Construction And Analysis Of Cryptographic Functions With Five-Valued Walsh Spectra

One of the core issues of cryptography is about the security of cryptographic functions.The security of cryptosystems mainly depends on the cryptographic nature of Boolean functions.Because there are constraints between various cryptographic properties,it is impossible for the various performances of a cryptographic function to reach the optimal at the same time.In order to achieve multiple compromises in cryptographic properties,people began to study a class of cryptographic functions with five-valued Walsh spectral characteristics.This paper is mainly to design and construct five-valued Walsh spectral functions.The following are the main work of this article:1.Referring to the idea of M-M construction method,three direct constructions of five-spectrum cryptographic functions are designed by modifying the mapping of the functions.The first method is to design the function mapping(?)as a two-to-one and one-to-one combination.Considering the dimensional parity of the input variables,a class of cryptographic functions with five-valued Walsh spectral features are constructed.Such functions have cryptographic properties such as balanceness and SAC.Based on this method,the second method was obtained by considering the relevant immunity.The second method is to design the function map(?)as a combination of four to one.Thus,a class of cryptographic functions with five-valued Walsh spectral characteristics is constructed,which has cryptographic properties such as balanceness,correlation immunity,and SAC.That is,the resilient Boolean function of the five-valued Walsh spectral feature.It also discusses the case when the dimensions of the input variables have different parity.The third method is to design the mapping(?)of each component function.Resilient Boolean functions with five-valued Walsh spectral and multi-dimensional vectorial outputs are constructed.2.From the perspective of indirect construction,two methods for constructing a Boolean function with a five-valued Walsh spectrum are given.The first method refers to the direct sum method.Plateaued functions are used to indirectly construct a Boolean function whose Walsh spectral value is (?).The second method is the reference cascade construction method.Plateaued function is used to construct a Boolean function with a Walsh spectrum of (?).These two methods are relatively simple and easy to operate.Finally,a class of 2-valued Walsh spectral feature cryptographic functions on vector space are designed using disjoint linear codes on vector space and PS class construction method.In addition,a Boolean function of the six-valued Walsh spectrum is constructed indirectly through the cascade construction method...