Constructions, Enumeration And Discrimination Methods Of Resilient Rotation Symmetric Boolean Functions

Boolean functions, an indispensable tool of cipher systems and analysis, are important objects in the study of cryptography. As a special kind of Boolean functions, rotation symmetric Boolean functions (RSBFs) have received a lot of attention in the domain of symmetric cryptography. They play a significant, role in the round of a hashing algorithm and the implement of MD4, MD5 and HAVAL. There also exist relations between RSBFs and design of experiment. This thesis studies the properties of orbit matrix and gives a formula to compute the number of these orbit matrices on n variables, where n is an integer. The constructions and enumeration of 1-resilient RSBFs on 4p and prqs variables are presented respectively, where p, q are different. primes, and r,s are integers. By the proposed method, all 1-resilient RSBFs on 12 variables can be constructed. With the help of the special property on the support tables of RSBFs, we obtain the discrimination methods of 3- and 4-resilience. As an application of our results, some 1-resilient RSBFs and the 3-, 4-resilient discrimination on 12 variables are shared. The thesis consists of four chapters and is organized as follows.Chapter 1 introduces the research background of the thesis, the related concepts and some existing results.Chapter 2 studies the properties of orbit matrix and gives a formula to compute the number of these orbit matrices on n variables. It has been demonstrated that the con-structions of 1-resilient RSBFs on 4p and prqs variables are equivalent to solving equation systems, where p, q are different primes. Moreover, we present counting formulas for the total number of all 1-resilient RSBFs on 4p and prqs variables. Some 1-resilient RSBFs on 12 variables are shown as well.Chapter 3 provides the discrimination methods of RSBFs with orders 3 and 4 according to the special property on the support tables of RSBFs. Besides, we apply the result to the resilient RSBFs on 12 variables.Chapter 4 summarizes the main content of this thesis and puts forward some sugges-tions.