| This dissertation studies the cryptographic properties of "composition" logical function. The main results are as follows:Firstly, we present the decomposition formula of coincidence ratio between boolean "composition" function and any boolean function by using the decomposition formula of joint distribution of Boolean random vectors, and present the formula of Walsh spectrum and auto-correlation function of boolean "composition" function. By using them we discuss properties of boolean "composition" function and present some conditions under which boolean "composition" function is separate balanced, t-order correlation-immune, a (n,l,t) resilient function or t-order generalized e- correlation-immune, and give two conditions under which boolean "composition" function fufill separately the Strict Avalanche Criterion(SAC). We also construct a kind of boolean "composition" function which fufills SAC. Moreover, we study the properties of boolean "composition" vector function by using the conclusion about homologous properties of boolean "composition" function.Secondly, we present the formula of Chrestenson spectrum of m-value "composition" logical function by using inversion formula, and give the formula of auto-correlation function of m-value "composition" logical function. Furthermore, we give some conditions under which m-value "composition" logical function is separate balanced , correlation-immune or a (n,l,t) resilient function., and analyze the auto-correlation function of m-value "composition" logical function. Besides, we present the formular of nonzero linear combination of several "composition" logical functions.Finally, we discuss properties of multilevel boolean "composition" function, and present respectively the formula of Walsh spectrum of d-level "composition" boolean function. By using the formula we discuss properties of d-level "composition"boolean function, and present some conditions under which d-level "composition " boolean function is separate balanced, t-order correlation-immune or a (n,l,t) resilient function. |
