Chapter 5 - Hash Functions

Abstract

This chapter discusses the integrity aspects of hash functions. Secure one-way hash functions are recurring tools in cryptosystems just like the symmetric block ciphers. They are highly flexible primitives that can be used to obtain privacy, integrity and authenticity. A hash function (formally known as a pseudo random function or PRF) maps an arbitrary sized input to a fixed size output through a process known as compression. This form of compression is not typical data compression, but a noninvertible mapping. Checksum algorithms are forms of “hash functions,” and in many independent circles they are called just that. For example, mapping inputs to hash buckets is a simple way of storing arbitrary data that is efficiently searchable. In the cryptographic sense, hash functions must have two properties to be useful: they must be one-way and must be collision resistant. For these reasons, simple checksums and CRCs are not good hash functions for cryptography. Being one-way implies that given the output of a hash function, learning anything useful about the input is nontrivial. This is an important property for a hash, since they are often used in conjunction with RNG seed data and user passwords. Most trivial checksums are not one-way, since they are linear functions. For short enough inputs, deducing the input from the output is often a simple computation.