Simulation of Modular Exponential Circuit via Quantum Fourier Transform in Qiskit

Modular exponents are the most widely used functions in the field of computational science and cryptography. In the RSA cryptographic system, proposed by Ron Rivest, Adi Shamir, and Leonard Adleman, the modular exponential function is used for integer factorization. Peter Shor in 1994 had used the approach of quantum computation to determine the period of the modular exponential function. In 2012, Archimedes Pavlidis and Dimitris Gizopoulos proposed a new approach to increase the efficiency of modular exponential calculations by performing the quantum Fourier transform (QFT). This paper will discuss the simulation to construct a quantum circuit that implements the modular exponential function via quantum Fourier transform. The outcome of this study is a Python program applying the modular exponential quantum circuit via QFT using the quantum computing package, Qiskit. This construction consists of four stages, i.e. adder by Draper’s QFT adder, multiplier/accumulator from modified Beauregard’s multiplier/accumulator, divider by constant applying Granlund-Montgomery classical division by a constant algorithm, and generic modular multiplier based on VBE modular exponentiation circuit. This program is expected to be useful for researchers in the field of cryptography, mathematics, science computations, and other fields that require optimizing the calculation time or the new approach of modular exponential.