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Study on Implementation of Shor’s Factorization Algorithm on Quantum Computer

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Abstract

The fundamental security aspect of the classical crypto-system depends on integer factorization and discrete logarithm problems. The quantum factorization problem is a crucial problem in quantum computing as it has significant implications for cryptography and security. Shos’s paper on “Polynomial-time algorithms for discrete logarithms and factoring on a quantum compute” has become a threat to the classical crypto-system, influencing many researchers to work on factorization problems using quantum computing. Quantum Computers (QC) can be essential in running different factorization algorithms in polynomial time. However, practical implementation on larger numbers is still a major challenge due to the requirement for error correction and massive quantum devices. Although the quantum factorization issue puts traditional cryptographic systems at risk, it also opens up new possibilities for quantum communication and encryption. The challenge of factorization opens up an entirely new field for research into quantum communication protocol security, including quantum key distribution and the development of quantum-resistant cryptographic systems. This paper surveys the various quantum algorithms for factoring a number into prime integers. We present a simulation study of the Quantum factorization algorithm to determine the period of a process. Turning the factoring problem into the challenge of determining a function’s period is the essential strategy of practical implementation using the quantum circuit.

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  1. Department of Computer Science and Engineering, National Institute of Technology Patna, Patna, 800005, India

    Mandeep Kumar & Bhaskar Mondal

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  1. Mandeep Kumar
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Mandeep Kumar drafted the main manuscript text, Dr. Bhaskar Mondal prepared all the figures and did the proofreading and arranging the systematic review throughout. All authors equally contributed to the scientific work and reviewed the manuscript.

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Correspondence to Mandeep Kumar or Bhaskar Mondal.

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This article is part of the topical collection “Security and Privacy 2020” guest edited by Pantelimon Stanica, Odelu Vanga and Sumit Kumar Debnath.

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Kumar, M., Mondal, B. Study on Implementation of Shor’s Factorization Algorithm on Quantum Computer. SN COMPUT. SCI. 5, 413 (2024). https://doi.org/10.1007/s42979-024-02771-y

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