Niho Bent Functions and Subiaco/Adelaide Hyperovals
نویسندگان
چکیده
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).
منابع مشابه
Innovations in Incidence Geometry
We show that dimensional doubly dual hyperovals over F2 define bent functions. We also discuss some known and a few new examples of dimensional doubly dual hyperovals and study the associated bent functions.
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 کاملCollineations of Subiaco and Cherowitzo hyperovals
A Subiaco hyperoval in PG(2, 2h), h ≥ 4, is known to be stabilised by a group of collineations induced by a subgroup of the automorphism group of the associated Subiaco generalised quadrangle. In this paper, we show that this induced group is the full collineation stabiliser in the case h 6≡ 2 (mod 4); a result that is already known for h ≡ 2 (mod 4). In addition, we consider a set of 2h + 2 po...
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1210.4732 شماره
صفحات -
تاریخ انتشار 2012