Theory and Analysis of Cryptographic Hash Functions

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Hash functions are essential primitives in Symmetric Cryptography, with great relevance for Asymmetric Cryptography as well. Hash functions require neither secret nor public keys and are used to generate short "fingerprints" of a fixed size from arbitrarily sized messages.There are two very different approaches to study the security of hash functions. one focuses on deficits, the other one on formal proofs. I.e., either a hash function is carefully analysed for potential flaws and weaknesses, or one formally proofs certain security properties for a given hash function to hold under certain assumptions, and within certain theoretical models. The project shall combine both approaches with each other -- the more theoretical approach to prove good properties and the more practical approach to search for attacks. Additionally, the project considers what hash functions are used for, in practice. Which requirements (security requirements, but also functional requirements) shall a hash function satisfy to be used secure, efficiently and at ease, in practice?