New Constructions of Resilient Boolean Functions with Maximal Nonlinearity

نویسنده

  • Yuriy Tarannikov
چکیده

In this paper we develop a technique that allows to obtain new effective constructions of highly resilient Boolean functions with high nonlinearity. In particular, we prove that the upper bound 2n−1 − 2 on nonlinearity of m-resilient n-variable Boolean functions is achieved for 0.6n− 1 ≤ m ≤ n− 2.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

New Constructions for Resilient and Highly Nonlinear Boolean Functions

We explore three applications of geometric sequences in constructing cryptographic Boolean functions. First, we construct 1-resilient functions of n Boolean variables with nonlinearity 2n−1−2(n−1)/2, n odd. The Hadamard transform of these functions is 3-valued, which limits the efficiency of certain stream cipher attacks. From the case for n odd, we construct highly nonlinear 1-resilient functi...

متن کامل

Nonlinearity Bounds and Constructions of Resilient Boolean Functions

In this paper we investigate the relationship between the nonlinearity and the order of resiliency of a Boolean function. We first prove a sharper version of McEliece theorem for Reed-Muller codes as applied to resilient functions, which also generalizes the well known XiaoMassey characterization. As a consequence, a nontrivial upper bound on the nonlinearity of resilient functions is obtained....

متن کامل

Balanced Boolean Functions with (Almost) Optimal Algebraic Immunity and Very High Nonlinearity

In this paper, we present a class of 2k-variable balanced Boolean functions and a class of 2k-variable 1-resilient Boolean functions for an integer k ≥ 2, which both have the maximal algebraic degree and very high nonlinearity. Based on a newly proposed conjecture by Tu and Deng, it is shown that the proposed balanced Boolean functions have optimal algebraic immunity and the 1-resilient Boolean...

متن کامل

Generalized Maiorana-McFarland Constructions for Almost Optimal Resilient Functions

In a recent paper [1], Zhang and Xiao describe a technique on constructing almost optimal resilient functions on even number of variables. In this paper, we will present an extensive study of the constructions of almost optimal resilient functions by using the generalized MaioranaMcFarland (GMM) construction technique. It is shown that for any given m, it is possible to construct infinitely man...

متن کامل

On Resilient Boolean Functions with Maximal Possible Nonlinearity

It is proved that the maximal possible nonlinearity of n-variable m-resilient Boolean

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000