On $2k$-Variable Symmetric Boolean Functions With Maximum Algebraic Immunity $k$
نویسندگان
چکیده
منابع مشابه
On $2k$-Variable Symmetric Boolean Functions with Maximum Algebraic Immunity $k$
Algebraic immunity of Boolean function f is defined as the minimal degree of a nonzero g such that fg = 0 or (f + 1)g = 0. Given a positive even integer n, it is found that the weight distribution of any n-variable symmetric Boolean function with maximum algebraic immunity n 2 is determined by the binary expansion of n. Based on the foregoing, all n-variable symmetric Boolean functions with max...
متن کاملConstruction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity
In this paper we present a theoretical construction of Rotation Symmetric Boolean Functions (RSBFs) on odd number of variables with maximum possible AI and further these functions are not symmetric. Our RSBFs are of better nonlinearity than the existing theoretical constructions with maximum possible AI . To get very good nonlinearity, which is important for practical cryptographic design, we g...
متن کاملOn the Algebraic Immunity of Symmetric Boolean Functions
In this paper, we analyse the algebraic immunity of symmetric Boolean functions. We identify a set of lowest degree annihilators for symmetric functions and propose an efficient algorithm for computing the algebraic immunity of a symmetric function. The existence of several symmetric functions with maximum algebraic immunity is proven. In this way, a new class of function which have good implem...
متن کاملConstruction of Rotation Symmetric Boolean Functions with optimal Algebraic Immunity
En este artículo, presentamos construcciones teóricas de funciones Booleanas de rotación simétrica (RSBFs por sus siglas en inglés) con un número impar de variables y con máxima inmunidad algebraica. Con el objeto de obtener funciones Booleanas de muy alta no linealidad, generalizamos nuestra construcción a una técnica de búsqueda en la clase RSBF. Presentamos así RSBFs con inmunidad algebraica...
متن کاملBalanced Boolean Functions with (more than) Maximum Algebraic Immunity
In this correspondence, construction of balanced Boolean functions with maximum possible algebraic (annihilator) immunity (AI) is studied with an additional property which is necessary to resist fast algebraic attack. The additional property considered here is, given an n-variable (n even) balanced function f with maximum possible AI n 2 , and given two n-variable Boolean functions g, h such th...
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: IEEE Transactions on Information Theory
سال: 2012
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2012.2201350