This Thesis focuses on hash functions, which are used in numerous cryptographic mechanisms. We present various results, that belong to the fields of design and security analysis of hash functions. In the first part we introduce the field of hash functions. We describe how they are used in cryptography, and how to formalize security notions that guarantee their robustness in their various use cases. We also display the design rationale on which the most widely used hash functions are based. Then, we summarize the current situation of hash functions. A few years ago, differential cryptanalysis gave way to attacks on most of the recent hash algorithms. The adoption process for a new standard is under way, it will be the winner of the SHA-3 competition run by the NIST. In the second part we present the results that are related to the design of Shabal, a candidate to the SHA-3 competition. Firstly, we describe this function. We display some security analysis of the Shabal compression function and we give a security proof of the Shabal domain extender in the indifferentiability model, when it is combined with an idealized version of the compression function. We then describe a new model that enables the security analysis of domain extenders under weaker assumptions on the compression function. In the third part, we focus on cryptanalysis of hash functions. We present attacks on two different algorithms: the best known attack on RadioGatun, which was defined before the SHA-3 competition; and an attack against Hamsi-256, which was the first complete attack on a second-round SHA-3 candidate.
