This paper gives a survey on cryptographic hash functions. It gives an overview of all types of hash functions and reviews design principals and possible methods of attacks. It also focuses on keyed hash functions and provides the applications, requirements, and constructions of keyed hash functions.

When we ask what makes a hash function `good', we usually get an answer which includes collision freedom as the main (if not sole) desideratum. However, we show here that given any collision-free function, we can derive others which are also collision-free, but cryptographically useless. This explains why researchers have not managed to find many interesting consequences of this property. We also prove Okamoto's conjecture that correlation freedom is strictly stronger than collision freedom. We go on to show that there are actually rather many properties which hash functions may need. Hash functions for use with RSA must be multiplication free, in the sense that one cannot find X , Y and Z such that h(X)h(Y ) = h(Z); and more complex requirements hold for other signature schemes. Universal principles can be proposed from which all the freedom properties follow, but like most theoretical principles, they do not seem to give much value to a designer; at the practical level, the main imp...