Gold and Kasami-Welch functions, quadratic forms, and bent functions
نویسندگان
چکیده
We use elementary facts about quadratic forms in characteristic 2 to evaluate the sign of some Walsh transforms in terms of a Jacobi symbol. These results are applied to the Walsh transforms of the Gold and KasamiWelch functions. We prove that the Gold functions yield bent functions when restricted to certain hyperplanes. We also use the sign information to determine the dual bent function.
منابع مشابه
On Kasami Bent Functions
It is proved that no non-quadratic Kasami bent is affine equivalent to MaioranaMacFarland type bent functions.
متن کاملA class of quadratic APN binomials inequivalent to power functions
We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n ≥ 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZ-inequivalent to any known APN function, and in particular for n = 12,...
متن کاملKasami Bent Functions are Not Equivalent to Their Duals
A difficult task in the theory of bent functions is to determine whether a bent function is equivalent to its dual bent function. In this paper we use certain results on the divisibility of Gauss Sums, mainly Stickelberger’s Theorem, to study monomial bent functions. We find the degree of the dual bent function of the Kasami function, which in general is different from the degree of the Kasami ...
متن کاملProgress Towards the Conjecture on APN Functions and Absolutely Irreducible Polynomials
Almost Perfect Nonlinear (APN) functions are very useful in cryptography, when they are used as S-Boxes, because of their good resistance to differential cryptanalysis. An APN function f : F2n → F2n is called exceptional APN if it is APN on infinitely many extensions of F2n . Aubry, McGuire and Rodier conjectured that the only exceptional APN functions are the Gold and the Kasami-Welch monomial...
متن کاملNew infinite families of p-ary weakly regular bent functions
The characterization and construction of bent functions are challenging problems. The paper generalizes the constructions of Boolean bent functions by Mesnager [33], Xu et al. [40] and p-ary bent functions by Xu et al. [41] to the construction of p-ary weakly regular bent functions and presents new infinite families of p-ary weakly regular bent functions from some known weakly regular bent func...
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:
- Adv. in Math. of Comm.
دوره 1 شماره
صفحات -
تاریخ انتشار 2007