الفهرس 
Cryptology
Cryptanalysis typesOnly 14 pages are availabe for public view
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Abstract
In our thesis we focus in Algebraic Cryptanalysis of AES ”Advanced Encryption Standard” hence Algebraic cryptanalysis is a relatively new field of cryptology. Algebraic cryptanalysis on Rijndael AES, is based on its rich algebraic structure. The basic idea is to model a cipher using a system of polynomial equations over a finite field. This approach has gained attention since Nicolas Courtois claimed that it could be used to attack AES, which has a simple algebraic structure [1]. This attack has also been attempted on other ciphers such as DES [2]. Algebraic cryptanalysis has been shown very effective for families of stream ciphers. Gröbner bases algorithms a well-known method to solve this problem. This thesis has described a description of cryptanalysis types, including Algebraic cryptanalysis type. We also describe the mathematical models of AES. There are three types of models to penetrate the AES cipher .Through this thesis we concentrate in the one which study the nonlinear part of the AES model .In general the equations of AES are divided into two groups, one linear which represents shift row , mix colum and add round key. The second group is the S-Box which is nonlinear.
S-box is the unique nonlinear operation in Rijndael cipher, and it determines the performance of AES cipher . So much work has concentrated on Rijndael S-box. Many researchers devote time to design and improve the algebraic cryptanalysis scheme
[3, 4,]. Algebraic cryptanalysis consists of two steps. First step converts the cipher into a system of polynomial equations, usually over GF(2), or over other rings. Second step, solves the system of equations and obtain from the solution the secret key of the cipher. Many researchers focus on these two steps. Courtois and Pieprzyk [7] analyzed the over defined system . Our focus on solving nonlinear system of equations GF( ) applying a powerful algebraic tool; Gröbner basis; to overcome the nonlinearity features of S-Box. Finally, the analysis shows that how applying Gröbner basis of AES constructs a spare matrix which makes the system easy to be solved. Moreover, we have proved the “Resistance of Algebraic Attack” RAA value ( ) has been reduced. We apply Gröbner basis on two models of nonlinear S-Box [7,8] .
Key words: Algebraic cryptanalysis, multivariate quadratic polynomial equation system, S-box, Gröbner bases, Rijndael AES, RAA.