Spectrum is an important tool in researching functions. Two kinds of Chrestenson spectra, Chrestenson linear spectrum and cycle spectrum, are introduced in order to discuss multivalued logical functions. In ref. [1], ...Spectrum is an important tool in researching functions. Two kinds of Chrestenson spectra, Chrestenson linear spectrum and cycle spectrum, are introduced in order to discuss multivalued logical functions. In ref. [1], based on the spectral techniques’展开更多
There are many kinds of special relationships between multiple-valued logical func-tions and their variables, and they are difficult to be judged from their expressions. In thispaper, some sufficient and necessary con...There are many kinds of special relationships between multiple-valued logical func-tions and their variables, and they are difficult to be judged from their expressions. In thispaper, some sufficient and necessary conditions of the independence and statistical independenceof multiple-valued logical functions on their variables are given. Some conditions of algebraicindependence of multiple-valued logical functions on some of their variables and the way to de-generate a function to the greatest extent are proposed, and some applications of these resultsare indicated. All the results are studied by using Chrestenson spectral techniques.展开更多
Calculation of a variation of discrete Fourier transform.Chrestenson spectraof functions of n indeterminates over integer modulo m(composite integer),is con-sidered.Based on sparse matrix decomposition,two fast algori...Calculation of a variation of discrete Fourier transform.Chrestenson spectraof functions of n indeterminates over integer modulo m(composite integer),is con-sidered.Based on sparse matrix decomposition,two fast algorithms with complexityO(mnn∑ri=1pi)are given to calculate the Chrestenson spectra,where p1p2…p2 is theprime factor decomposition of m.展开更多
In this paper, a sufficient and necessary condition of quick trickle permutations is given from the point of inverse permutations. The bridge is built between quick trickle permutations and m-value logic functions. By...In this paper, a sufficient and necessary condition of quick trickle permutations is given from the point of inverse permutations. The bridge is built between quick trickle permutations and m-value logic functions. By the methods of the Chrestenson spectrum of m-value logic functions and the auto-correlation function of m-value logic functions to investigate the Chrestenson spectral characteristics and the auto-correlation function charac- teristics of inverse permutations of quick trickle permutations, a determinant arithmetic of quick trickle permutations is given. Using the results, it becomes easy to judge that a permutation is a quick trickle permutation or not by using computer. This gives a new pathway to study constructions and enumerations of quick trickle permutations.展开更多
Correlation-immunity is an important concept in cryptology. In ref. [1] Siegenthaler introduced the mathematical definition of correlation-immunity and used the correlation-immunity order of logic functions as a measu...Correlation-immunity is an important concept in cryptology. In ref. [1] Siegenthaler introduced the mathematical definition of correlation-immunity and used the correlation-immunity order of logic functions as a measure for cipher systems to defend against correlation attacks. In terms of Walsh transform, the correlation immunity of binary-valued logic functions, i.e. Boolean functions, was studied in ref. [2], and a展开更多
文摘Spectrum is an important tool in researching functions. Two kinds of Chrestenson spectra, Chrestenson linear spectrum and cycle spectrum, are introduced in order to discuss multivalued logical functions. In ref. [1], based on the spectral techniques’
文摘There are many kinds of special relationships between multiple-valued logical func-tions and their variables, and they are difficult to be judged from their expressions. In thispaper, some sufficient and necessary conditions of the independence and statistical independenceof multiple-valued logical functions on their variables are given. Some conditions of algebraicindependence of multiple-valued logical functions on some of their variables and the way to de-generate a function to the greatest extent are proposed, and some applications of these resultsare indicated. All the results are studied by using Chrestenson spectral techniques.
基金Supported by the National Natural Science Foundation of China(90104034)the 863 Program(2002AA141020)the Guangdong Provincial Natural Science Foundation(990336)
文摘Calculation of a variation of discrete Fourier transform.Chrestenson spectraof functions of n indeterminates over integer modulo m(composite integer),is con-sidered.Based on sparse matrix decomposition,two fast algorithms with complexityO(mnn∑ri=1pi)are given to calculate the Chrestenson spectra,where p1p2…p2 is theprime factor decomposition of m.
基金the Opening Foundation of State Key Labo-ratory of Information Security (20050102)
文摘In this paper, a sufficient and necessary condition of quick trickle permutations is given from the point of inverse permutations. The bridge is built between quick trickle permutations and m-value logic functions. By the methods of the Chrestenson spectrum of m-value logic functions and the auto-correlation function of m-value logic functions to investigate the Chrestenson spectral characteristics and the auto-correlation function charac- teristics of inverse permutations of quick trickle permutations, a determinant arithmetic of quick trickle permutations is given. Using the results, it becomes easy to judge that a permutation is a quick trickle permutation or not by using computer. This gives a new pathway to study constructions and enumerations of quick trickle permutations.
基金Project supported by the National Natural Science FoundationDoctoral Programme Foundation of Institutions of Higher Education
文摘Correlation-immunity is an important concept in cryptology. In ref. [1] Siegenthaler introduced the mathematical definition of correlation-immunity and used the correlation-immunity order of logic functions as a measure for cipher systems to defend against correlation attacks. In terms of Walsh transform, the correlation immunity of binary-valued logic functions, i.e. Boolean functions, was studied in ref. [2], and a
