In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer n, not depending on special form or properties. It was described by D. H. Lehmer and R. E. Powers in 1931,[1] and developed as a computer algorithm by Michael A. Morrison and John Brillhart in 1975.[2]
The continued fraction method is based on Dixon's factorization method. It uses convergents in the regular continued fraction expansion of
- .
Since this is a quadratic irrational, the continued fraction must be periodic (unless n is square, in which case the factorization is obvious).
It has a time complexity of , in the O and L notations.[3]
![O\left(e^{{{\sqrt {2\log n\log \log n}}}}\right)=L_{n}\left[1/2,{\sqrt {2}}\right]](https://wikimedia.org/api/rest_v1/media/math/render/svg/d252c7723eefcda234a20f8c89f10bd0ed364a5d)
YouTube Encyclopedic
-
1/3Views:1 0801 88437 793
-
Cryptanalysis - L1 Factoring & Continued Fractions
-
Zeros of polynomials via matrix theory and continued fractions - Olga Holtz
-
Continued Fractions 1: Introduction and Basic Examples - LearnMathsFree
Transcription
References
- ^ Lehmer, D.H.; Powers, R.E. (1931). "On Factoring Large Numbers". Bulletin of the American Mathematical Society. 37 (10): 770–776. doi:10.1090/S0002-9904-1931-05271-X.
- ^ Morrison, Michael A.; Brillhart, John (January 1975). "A Method of Factoring and the Factorization of F7". Mathematics of Computation. American Mathematical Society. 29 (129): 183–205. doi:10.2307/2005475. JSTOR 2005475.
- ^ Pomerance, Carl (December 1996). "A Tale of Two Sieves" (PDF). Notices of the AMS. Vol. 43, no. 12. pp. 1473–1485.
Further reading
- Samuel S. Wagstaff, Jr. (2013). The Joy of Factoring. Providence, RI: American Mathematical Society. pp. 143–171. ISBN 978-1-4704-1048-3.
 | This number theory-related article is a stub. You can help Wikipedia by expanding it. |
This page was last edited on 30 September 2022, at 21:00