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Lecture notes in networks and systems

Quantum Threat to Cryptographic Security: Implementation and Analysis of Shor’s Algorithm for Integer Factorization Using IBM Qiskit

Anubhav Saxena, Dinesh Kumar Saini, Satpal Singh Kushwaha

Published Oct 29, 2025• 1 citation
Publisher
DOI
10.1007/978-981-96-8901-9_5

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The advancement of quantum computing in recent years poses severe threats to the RSA public-key cryptosystem. The RSA cryptosystem fundamentally relies its security on the computational hardness of number theory problems: prime factorization (integer factoring). Shor’s quantum factoring algorithm could theoretically answer the computational problem in polynomial time. This paper contributes to the experiment and demonstration of Shor’s quantum factoring algorithm for RSA prime factorization using IBM Qiskit. The performance of the quantum program is evaluated based on user time and the success probability. The results show that a more significant public modulus N in the RSA public key improves factorization’s computational hardness, requiring more quantum bits to solve. A further enhancement on implementing Shor’s oracle function is essential in increasing success probability and reducing the number of shots required.
To factor an integer N into a product of two other numbers N1 and N2, Shor’s algorithm uses the Quantum Fourier Transform on n qubits, denoted QFTn, to determine the period r of a Modular Exponentiation Function (MEF), which is later used to compute a factor of N. In this work, we present Shor’s algorithm for factoring an integer of n qubits and illustrate an example with n=4. We implement our algorithm using Qiskit and IBM quantum computers, which also can be adapted on other quantum computing platforms with minor adjustments. We discuss the IBM quantum computer limitations for running our circuit and show the impact of device imperfections on the factored result.