[PDF][PDF] A note on the Walsh spectrum of Dobbertin APN functions
Proceedings of SETA, 2020•seta-2020.etu.ru
Among the six known classes of APN power functions on F2n, the Dobbertin function is the
only one whose Walsh spectrum and, in particular, nonlinearity, are unknown. This problem
has already been open for 20 years without any progress since the seminal work of
Canteaut, Charpin and Dobbertin from 2000, in which they proved that all Walsh coefficients
of the Dobbertin function over F25m are divisible by 22m. In this paper, we present a
conjecture fully describing the Walsh spectrum of the Dobbertin function. We also show that …
only one whose Walsh spectrum and, in particular, nonlinearity, are unknown. This problem
has already been open for 20 years without any progress since the seminal work of
Canteaut, Charpin and Dobbertin from 2000, in which they proved that all Walsh coefficients
of the Dobbertin function over F25m are divisible by 22m. In this paper, we present a
conjecture fully describing the Walsh spectrum of the Dobbertin function. We also show that …
Abstract
Among the six known classes of APN power functions on F2n, the Dobbertin function is the only one whose Walsh spectrum and, in particular, nonlinearity, are unknown. This problem has already been open for 20 years without any progress since the seminal work of Canteaut, Charpin and Dobbertin from 2000, in which they proved that all Walsh coefficients of the Dobbertin function over F25m are divisible by 22m.
In this paper, we present a conjecture fully describing the Walsh spectrum of the Dobbertin function. We also show that the Dobbertin function can be represented as the composition of a cubic power function and the inverse of a quadratic power function; more precisely, the Dobbertin exponent over F25m has the form
seta-2020.etu.ru
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