Cryptographic hash function: Difference between revisions

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{{short description|Hash function that is suitable for use in cryptography}}

{{More citations needed|date=May 2016}}

[[Image:Cryptographic Hash Function.svg|thumb|375px|right|A cryptographic hash function (specifically [[SHA-1]]) at work. A small change in the input (in the word "over") drastically changes the output (digest). This is called the [[avalanche effect]].]][[
{{SHA-box}}

A]] '''cryptographic hash function''' ('''CHF''') is a [[hash algorithm]] (a [[map (mathematics)|map]] of an arbitrary binary string to a binary string with a fixed size of <math>n</math> bits) that has special properties desirable for a [[cryptography|cryptographic]] application:{{sfn|Menezes|van Oorschot|Vanstone|2018|p=33}}

* the probability of a particular <math>n</math>-bit output result ([[hash value]]) for a random input string ("message") is <math>2^{-n}</math> (as for any good hash), so the hash value can be used as a representative of the message;

* finding an input string that matches a given hash value (a ''pre-image'') is infeasible, ''assuming all input strings are equally likely.'' The ''resistance'' to such search is quantified as [[security strength]]: a cryptographic hash with <math>n</math> bits of hash value is expected to have a ''preimage resistance'' strength of <math>n</math> bits, unless the space of possible input values is significantly smaller than <math>2^{n}</math> (a practical example can be found in {{section link||Attacks on hashed passwords}});