm, and Shor's algorithmevaluated across a dataset of increasing semiprime inputs representative of scaled-down RSA encryption keys. Through Python-based implementations and simulations, we empirically measure and plot runtime complexity for classical methods while modeling theoretical runtimes for Shor's algorithm, given hardware limitations. Our findings reveal the exponential scaling limitations of classical algorithms, and contrast them with the polynomial-time behavior of Shor's algorithm. Despite being simulated, Shor's consistently flatter runtime trendline demonstrated its theoretical superiority and the critical urgency of post-quantum cryptography. This study not only visualizes the performance divide between classical and quantum paradigms but also underscores the transformational potential of quantum computing in modern cryptanalysis.
The advent of quantum computing poses a fundamental threat to classical cryptographic systems, particularly RSA encryption, which relies on the computational limit of prime factorization. This paper presents a comparative analysis of four integer factorization approaches-a selfcurated brute-force classical implementation, optimized Trial Division, Pollard's Rho algorithm, and Shor's algorithmevaluated across a dataset of increasing semiprime inputs representative of scaled-down RSA encryption keys. Through Python-based implementations and simulations, we empirically measure and plot runtime complexity for classical methods while modeling theoretical runtimes for Shor's algorithm, given hardware limitations. Our findings reveal the exponential scaling limitations of classical algorithms, and contrast them with the polynomial-time behavior of Shor's algorithm. Despite being simulated, Shor's consistently flatter runtime trendline demonstrated its theoretical superiority and the critical urgency of post-quantum cryptography. This study not only visualizes the performance divide between classical and quantum paradigms but also underscores the transformational potential of quantum computing in modern cryptanalysis.
The advent of quantum computing presents a paradigm shift in the field of cryptanalysis, challenging the security of classical encryption schemes that underpin modern digital communications. This study explores the capabilities of quantum algorithms, particularly Shor's algorithm and Grover's algorithm, in undermining widely used cryptographic systems. Shor's algorithm poses a direct threat to publickey cryptosystems such as RSA and ECC by enabling efficient integer factorization and discrete logarithm computation, which are computationally infeasible for classical computers. Meanwhile, Grover's algorithm provides a quadratic speedup for bruteforce attacks on symmetric-key cryptosystems like AES, significantly reducing their effective security. Through theoretical analysis and simulation-based evaluation, this paper highlights the vulnerabilities of classical encryption in the face of quantum advances and underscores the urgent need for post-quantum cryptographic solutions. The findings emphasize the critical importance of transitioning to quantum-resistant algorithms to ensure long-term data confidentiality in a future dominated by quantum technologies.
This dissertation analyzes the impact of quantum computing on the security of classical cryptographic systems, with a focus on the vulnerability of the RSA algorithm. RSA cryptography is based on the difficulty of factoring large prime numbers, a task considered computationally very difficulty for classical computers. However, with quantum computing, especially through Shor’s algorithm—this barrier can be overcome. Shor’s algorithm allows factorization in polynomial time, which would completely compromise the security of RSA.The dissertation presents the theoretical foundations of both cryptography and quantum computing, explaining key concepts such as qubits, superposition, entanglement, and quantum parallelism. It details the operation of Shor’s algorithm, from identifying the period of the modular exponential function to applying the Quantum Fourier Transform (QFT) and phase estimation to obtain the prime factors of a composite number.In addition to the theoretical component, the work includes practical implementations of the algorithm in both classical and simulated quantum environments, using IBM’s Qiskit library. Finally, it discusses post-quantum cryptography as a secure alternative in light of technological advancements, highlighting methods based on lattices, codes, hash functions, and multivariate systems.The conclusion emphasizes the urgency of adopting cryptographic systems resistant to quantum computing, as ongoing advances increasingly make the breaking of RSA a realistic threat. Post-quantum cryptography is mentioned as a necessary response to the challenge posed by quantum computing.In conclusion, although current quantum computers do not yet have sufficient power to break RSA in practice, technological progress is steadily bringing that scenario closer. Therefore, it is essential to develop and adopt quantum-resistant cryptographic systems to ensure information security in the coming decades.
Quantum computing poses a fundamental threat to modern cryptographic protocols by exploiting quantum algorithms that surpass classical computational limits. Shor’s algorithm can efficiently factor large integers, breaking RSA and other public-key cryptosystems, while Grover’s algorithm accelerates brute-force attacks against symmetric encryption. As quantum hardware advances, traditional cryptographic schemes risk obsolescence, necessitating the development of quantum-resistant cryptographic techniques. This paper explores the theoretical foundations of quantum cryptanalysis, examining key algorithms, their implications for cybersecurity, and the current state of post-quantum cryptographic solutions. By analyzing resource estimates for quantum attacks and potential mitigation strategies, this study provides a comprehensive overview of the evolving cryptographic landscape in the quantum era.
This paper explores a quantum-inspired technique for factoring semi-prime integers, a problem central to the security of RSA cryptography. While Shor's algorithm offers a polynomial-time solution on a quantum computer, posing a significant threat to RSA, current quantum hardware limitations hinder its practical implementation. This study simulates Shor's algorithm classically, replacing the quantum period-finding subroutine—the source of the quantum speedup—with a classical method to analyze its performance. The experiments factored semi-primes ranging from 2 to 8 digits, demonstrating that while the technique works, the execution time increases exponentially with the size of the number, escalating from seconds for small integers to an order of minutes for an 8-digit number. This highlights the inefficiency of classical period-finding compared to the quantum approach. The results validate the theoretical framework of Shor's algorithm but underscore the impracticality of classical simulations for cryptographic-scale integers. This work also explores the necessity of advancing quantum computing to realize scalable factorization while classical methods remain confined to pedagogical or small-scale applications. The study emphasizes the urgency of hybrid quantum-classical optimizations and reinforces Shor's algorithm as pivotal for future cryptographic vulnerability assessments and quantum-ready solutions.
Quantum computing has raised significant concerns regarding the security of classical cryptographic systems, particularly RSA, as it depends on the computational difficulty of factoring large semiprime numbers.In this study, we demonstrate the practical application of Shor's algorithm by successfully factorizing a semiprime integer, up to 30 bits (857830637 = 29167 X 29411) using the QuantumRings simulator.Our work highlights the effectiveness of Shor's algorithm in solving the factorization problem in polynomial time, which will significantly improve over the classical method for a large number.The results suggest that with advances in quantum hardware, such as increasing qubit counts and improving error correction, breaking larger RSA keys (e.g., RSA-2048) may soon become feasible.This seriously threatens current cryptographic systems, emphasizing the need to adopt post-quantum cryptography.Our findings aim to raise awareness among researchers, policymakers, and industry leaders of the importance of preparing for a quantum-safe future.
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.