Hash Functions

Synonyms

Cryptographic hash functions; One-way hash functions

Definition

A hash function h is a well-defined deterministic algorithm that takes as input data of arbitrary length and produces a short fixed-length digital representation of the data, or a digest, as its output. The output of a hash function can serve the role of a digital “fingerprint” of the input data. A cryptographic hash function is often expected to have the following security properties:

• 1. One-way (or preimage resistance): given a hash value y, it is infeasible to find an input x that hashes to y, i.e., h(x) = y.

• 2. Weak collision resistance (or second preimage resistance): given an input x and the corresponding digest of that input h(x), it is infeasible to find another input x′; that matches the digest, i.e., h(x) = h(x′).

• 3. Strong collission resistance (or simply collision resistance): it is infeasible to find two different inputs x and x′; that hash to the same value, i.e., h(x) = h(x′).

The third property is...