Quantum Cryptanalysis of the RSA Cipher
Year: 2025
Type: dissertation
Abstract: 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.
Author: Machado, Pedro Dinis de Paulo
Language: Portuguese
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7112795396