# Conception, développement et analyse de systèmes de fonction booléennes décrivant les algorithmes de chiffrement et de déchiffrement de l'Advanced Encryption Standard

Abstract : Cryptology is one of the mathematical fields, it is composed of two subsets: cryptography and cryptanalysis. While cryptography focuses on algorithms to modify an information by making it unintelligible without knowledge of a secret, the second focuses on mathematical methods to recover the original information from the only knowledge of the encrypted element.Cryptography itself is subdivided into two subsets: symmetric cryptography and asymmetric cryptography. The first uses the same key for encryption and decryption operations, while the second uses one key for encryption and another key, different from the previous one, for decryption. Finally, symmetric cryptography is working either on blocks of information either on continuous flow of information. These are algorithms block cipher that interests us here.The aim of cryptanalysis is to recover the original information without knowing the encryption key and this, into a shorter time than the brute-force attack. There are many methods of cryptanalysis as frequency cryptanalysis, differential cryptanalysis, integral cryptanalysis, linear cryptanalysis...Many of these methods are defeated by modern encryption algorithms. Indeed, in a game of spear and shield, cryptographers develop encryption algorithms more efficient to protect the encrypted information from an attack by cryptanalysis. This is the case of the Advanced Encryption Standard (AES). This block cipher algorithm was designed by Joan Daemen and Vincent Rijmen and transformed into standard by the National Institute of Standards and Technology (NIST) in 2001. To counter the usual methods of cryptanalysis of AES designers have given it a strong algebraic structure.This choice eliminates brilliantly any possibility of statistical attack, however, recent work suggests that what is supposed to be the strength of the AES, could prove to be his weak point. According to these studies, the AES cryptanalysis comes down to solve'' a quadratic equations symbolizing the structure of the AES encryption. Unfortunately, the size of the system of equations obtained and the lack of efficient resolution algorithms make it impossible, at this time, to solve such systems in a reasonable time.The challenge of this thesis is, from the algebraic structure of the AES, to describe its encryption and decryption processes in the form of a new Boolean equations system. Then, based on a specific representation of these equations, to achieve a combinatorial analysis to detect potential statistical biases.
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Cited literature [182 references]

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DUBOIS.pdf
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• HAL Id : tel-01799562, version 1

### Citation

Michel Dubois. Conception, développement et analyse de systèmes de fonction booléennes décrivant les algorithmes de chiffrement et de déchiffrement de l'Advanced Encryption Standard. Automatique / Robotique. Ecole nationale supérieure d'arts et métiers - ENSAM, 2017. Français. ⟨NNT : 2017ENAM0024⟩. ⟨tel-01799562⟩

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