New Algorithmic Algebraic Techniques for Cryptanalysis of Cryptographic Ciphers

Abstract

Thesis Summary 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.