Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer (1982)

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by Peter W. Shor

Venue:	SIAM JOURNAL ON COMPUTING
Citations:	1275 - 4 self

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@ARTICLE{Shor82polynomial-timealgorithms,
    author = {Peter W. Shor},
    title = {Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer },
    journal = {SIAM JOURNAL ON COMPUTING},
    year = {1982},
    volume = {26},
    pages = {1484--1509}
}

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Abstract

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

Keyphrases

classical computer physical computing device polynomial factor am subject classification discrete logarithm hypothetical quantum computer input size quantum mechanic subsequent development digital computer computation time first result theoretical computer science

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