Research On The Properties Of Permutations In Cryptosystems

Block ciphers have been extensively applied in computer communication and the safety field of information systems. In the design and the analysis of block ciphers, the permutations play an important role. It can be considered the permutation that is any cryptosystems lacking outstretched information. For example, DES, which is a standard encryption system, is the permutation in which the proclaimed in writing controlled by the secret key and RSA is also the multinomial permutation. So studying on properties and constructions of the permutations is significative not only on theory but also on application.Using the theories of probability, algebra, logical function in cryptology and spectral theory comprehensively, the dissertation investigates the properties and constructions of orthomorphic permutations, omni-direction permutations, quick trickle permutations and generalized orthomorphic permutations. Several new results are obtained. The main results of this dissertation are as following:1. The generalized Walsh spectral characteristics and the generalized auto-correlation function characteristics of orthormophic permutations are studied by using of knowledge about the relation between orthomorphic permutations and vector Boolean functions. Several results and construction of orthormophic permutations are obtained.2. The Chrestenson spectral characteristics and the auto-correlation function characteristics of inverse permutations of quick trickle permutations are given from the point of the inverse permutations.3. Using of knowledge about m -value logic functions to investigate the Chrestenson spectral characteristics and the auto-correlation function characteristics of omni-direction permutations, several results are obtained. Lastly, applying the results, give two sufficient and necessary conditions for an order complex number set to form the Chrestenson cyclic spectral of an omni-direction permutation.4. Based on orthomorphic permutations in F₂ⁿ and omni-direction permutations in Z_m , the definitions of generalized orthomorphic permutations and generalized orthomorphic matrices in Z_mⁿ are given. Some properties of them are obtained. The generalized Chrestenson spectral characteristics and the generalized auto-correlation function characteristics of generalized orthomorphic permutations are reseached and some constructions of generalized orthomorphic permutations are given.