Introduction to Hash Functions

Security Requirements

The security properties that hash functions are expected to provide, are summarized in the following three basic requirements:

- Collision resistance: it is infeasible in practice to find two messages m and m^* != m such that h(m) = h(m^*).

- Second preimage resistance: for a given message m, it is infeasible in practice to find a second message m^* != m such that h(m) = h(m^*).

- Preimage resistance: it is infeasible in practice to find, for a given hash value y, a message m such that h(m) = y.

In practice there are several other requirements, but for sake of simplicity we stick to them.