Hash function security:cryptanalysis of the Very Smooth Hash and multicollisions in generalised iterated hash functions

In recent years, the amount of electronic communication has grown enormously. This has posed some new problems in information security. In particular, the methods in cryptography have been under much scrutiny. There are several basic primitives that modern cryptographic protocols utilise. One of these is hash functions, which are used to compute short hash values from messages of any length. In this thesis, we study the security of hash functions from two different viewpoints. First of all, we analyse the security of the Very Smooth Hash against preimage attacks. We develop an improved method for finding preimages of Very Smooth Hash, compare this method with existing methods and demonstrate its efficiency with practical results. Furthermore, we generalise this method to the discrete logarithm variants of the Very Smooth Hash. Secondly, we describe the methods for finding multicollisions in traditional iterated hash functions and give some extensions and improvements to these. We also outline a method for finding multicollisions for generalised iterated hash functions and discuss the implications of these findings. In addition, we generalise these multicollision finding methods to some graph-based hash functions.