Article contents
ITERATION OF QUADRATIC POLYNOMIALS OVER FINITE FIELDS
Published online by Cambridge University Press: 29 November 2017
Abstract
For a finite field of odd cardinality $q$, we show that the sequence of iterates of $aX^{2}+c$, starting at $0$, always recurs after $O(q/\text{log}\log q)$ steps. For $X^{2}+1$, the same is true for any starting value. We suggest that the traditional “birthday paradox” model is inappropriate for iterates of $X^{3}+c$, when $q$ is 2 mod 3.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 2017
References
- 6
- Cited by