Construction And Study Of A Class Of Cryptographic Functions

With the development of the communication and the computer technology, the status and function of information becomes more and more important in society. At the same time, the information security issues have become a social problem which is people's uppermost concern. Cryptography is the core of information security technology. Boolean functions can be used to construct some cryptosystems widely. The studies of many problems of symmetric cipher system, such as the S-boxes in block cipher and the combining functions in stream cipher, are equivalent to the studies of Boolean functions. Boolean functions also play important roles in coding theory, combinatorial design and sequence design. The focus of this thesis is on properties and constructions of Plateaued functions. The main results are as follows:(1) A class of cubic Plateaued functions has been investigated. It is shown that the functions have high nonlinearity and no nonzero linear structures. A condition is given that the functions are equivalent to cubic homogenous Plateaued functions by means of the symmetric matrixes. Besides, a method for constructing a class of cubic homogenous Plateaued functions is presented too.(2) A class of Plateaued functions has been gotten by way of using the Maiorana-McFarland construction. By the character of the state transform matrix of m-sequence, a class of (n+1)/2-dimension Plateaued functions with n variables is constructed. A variety of cryptographically desirable criteria for multi-dimension functions could be satisfied: high nonlinearity, nonexistence of nonzero linear structures, balance and the highest algebraic degree etc.