New constructions of even-variable rotation symmetric Boolean functions with maximum algebraic immunity

New Construction of Even-variable Rotation Symmetric Boolean Functions with Optimum Algebraic Immunity

“…We have also studied the nonlinearity of our construction. Because there was only one paper [16] that has given a type of even-variable RSBFs with optimum AI in which there are 1 2 n  different constructions in all, we hope that our contribution to a new method of construction can be of help to the study of RSBFs.…”

“…In order to clearly illustrate our constructions of even-variable RSBFs with optimum AI, some notations and lemmas should be given, and from now on , we assume that n is an even positive integer and 16 n  . Let…”

“…So far, many rotation symmetric Boolean functions with optimum AI have been obtained [12][13][14][15][16][17]. In 2007, Sarkar and Maitra [12] constructed odd-variables rotation symmetric Boolean functions with optimum AI and the nonlinearity of [14] gave a construction of Boolean functions with optimum AI on even-variable.…”

“…Furthermore, their new functions were of much better nonlinearity than all the existing construction. We propose a well construction which have / 4 3 n    different RSBFs by giving an even ( 16) nn  , and the nonlinearity of our construction is high enough. The paper is organized as follows.…”

A Secure Random Number Generator with Immunity and Propagation Characteristics for Cryptography Functions

“…Such a lower bound in evaluated in [15]. The relation of algebraic immunity and extended algebraic immunity is researched in [16,17]. The bent functions are also in use for construction of a class of functions in infinity [18].…”