Fourier transforms Archives - IEEE Transactions on Quantum Engineering

Simulation of Shor Algorithm for Discrete Logarithm Problems With Comprehensive Pairs of Modulo p and Order q

July 21, 2025Kaito Kishi; Junpei Yamaguchi; Tetsuya Izu; Noboru KunihiroQuantum InformationComputers, Cryptography, Fourier transforms, Logic gates, Noise measurement, Quantum algorithm, Quantum circuit, Quantum computing, Qubit, Registers

Abstract: The discrete logarithm problem (DLP) over finite fields, commonly used in classical cryptography, has no known polynomial-time algorithm on classical computers. However, Shor has provided its polynomial-time algorithm on quantum computers. Nevertheless, there are only few examples simulating quantum circuits that operate on general pairs of modulo p and order q. In this article, […]

Shor’s Algorithm Using Efficient Approximate Quantum Fourier Transform

Shor’s algorithm solves the integer factoring and discrete logarithm problems in polynomial time. Therefore, the evaluation of Shor’s algorithm is essential for evaluating the security of currently used public-key cryptosystems because the integer factoring and discrete logarithm problems are crucial for the security of these cryptosystems. In this article, a new approximate quantum Fourier transform […]