The Study Of New Cryptographic Properties Of Boolean Functions

Boolean function is a very important tool in cryptography especially in stream ciphers .In this paper ,we propose the definition of complexity coefficient of a Boolean function for the first time . And we conclude that the linear complexity of a Boolean function is equal to its complexity coefficient .Given the true table of a Boolean function , we introduce a fast algorithm for computing its polynomial form according to the complexity coefficient theory .As an example ,we computed the polynomial form of all the 4-stage de Bruijn sequence whose linear complexity is 12 .After studied the complexity coefficient of Bent function ,we propose that Bent function can be classified according to its complexity coefficient, we got the possible range of Bent function's complexity coefficient and we proved that it is the best bound .We counted the exact number of Bent functions for some concrete complexity coefficient value, a new necessary condition for Bent function is also given in this article .A new method to attack nonlinear combined stream cipher was proposed in this paper. It only needs to know the stage of the LFSRs and enough sample bits to recover the initial states and the feedback polynomials. The complexity of the algorithm was studied , and we can conclude that the security can not be improved essentially by only increasing the number of LFSRs. Based on this attack, we put forward δ_F to measure the cryptographic ability of F to resisting this kind of attack and studied some properties of δ_F. We got the conclusion that when designing nonlinear combining stream cipher, δ_F should be possibly small. We gave all the functions that satisfy δ_F = 0 when n is 2 and 3 ,and an up bound of the number of thefunctions is 2^2n-n-2(n+ l)when n≥4...