PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
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.
 Publication:

arXiv eprints
 Pub Date:
 August 1995
 arXiv:
 arXiv:quantph/9508027
 Bibcode:
 1995quant.ph..8027S
 Keywords:

 Quantum Physics
 EPrint:
 28 pages, LaTeX. This is an expanded version of a paper that appeared in the Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, Nov. 2022, 1994. Minor revisions made January, 1996