## Overview#

A Cryptographic Hash Function is a Hash Function with some additional properties:

A Cryptographic Hash Function must with a high Level Of Assurance:

• generate a Unique Hash for every different Message.
• generate a the same Hash for the same Message every time.
If a Cryptographic Hash Function can NOT produce a Unique Cryptographic Hash Function for every different Message, then that algorithm is considered NOT Collision Resistance and could be Exploited.

### Most Common Cryptographic Hash Function#

The most commonly used Cryptographic Hash Function function today (2015-03-15) is SHA-1, which has output of 160 bits.

### Strength of Cryptographic Hash Function#

Unlike with Ciphers, the strength of a Cryptographic Hash Function doesn’t equal the Hash length. Because of the Birthday Paradox (a well-known problem in probability theory), the strength of a Cryptographic Hash Function is at most one half of the Hash length.

### One-way function#

A one-way function is a Cryptographic Hash Function that is easy to compute but "hard to invert" (in the sense defined below).
• "Easy to compute" means that some algorithm can compute the function in polynomial time (in the input size).
• "Hard to invert" means that no probabilistic polynomial-time algorithm can compute a preimage element of f(x) with better than negligible probability, when x is chosen at random.
The harder it is to compute raises the Level Of Assurance.

Note that unlike hardness in most of complexity theory (e.g., NP-hardness), "hard" in the context of one-way functions refers to average-case hardness rather than worst-case hardness.

The existence of "pure" one-way functions is an open conjecture. for more information see Wikipedia:One-way_function

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