Cryptographic hash function: Difference between revisions

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

[[Image:Cryptographic{{More Hashcitations needed|date=May 2016}} 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]].]]

{{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}});

* a ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of finding a second message that matches the given hash value when one message is already known;

* finding any pair of different messages that yield the same hash value (a ''collision'') is also infeasible: a cryptographic hash is expected to have a ''collision resistance'' strength of <math>n/2</math> bits (lower due to the [[birthday paradox]]).

A '''cryptographic hash function''' ('''CHF''') is a [[hash algorithm]] (a [[map (mathematics)|map]] of an arbitrary binary stringastring 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 OorschotapplicOorschot|Vanstone|2018|p=333}}

Cryptographic hash functions have many [[information security|information-security]] applications, notably in [[digital signature]]s, [[message authentication code]]s (MACs), and other forms of [[authentication]]. They can also be used as ordinary [[hash function]]s, to index data in [[hash table]]s, for [[fingerprint (computing)|fingerprinting]], to detect duplicate data or uniquely identify files, and as [[checksum]]s to detect accidental data corruption. Indeed, in information-security contexts, cryptographic hash values are sometimes called (''digital'') ''fingerprints'', ''checksums'', or just ''hash values'', even though all these terms stand for more general functions with rather different properties and purposes.<ref name="wjryW">{{cite web|last1=Schneier|first1=Bruce|author-link1=Bruce Schneier|title=Cryptanalysis of MD5 and SHA: Time for a New Standard|url=https://www.schneier.com/essays/archives/2004/08/cryptanalysis_of_md5.html|url-status=dead|archive-url=https://web.archive.org/web/20160316114109/https://www.schneier.com/essays/archives/2004/08/cryptanalysis_of_md5.html|archive-date=2016-03-16|access-date=2016-04-20|website=Computerworld|quote=Much more than encryption algorithms, one-way hash functions are the workhorses of modern cryptography.}}</ref>

* 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}});

* a ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of finding a second message that matches the given hash value when one message is already known;

* finding any pair of different messages that yield the same hash value (a ''collision'') is also infeasible: a cryptographic hash is expected to have a ''collision resistance'' strength of <math>n/2</math> bits (lower due to the [[birthday paradox]]).

Cryptographic hash functions have many [[information security|information-security]] applications, notably in [[digital signature]]s, [[message authentication code]]s (MACs), and other forms of [[authentication]]. They can also be used as ordinary [[hash function]]s, to index data in [[hash table]]s, for [[fingerprint (computing)|fingerprinting]], to detect duplicate data or uniquely identify files, and as [[checksum]]s to detect accidental data corruption. Indeed, in information-security contexts, cryptographic hash values are sometimes called (''digital'') ''fingerprints'', ''checksums'', or just ''hash values'', even though all these terms stand for more general functions with rather different properties and purposes.<ref name="wjryW">{{cite web|last1=Schneier|first1=Bruce|author-link1=Bruce Schneier|title=Cryptanalysis of MD5 and SHA: Time for a New Standard|url=https://www.schneier.com/essays/archives/2004/08/cryptanalysis_of_md5.html|url-status=dead|archive-url=https://web.archive.org/web/20160316114109/https://www.schneier.com/ essays/archives/2004/08/cryptanalysis_of_md5.html|archive-date=2016-03-16|access-date=2016-04-20|website=Computerworld|quote=Much more than encryption algorithms, one-way hash functions are the workhorses of modern cryptography.}}</ref>

[[Non-cryptographic hash function]]s are used in [[hash table]]s and to detect accidental errors; their constructions frequently provide no resistance to a deliberate attack. For example, a [[denial-of-service attack]] on hash tables is possible if the collisions are easy to find, as in the case of linear [[cyclic redundancy check]] (CRC) functions.{{sfn|Aumasson|2017|p=106}}

== Properties ==