Volume 20, No 1, 2013, P. 77-92
Frolova A. A.
Essential dependence of the Kasami bent functions on the products of variables
The Kasami bent functions are the most complicated of the class of monomial bent functions. It is proved that an arbitrary Kasami bent function of degree t has nonzero (t −2)-multiple derivatives if 4 ≤ t ≤ (n + 3)/3 and nonzero (t − 3)-multiple derivatives if (n + 3)/3 < t ≤ n/2. It is obtained that the order of essential dependence of a Kasami bent function is not less than t − 3.
Keywords: Kasami Boolean function, bent function, algebraic normal form, derivative of a Boolean function.
Frolova Anastasia Alexandrovna 1
1. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia