Hash Functions

Introduction

One of the most important cryptographic primitives is hash functions, which are used in many cryptographic protocols, particularly in signature schemes. Hash functions transform any kind of input data, regardless of its size, into a unique fixed-length bit-string. In contrast to all other cryptographic algorithms, hash functions don’t have a key.

Hash function

Let $\{0,1\}^{*}$ be an arbitrary sized, possibly infinite set, and $\{0,1\}^{n}$ a fixed finite. Then, a one-way funcion $H:\{0,1\}^{*} \rightarrow$ $\{0,1\}^{n}$ is called a hash function.

The computed value $y \in\{0,1\}^{n}$ is called message digest or hash value and can be seen as the fingerprint of a message, i.e., a fixed-length ( $n$ bits) unique representation of a message.

Figure 1