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On Some Mathematical Problems in Advanced Encryption Standard

Author: ZhangAnYuan
Tutor: XieMin
School: Xi'an University of Electronic Science and Technology
Course: Cryptography
Keywords: Cryptography Advanced Encryption Standard Irreducible polynomials Branch number Algebraic
CLC: TN918.1
Type: Master's thesis
Year: 2011
Downloads: 36
Quote: 0
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Abstract


The mathematical theory is the theoretical basis for the support of cryptographic techniques , in-depth study of the mathematical theory is the premise and foundation to ensure the security of cryptographic algorithms . This paper first describes the course of development of cryptography and mathematical theory on the important role of cryptography , the next details the Advanced Encryption Standard , and a study for its algebraic properties of finite field irreducible polynomial . The main results are as follows : the S- box polynomial representation of Boolean functions and columns mixed transform sticks . According to the method represented by the small items of the Boolean function , there is given a method of calculating the polynomial representation of the Boolean function , the method can quickly calculate the number of the polynomial algebra . The algebraic properties mixcolumn transformation analysis , several special columns mixed transform definition and analysis of its security indicators - branch number . Maximum branch number under certain conditions, the construction method . Analysis of the relationship between the finite field on the degree of the polynomial order of the multiplicative group of the extension field finite field polynomial is irreducible polynomials of necessary and sufficient conditions , judged not on the limited domain about polynomials an efficient new method .

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CLC: > Industrial Technology > Radio electronics, telecommunications technology > Communicate > Confidentiality of communications and communications security > Theory
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