Design And Analysis Of Key Components For Symmetric Ciphers

Symmetric cryptography is an important branch of morden cryptography, and it hasimportant theoretical value and extensive application prospect. Cryptographic functionsespecially Boolean functions and S-boxes are the key cryptographic components forsymmetric cryptosystems, their cryptographic properties directly influence the securityof the cryptosystems, and thus their studies play an important role in cryptography. Inthis dissertation, several problems about the construction, security test algorithm, andoptimization design of Boolean functions and S-boxes are investigated. The main resultsare as follows:1) The exact Walsh spectrum relationship between one Boolean function and its allsubfunctions is obtained. Using this important relationship and analysis method ofthe Walsh spectrum characteristic matrix for one Boolean function, we propose arecursive construction method for disjoint spectra functions. On the basis of this,an effective algorithm of constructing highly nonlinear resilient Boolean functionsis presented by concatenating plateaued functions.2) We generalize the concatenation techniques for Boolean functions to S-boxes andgive necessary and sufficient conditions for the concatenation S-box satisfying thestrict avalanche criterion (SAC). Using the idea of concatenating small variable S-boxes, we present a simple yet effective construction method for the SAC S-boxes.Combining the cryptographic technique of determining the bijective property foran S-box, we also give a method of designing the bijective SAC S-boxes.3) We provide a novel method for constructing new resilient S-boxes from old ones.The proposed method is a modification on the recursive construction technique ofresilient S-boxes due to Zhang et al. The modified construction has better perfor-mance since it increases the output dimensions of S-boxes, whereas having thesame resiliency as the existing method.4) Based on the generalized global avalanche characteristics (GGAC) between twoBoolean functions, a new security criterion which is called the cross-correlationcriterion for an S-box is proposed: the sum-of-squares indicator and the absoluteindicator. An algorithm of cross-correlation test on S-boxes is also presented. Inaddition, by studying the related properties of the cross-correlation between twobalanced functions, we give the theoretical and practical lower bounds on the sum -of-squares indicator related to GGAC for two balanced functions and an S-box.In short, our cross-correlation indicators provid the new security consideration fordesign and analysis of S-boxes.5) In view of the cryptanalysis method by fixing the coordinates of a cryptosystem,two security test for the S-boxes are presented. Firstly, from the point of statisticaltest, an algorithm of high-order bit independence criterion test for an S-box isgiven, which can be used to measure the output randomness when we keep someinput bits of an S-box constant. Secondly, we propose the concept of nonlinearityprofile for an S-box. An algorithm of nonlinearity profile test is presented, whichcan be used to measure how the nonlinearity degrades when a subset of the inputcoordinates are fixed. So the test tool can evaluate the global nonlinear ability ofan S-box.6) An intelligent optimization algorithm, called hill-climbing algorithm is analysed.Using the idea of swapping two output vectors to increase the nonlinearity of anS-box, we give a method to improve the nonlinearity by swapping three outputvectors. The method is simple and efficient in implementation. On basis of this,an optimization algorithm based on the hill-climbing algorithm for improving thenonlinearity of an S-box is also presented, which overcomes the disadvantage ofexisting algorithms that cannot improve the nonlinearity furthermore.