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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer (1997)

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by Peter W. Shor
Venue:SIAM J. on Computing
Citations:1254 - 4 self
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BibTeX

@ARTICLE{Shor97polynomial-timealgorithms,
    author = {Peter W. Shor},
    title = {Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer},
    journal = {SIAM J. on Computing},
    year = {1997},
    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 by 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 which 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

discrete logarithm    polynomial-time algorithm    prime factorization    quantum computer    classical computer    physical computing device    hypothetical quantum computer    input size    polynomial factor    digital computer    computation time    quantum mechanic   

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