Equivalence classes of Niho bent functions
نویسندگان
چکیده
Equivalence classes of Niho bent functions are described for all known types hyperovals.
منابع مشابه
Niho Bent Functions and Subiaco/Adelaide Hyperovals
In this paper, the relation between binomial Niho bent functions discovered by Dobbertin et al. and o-polynomials that give rise to the Subiaco and Adelaide classes of hyperovals is found. This allows to expand the class of bent functions that corresponds to Subiaco hyperovals, in the case when m ≡ 2 (mod 4).
متن کاملConstruction of bent functions via Niho power functions
A Boolean function with an even number n = 2k of variables is called bent if it is maximally nonlinear. We present here a new construction of bent functions. Boolean functions of the form f(x) = tr(α1x1 + α2x2), α1, α2, x ∈ F2n , are considered, where the exponents di (i = 1, 2) are of Niho type, i.e. the restriction of xi on F2k is linear. We prove for d1 = 2 + 1 and d2 = 3 · 2k−1 − 1, d2 = 2 ...
متن کاملOn Dillon's class H of bent functions, Niho bent functions and o-polynomials
One of the classes of bent Boolean functions introduced by John Dillon in his thesis is family H. While this class corresponds to a nice original construction of bent functions in bivariate form, Dillon could exhibit in it only functions which already belonged to the wellknown Maiorana-McFarland class. We first notice that H can be extended to a slightly larger class that we denote by H. We obs...
متن کاملOn lower bounds on second-order nonliearities of bent functions obtained by using Niho power functions
In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form f(x) = Tr 1 (α1x d1 + α2x 2), where d1 and d2 are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a result proved by Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is demonstrated that for large values of n the...
متن کاملNew Classes of Ternary Bent Functions from the Coulter-Matthews Bent Functions
It has been an active research issue for many years to construct new bent functions. For k odd with gcd(n, k) = 1, and a ∈ F3n , the function f(x) = Tr(ax 3k+1 2 ) is weakly regular bent over F3n , where Tr(·) : F3n → F3 is the trace function. This is the well-known Coulter-Matthews bent function. In this paper, we determine the dual function of f(x) completely. As a consequence, we find many c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2021
ISSN: ['0925-1022', '1573-7586']
DOI: https://doi.org/10.1007/s10623-021-00885-5