A family of crooked functions
Document Type
Article
Publication Date
2-2009
Department
Department of Mathematical Sciences
Abstract
It has been proved in Bierbrauer and Kyureghyan (Des. Codes Cryptogr. 46:269-301, 2008) that a binomial function aX i + bX j can be crooked only if both exponents i, j have 2-weight ≤ 2. In the present paper we give a brief construction for all known examples of crooked binomial functions. These consist of an infinite family and one sporadic example. The construction of the sporadic example uses the properties of an algebraic curve of genus 3. Computer experiments support the conjecture that each crooked binomial is equivalent either to a member of the family or to the sporadic example.
Publication Title
Designs, Codes, and Cryptography
Recommended Citation
Bierbrauer, J.
(2009).
A family of crooked functions.
Designs, Codes, and Cryptography,
50(2), 235-241.
http://doi.org/10.1007/s10623-008-9227-1
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4873