Propriétés algébriques de chiffrements symétriques et de leurs composants non-linéaires

Cryptography refers to the techniques providing secrecy in the presence of untrusted parties. In a digital world, this includes the case of stored data that should remain confidential, or of online communications which should remain private. In particular, symmetric cryptography is dedicated to the techniques which assume that a common secret is shared by the protagonists. These data, known as key, can then be used to encrypt and decrypt a message. Since the dawn of the Internet, the usage of cryptography has been driven by standardization. This enables the community to gain more trust in only a few primitives. This is the case of the AES, an American standard, which is now the most widespread symmetric cipher in the world. However, these standards have to evolve to follow the new constraints dictated by emerging use cases. For instance, lightweight cryptography ensures the security of very-constrained devices such as connected objects, or RFID tags. Last year, the American NIST institute has then chosen Ascon as their soon-to-be lightweight encryption standard. However, with the emergence of lightweight primitives, new security flaws were also discovered. Indeed, the balance between security, performance and cost is very fragile and is still not completely understood. It is therefore necessary to continue the cryptanalysis effort of the schemes that are used today to assess their resistance, but also the analysis of the ones that seem weaker to move toward a precise definition of weakness. This thesis contributes to the cryptanalysis of symmetric ciphers. First, we present a confidentiality issue which impacts Ascon when the cipher is used incorrectly. This attack can be implemented in practice and is based on a thorough analysis of the algebraic representation of the cipher. Next, we study Midori, another lightweight block cipher, which is heavily inspired from the structure of the AES. Despite security arguments given by the designers and which are endorsed by the community, serious flaws were recently discovered, for some specific classes of keys. We continue in this direction, by presenting another unexpected flaw, of a differential nature, that Midori was supposed to resist to. The methodology we use was never applied to these attacks, we therefore also fill the gap between well-studied methods and our new approach. Then, we study the differential resistance of the non-linear components used in every block ciphers. This analysis is purely theoretical and focuses on APN functions, which are optimal functions with respect to resistance to differential attacks. The same tools also enable us to study in detail a subfunction used in current Russian standards. Finally, we present two new designs for two emerging use cases other than the ones addressed by lightweight cryptrography. The first one is a family of message authentication codes (MAC), which are so far the fastest ones to be used on a PC. These MACs are based on the AES round function, which enables us to obtain strong security arguments. The second design is a stream cipher to be used as a transciphering method in an implementation of a fully homomorphic encryption called TFHE. This cipher is optimized for TFHE and in particular takes advantage of its programmable bootstrapping. Its design strategy is new and inspired from the design of block ciphers, and in particular from the AES.