Analysis And Design Of Cryptographic Functions For Stream Ciphers

Boolean functions play a vital role in the design of stream cipher systems,and their cryptographic properties are closely related to the security of stream cipher systems.The ability of stream cipher systems to resist various cipher attacks can be measured by the corresponding cryptographic indicators of its core component Boolean function,such as re-siliency,high nonlinearity,high algebraic degree,good autocorrelation properties,and good algebraic immunity,etc.Since many problems in designing stream cipher schemes can ultimately be attributed to the construction of Boolean functions,and these various crypto-graphic indicators of Boolean functions are mutually constrained,it is a hot research topic to construct and analyse Boolean functions that satisfy multiple cryptographic indicators at the same time.In the dissertation,using powerful tools such as disjoint linear codes and fragmentary Walsh transform,we mainly study the problem of the constructions and analysis of resilient Boolean functions with good autocorrelation properties,resilient Boolean functions with high nonlinearity.The main results are as follows:(1)Based on a suitable modification of the classical partial spread bent functions,we have obtained a large class of 1-resilient Boolean functions in even variables with high algebraic degree,strictly almost optimal nonlinearity,and good global avalanche property.By using disjoint linear codes and the distribution characteristics of Walsh spectrum,the upper bounds of the absolute and sum-of-squares indicators of this kind of resilient Boolean functions are given.Compared with similar functions,and under the premise of keeping currently best known nonlinearity,the absolute and sum-of-squares indicators of this type of functions are better.(2)With the help of fragmentary Walsh transform and High-Meets-Low technology,by using a 21-variable 1-resilient Boolean function with high nonlinearity,a large class of highly nonlinear resilient Boolean functions functions in odd variables with higher resiliency order are constructed.It is to make direct sum and concatenation in the four sets divided in the n-dimensional vector space,so as to obtain odd-variable high order resilient Boolean functions with strictly almost optimal nonlinearity,and the nonlinearity can reach 2^n-1-2^(n-1)/2+2^(n-7)/2.In addition,under the premise of the same nonlinearity,the resiliency order increases rapidly along with the growth of variable dimension.It is shown that this method can achieve a better tradeoff between nonlinearity and resiliency than those of the previous research results.