On Cryptographic Hash Functions: Definitions, Ideas and Practical Cryptographic Attacks

Hash functions, and cryptographic hash functions in particular, underpin the technologies on which modern life is built. Efficient databases, the Internet, the World Wide Web, online payments and more, would not be possible without the security and efficiency gains derived from the use of these functions. In this thesis we will introduce the definitions of hash functions and cryptographic hash functions, comment on the ideas that underlie and inspire these definitions and design the probabilistic models in which they become rigorous mathematical concepts. In Chapter 3, we will examine three cryptographic attacks against specific hash functions, calculate the expected cost of execution and estimate the real-world security associated with such functions.