This paper has studied the permutation formed by multiple -valued logical function group, Costas arrays, Orthomorphic permutation and has gained the results as following:1) In the first chapter, the main study achievements and results of Costas arrays, Boolean permutation, Orthomorphic permutation have been summarized.
In order to investigate the cryptographical properties of the Multi-outputting Boolean functions under non-uniformity of arguments, this paper defines the spectrum and eigenvalue, presents the general expression and estimation formula, and computes the upper bounds of agonic functions and t -resilient functions.
Construction of Cryptographically Important Boolean Permutations
In this paper a new general methodology is developed to construct Boolean permutations such that any non-trivial linear combination of their components has the largest algebraic degree.
This paper presents a sufficient and necessary condition on judging m-sequence besed on the relationship between Boolean permutation and m-sequence.
Boolean permutations have very important applications in cryptosystems. In this paper, a new construction method of Boolean permutations is presented, and the best updated enumeration lower bounds are found.