The Study Of Bent Function In Cryptography

Bent function is a class of the highest nonlinearity Boolean function, and Boolean function is the key in the cipher system. The Bent function is very important in the construction of a high nonlinearity Boolean function which is applied in the design of the cipher system.First, in this dissertation the symmetric cipher, particularly the design of the nonlinearity part, is analyzed. And the cryptographic properties of a cipher system are generalized. Through deducing the representation of the nonlinearity part of the symmetric cipher in Boolean function, the equivalence between symmetric cipher design and Boolean function is verified.Second, in the viewpoint of crypto analysis, the practical requirement for the cryptographic function is to construct the function that can resist all the known crypto analysis and attacks. In advanced, the main cryptographic properties are compared, and the relation among these cryptographic properties is analyzed, including the trade-off ones. Get the conclusion that the construction of cryptographic Boolean function is to find out the proper Boolean function in the whole vector space under the restriction of several cryptographic properties required for the security system.At last, the construction and the cryptographic properties of Bent function is the studied deeply. A concatenation construction of one Bent function from several Bent functions is proposed. Based on the WHT and C languages the Bent sequence of PS class is computed. Additionally, the properties and normal extension construction of normal Boolean function is studied, and checking algorithm of normal is discussed.