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Orthomorphism research and construction

Author: ZhuHuaAn
Tutor: XieDuanQiang
School: National University of Defense Science and Technology
Course: Computational Mathematics
Keywords: Group Finite fields Orthomorphism Permutation polynomials Linear structure Differential uniformity Block cipher Sequence password
CLC: TN918.1
Type: Master's thesis
Year: 2003
Downloads: 103
Quote: 1
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Abstract


Orthomorphism with good cryptographic properties, in cryptography, especially in the design of block ciphers has important applications. Paper on orthomorphism structure and nature of the study, based on the proposed orthomorphism orthomorphic translation of the concept, obtained orthomorphism orthomorphic translation is still orthomorphism conclusions and pointed out they The orthomorphism translational equivalence relationships between classes. In addition, also discussed orthomorphism and orthomorphism polynomials have one relationship, and use the theory of permutation polynomials shows that for any integer m ≥ 2, ax 3 bx 2 < / sup> cx d (α ≠ 0) is not GF (2 m ) on a regular permutation polynomials. How to construct orthomorphism is currently a hot research cryptography. This paper describes the current construction method, discussed several tectonic orthomorphism new method, and gives specific examples. Pointed to a nonlinear orthomorphism panning through orthomorphic can become a new nonlinear orthomorphism; explains how to change a orthomorphism local output value, the resulting displacement is still a orthomorphism: discusses the one kind by a 2 n -order orthomorphism construct 2 n 1 -order orthomorphism, further prove that if n> m> 1 时, 2 n -order orthomorphism number is not less than 2 m -order orthomorphism number: From low orthomorphism through certain combinations that can recursively construct arbitrarily high order Order orthomorphism. About orthomorphism in cryptosystems for specific applications, the paper describes the use of orthomorphism strengthen block ciphers, use orthomorphism password security function constructor method, and gives an advantage of orthomorphism strengthen cryptographic security of specific programs . High orthomorphism computer search is a difficult problem. The paper uses the orthomorphism perfect balance of features, gives orthomorphism fast search algorithm, using the algorithm got all the 16-step orthomorphism, and the number of their linear structure and differential uniformity, etc. were statistics, statistical results that do not exist under the 16-step almost perfect nonlinear (APN) orthomorphism further proposed a conjecture: does not exist APN orthomorphism.

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