Design Of Cryptographic Functions That Meet Multiple Indicators

Cryptographic functions,including Boolean functions and multiple output Boolean functions,play an important role in block ciphers schemes and certain stream ciphers schemes such as nonlinear combiners and filtering generators.Generally,the Boolean functions used in the ciphers should satisfy several criteria.The widely accepted criteria are high nonlinearity,balancedness,correlation immunity,high algebraic degree,good algebraic immunity and so on.The main research of this dissertation are the constructions of cryptographic functions with some of the criteria mentioned above,and the main results are as follows:1)By modifying the classical Maiorana-McFarland?M-M?construction,two classes of balanced Boolean functions and two classes of resilient Boolean functions have been got.All of these functions have strictly almost optimal nonlinearity,specially,some of the functions possess the currently best know nonlinearity.Also,the obtained functions have high algebraic degree and some even achieving the Siegenthaler's bound.It is shown that the algebraic immunity is also very good by the computer simulations.2)Two construction methods are provided to obtain n variable?n?10,n even?balanced Boolean functions.The constructed functions also satisfy strict avalanche criterion and have good global avalanche characteristics property.Comparing with other constructions that to obtain balanced Boolean functions satisfying SAC,the nonlinearity of our results can be 2^n-1-2^n/2-1-2^[n/4].3)By modifying the classical PS construction,two new construction methods of multiple-output functions satisfying balancedness and first-order correlation immune with strictly almost optimal nonlinearity and high algebraic degree have been presented.For the first time,the first-order correlation immune functions with currently best known nonlinearity-2^n-1-2^n/2-1-2^[n/4] are obtained.4)A construction technique so called "GMM" has been presented.The constructed resilient multiple-output Boolean functions can possess strictly almost optimal nonlinearity and the largerest number of output bits at the same time.This is the first time that the nonlinearity bound 2^n-1-2^n/2-1 of resilient?n,m?function has been exceeded for[n/4]?m<n/2.In addition,when m?n/4,the construction still works,and some resilient?n,m?functions with currently best know nonlinearity can also be obtained.