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.
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.
- "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
- Cryptographic Primitive
- Digital Signature
- Keyed-Hash Message Authentication Code
- Master Secret
- Record Protocol
- Secure Hash Algorithm
- TLS 1.3
- Time-based One-time Password Algorithm
- Verifying Certificate Signatures
- Zero-knowledge proof