Quantum algorithmic techniques for the Shor algorithm

Abstract

Secure communication is one of the key parts of the Information Age, characterized by broad progress and adoption of information technology. Existing standards of internet communication are based on RSA cryptography. On classical computers, RSA is almost impossible to break, however, there is a threat made on quantum computers, where Shor's algorithm offers exponential speedup compared to the best classical algorithms for breaking RSA keys. In this work, the fundamental part of the RSA key, namely factorization, will be investigated along with classical and quantum approaches using Shor's algorithm to break it. State-of-the-art techniques are replicated and incorporated into the implementation in Qiskit, capable of running on multiple computing devices, including IBM hardware and simulators from IonQ, Rigetti, and Quantinuum.