dorsal/arxiv
View SchemaPolynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
| Authors | Peter W. Shor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9508027 |
| URL | https://arxiv.org/abs/quant-ph/9508027 |
| DOI | 10.1137/S0097539795293172 |
| Journal | SIAM J.Sci.Statist.Comput. 26 (1997) 1484 |
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.
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"abstract": "A digital computer is generally believed to be an efficient universal\ncomputing device; that is, it is believed able to simulate any physical\ncomputing device with an increase in computation time of at most a polynomial\nfactor. This may not be true when quantum mechanics is taken into\nconsideration. This paper considers factoring integers and finding discrete\nlogarithms, two problems which are generally thought to be hard on a classical\ncomputer and have been used as the basis of several proposed cryptosystems.\nEfficient randomized algorithms are given for these two problems on a\nhypothetical quantum computer. These algorithms take a number of steps\npolynomial in the input size, e.g., the number of digits of the integer to be\nfactored.",
"arxiv_id": "quant-ph/9508027",
"authors": [
"Peter W. Shor"
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"doi": "10.1137/S0097539795293172",
"journal_ref": "SIAM J.Sci.Statist.Comput. 26 (1997) 1484",
"title": "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer",
"url": "https://arxiv.org/abs/quant-ph/9508027"
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