Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively ...Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively studied over the past few decades,there has been limited research on the construction of almost optimal five-valued spectra vectorial Boolean functions.In this paper,we present a construction method for even-variable 2-output almost optimal five-valued spectra balanced Boolean functions,whose Walsh spectra values belong to the set{0,±2^(n/2),±2^(n/2+1)},at the same time,we discuss the existence of sufficient conditions in the construction.Additionally,this paper presents a novel construction method for balanced single-output Boolean functions with even variables featuring a special five-valued spectral structure,whose Walsh spectra values are constrained to the set{0,±2^(n/2),±3·2^(n/2)}.These functions provide new canonical examples for the study of Boolean function spectral theory.展开更多
The algorithm is based on constructing a disjoin kg t set of the minimal paths in a network system.In this paper, cubic notation was used to describe the logic function of a network in a well-balanced state,and then t...The algorithm is based on constructing a disjoin kg t set of the minimal paths in a network system.In this paper, cubic notation was used to describe the logic function of a network in a well-balanced state,and then the sharp-product operation was used to construct the disjoint minimal path set of the network.A computer program has been developed,and when combined with decomposition technology,the reliability of a general lifeline network can be effectively and automatically calculated.展开更多
基金National Natural Science Foundation of China(62272360)。
文摘Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively studied over the past few decades,there has been limited research on the construction of almost optimal five-valued spectra vectorial Boolean functions.In this paper,we present a construction method for even-variable 2-output almost optimal five-valued spectra balanced Boolean functions,whose Walsh spectra values belong to the set{0,±2^(n/2),±2^(n/2+1)},at the same time,we discuss the existence of sufficient conditions in the construction.Additionally,this paper presents a novel construction method for balanced single-output Boolean functions with even variables featuring a special five-valued spectral structure,whose Walsh spectra values are constrained to the set{0,±2^(n/2),±3·2^(n/2)}.These functions provide new canonical examples for the study of Boolean function spectral theory.
基金Key Project of Science and Technology from the State Plan Committee.No.101-9914003
文摘The algorithm is based on constructing a disjoin kg t set of the minimal paths in a network system.In this paper, cubic notation was used to describe the logic function of a network in a well-balanced state,and then the sharp-product operation was used to construct the disjoint minimal path set of the network.A computer program has been developed,and when combined with decomposition technology,the reliability of a general lifeline network can be effectively and automatically calculated.
