Introduction to Hash Functions

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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 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.

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
In Proceedings of CRYPTO, LNCS 435, pp. 416-427, Springer, 1989
[Electronic Edition] [Bibtex]
Author : Ivan Damg\aard
Title : A Design Principle for Hash Functions
In : In Proceedings of CRYPTO -

Ralph C. Merkle - One Way Hash Functions and DES
In Proceedings of CRYPTO, LNCS 435, pp. 428-446, Springer, 1989
[Electronic Edition] [Bibtex]
Author : Ralph C. Merkle
Title : One Way Hash Functions and DES
In : In Proceedings of CRYPTO -
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