Abstract
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed to be 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 that are generally thought to be hard on classical computers and that 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, for example, the number of digits of the integer to be factored.
Keywords
Quantum computerInteger factorizationDiscrete logarithmPrime factorLogarithmQuantum algorithmPolynomialInteger (computer science)Time complexityPost-quantum cryptographyCryptosystemAlgorithmComputationFactorizationComputer sciencePrime (order theory)MathematicsDiscrete mathematicsAlgebra over a fieldQuantumCryptographyCombinatoricsPure mathematics
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Publication Info
- Year
- 1999
- Type
- article
- Volume
- 41
- Issue
- 2
- Pages
- 303-332
- Citations
- 3541
- Access
- Closed
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Cite This
Peter W. Shor
(1999).
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer.
SIAM Review
, 41
(2)
, 303-332.
https://doi.org/10.1137/s0036144598347011
Identifiers
- DOI
- 10.1137/s0036144598347011