Crooked functions are combinatorial objects of great interest. It is already known that the only monomial and binomial crooked functions are quadratic. In this paper, we investigate conditions on the shape of a polynomial to be crooked. Furthermore, the notion of exceptional crooked is introduced, similarly to those of APN or PN exceptional functions. Via a connection with algebraic varieties over finite fields, we provide non-existence results of exceptional crooked functions.
Exceptional crooked functions / Bartoli, Daniele; Calderini, Marco; Timpanella, Marco. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 84:(2022), pp. 10210901-10210912. [10.1016/j.ffa.2022.102109]
Exceptional crooked functions
Calderini, Marco;
2022-01-01
Abstract
Crooked functions are combinatorial objects of great interest. It is already known that the only monomial and binomial crooked functions are quadratic. In this paper, we investigate conditions on the shape of a polynomial to be crooked. Furthermore, the notion of exceptional crooked is introduced, similarly to those of APN or PN exceptional functions. Via a connection with algebraic varieties over finite fields, we provide non-existence results of exceptional crooked functions.| File | Dimensione | Formato | |
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