Introduction to Hash Functions

1 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 <math>2^{62}</math> != m such that h(m) = h(m^*).

<math>2^{63}</math>

- 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.

2 On the construction of hash functions

Most hash functions in use today are designed following the Damgaard-Merkle design principle The idea is to split the input message m into l-bit blocks, which are then processed one after another by iterating a compression function f. Messages whose length is not a multiple of l bits need to be padded first.

Ivan Damg\aard - A Design Principle for Hash Functions

CRYPTO 435:416-427,1989

http://link.springer.de/link/service/series/0558/bibs/0435/04350416.htm
Bibtex

Author : Ivan Damg\aard
Title : A Design Principle for Hash Functions
In : CRYPTO -
Address :
Date : 1989

Ralph C. Merkle - One Way Hash Functions and DES

CRYPTO 435:428-446,1989

http://link.springer.de/link/service/series/0558/bibs/0435/04350428.htm
Bibtex

Author : Ralph C. Merkle
Title : One Way Hash Functions and DES
In : CRYPTO -
Address :
Date : 1989