We give a construction of 3-class and 4-class association schemes from s-nonlinear and differentially 2 s-uniform functions, and a construction of p-class association schemes from weakly regular p-ary bent functions, where p is an odd prime.
—Many block ciphers use permutations defined on with low differential uniformity, high nonlinearity, and high algebraic degree as their S-boxes to provide confusion. It is well known that, for a function on , the lowest differential uniformity is 2 and the functions achieving this lower bound are called almost perfect nonlinear (APN) functions. However, due… (More)
a r t i c l e i n f o a b s t r a c t Differentially 4 uniform permutations with high nonlinearity on fields of even degree are crucial to the design of S-boxes in many symmetric cryptographic algorithms. Until now, there are not many known such functions and all functions known are power functions. In this paper, we construct the first class of binomial… (More)
Differentially 4-uniform permutations on F 2 2k with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred functions, to construct a lot of infinite families of such permutations . In this paper, we propose a particular type of Boolean… (More)
— In this paper, we introduce a recursive construction of p-ary bent functions, where p is an odd prime. Several new non-quadratic bent functions over fields with characteristic 5, 7, 11, 13, 17, 19, 23 are found by computer search, all of which are homogeneous. A ternary bent function whose algebraic degree attains the upper bound is given. So far it is… (More)
We show that the there exists an infinite family of APN functions of the form F (x) = x
BACKGROUND The purpose of this community-based study was to develop a structural equation model for factors contributing to cervical cancer screening among Chinese American women. METHODS A cross-sectional design included a sample of 573 Chinese American women aged 18 years and older. The initial step involved use of confirmatory factor analysis, that… (More)