Bent Functions: Results and Applications to Cryptography offers a unique survey of the
objects of discrete mathematics known as Boolean bent functions. As these maximal …

In this paper, a combinatorial conjecture about binary strings is proposed. Under the
assumption that the proposed conjecture is correct, two classes of Boolean functions with …

Inspired by the previous work of Tu and Deng, we propose two infinite classes of Boolean
functions of 2 k variables where k≥ 2. The first class contains unbalanced functions having …

In this paper, we present a class of $2 k $-variable balanced Boolean functions and a class
of $2 k $-variable $1 $-resilient Boolean functions for an integer $ k\ge 2$, which both have …

It is a difficult challenge to find Boolean functions used in stream ciphers achieving all of the
necessary criteria and the research of such functions has taken a significant delay with …

For a nonnegative integer t, let c_t be the asymptotic density of natural numbers n for which
s(n+t)≧s(n), where s(n) denotes the sum of digits of n in base 2. We prove that c_t>1/2 for t …

In this paper, we construct a class of 2k-variable Boolean functions which have optimal
algebraic degree, very high nonlinearity, optimal algebraic immunity, and are 1-resilient …

A Class of 1−Resilient Function with High Nonlinearity and Algebraic Immunity Page 1 A Class
of 1−Resilient Function with High Nonlinearity and Algebraic Immunity Ziran Tu∗ Yingpu Deng† …

In this paper we prove a central limit theorem for some probability measures defined as
asymtotic densities of integer sets defined via sum-of-digit-function. To any integer a we can …

This thesis is concerned with the well-known sum-of-digits function and the related notions
of q-additive and q-multiplicative functions. In the work of C. Mauduit and J. Rivat on the so …