Constructions Of Highly Nonlinear Balanced Cryptographic Functions With Good Autocorrelation Properties

With the development of science and technology, cryptography, which is the theoretical foundation of the modern security system, attracts more and more attention. As an important part of modern cryptography, Symmetric cryptosystem has been widely used because of its faster encryption speed and easier realization of hardware. Boolean function, which is the most important component in symmetric cryptosystem, play a central role in the design of certain stream cipher and block cipher. Their cryptographic properties are crucial to the security of the whole system. The resistance against different attacks are largely measured by the cryptographic properties, such as nonlinearity, balanceness, correlation immunity, algebraic degree and algebraic immunity. Generally, we should ensure that these criteria can be as close to the optimal bound as possible when we construct a cryptographic function. However, there are many restricted relations among these criteria, and it has been an interesting problem to give a tradeoff.In this paper, we present a new construction of n-variable balanced Boolean functions with high nonlinearity. The value of the absolute indicator and the sum-of-squares indicator show that the function we obtained also have good global avalanche characteristics. And when n(28)4t(10)2,we also give another construction method to get balanced boolean functions which still have high nonlinearity and good global avalanche characteristics.In the modern design of a stream cipher, when we use an S-box instead of a single output one, it is possible to get more than one bits at each clock pulse and this increase the speed of the system. S-boxes also play an important role in block ciphers. Of course, these S-boxes we used should also satisfy some criteria such as high nonlinearity and good differential properties to resist different known attacks. In this paper, We also introduces a class of(n, n) S-boxes(n-input and n-output) by replace some output vectors in the source S-boxes. And the simulation results show that the S-boxes we get can have both high nonlinearity and good differential properties. Finally, based on the simulation results, we give a recommended number of the replaced vectors.