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

Mathematics

Journal of Physical Mathematics

Author(s): Peter W Shor

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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.

This article was published in SIAM J. Comput and referenced in Journal of Physical Mathematics

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