Reaearches On Permutation Theory Of Block Ciphers

The researches of permutation theoty of block ciphers is one of heat points in cryptogrophy, because in fact block ciphers are permutation ,the security of a system of block ciphers has much relation to permutation used in this system .The thesis is devoted to the study of permutation theory of block ciphers, it consist of permutation polynomials over finite field, permutation over finite field, orthomorphic permutation and quick trickle permutation. Main contributions of this work are as follows: ? We investigate the regularity of permutation polynomials in n indeterminate over finite field, show the use of characters of finite Abelian groups in study of the permutation polynomials; obtain some theories on the construction of orthognomal polynomials systems. ? We give a algorithm to determine orthognomal polynomials systems, and point out resilient function is a extension of orthognomal polynomials systems in finite field F. ? We study the Boolean permutation ,almost perfect nonlinear permutation and highly nonlinear permutation .Because they play an important role in block ciphers ,so men devote much attention to them in nearly years. We sunirnarize conclusion in these aspect, give the methods of the construction of these permutation. ? A orthomorphic permutation is a perfectly balanced mapping, so orthomorphic permutation has good property of cryptography .We give many properties about orthomorphic permutation, this lay a reliable base to study orthomorphic permutation. ? We research the construction of orthomorphic permutation through many methods, give an example to use orthomorphic permutation to heighten security of block ciphers. ? A n order quick trickle permutation is permutation of n objects (1,2, - ,n) ,such that the spacings 1 梸 2, 2 ?3, etc. are all different ,so it has good cryptographic properties. We give many necessary conditions of quick trickle permutation; and research the graphic representation of quick trickle permutation. ? On the definition of quick trickle Latin squares, we give a method of constructing quick trickle permutation.