## Overview#

A Cryptographic Hash Function is a Hash Function with some additional properties:- Preimage Resistance - it is Computationally not realistic to determine the input Message
- Second Preimage Resistance - A given Message and the Hash it is Computationally not realistic find different Message with the same Hash
- Collision Resistance - it is Computationally not realistic to find two messages which produce the same Hash

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.

**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#

The 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.

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

### More Information#

There might be more information for this subject on one of the following:- Certificate Signature
- Crypt
- Cryptographic Primitive
- Cryptography
- Digital Signature
- HMAC-MD5
- HMAC-SHA1
- HMAC-SHA2
- Hash
- Keyed-Hash Message Authentication Code
- MD5
- Master Secret
- Message-Digest
- PBKDF2
- Record Protocol
- SHA-1
- SHA-3
- SHAttered
- Secure Hash Algorithm
- TLS 1.3
- Time-based One-time Password Algorithm
- Verifying Certificate Signatures
- Zero-knowledge proof

- [#1] - Cryptographic Hash Functions - based on information obtained 2013-04-10

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