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* 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}});
*
* 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]]).
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[[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 ==
Most cryptographic hash functions are designed to take a [[string (computer science)|string]] of any length as input and produce a fixed-length hash value.
A cryptographic hash function must be able to withstand all known [[Cryptanalysis#Types of cryptanalytic attack|types of cryptanalytic attack]]. In theoretical cryptography, the security level of a cryptographic hash function has been defined using the following properties:
; Pre-image resistance : Given a hash value {{math|''h''}}, it should be difficult to find any message {{math|''m''}} such that {{math|1=''h'' = hash(''m'')}}. This concept is related to that of a [[one-way function]]. Functions that lack this property are vulnerable to [[preimage attack]]s.
; Second pre-image resistance : Given an input {{math|''m''{{sub|1}}}}, it should be difficult to find a different input {{math|''m''{{sub|2}}}} such that {{math|1=hash(''m''{{sub|1}}) = hash(''m''{{sub|2}})}}. This property is sometimes referred to as ''weak collision resistance''. Functions that lack this property are vulnerable to [[second-preimage attack]]s.
; [[Collision resistance]] : It should be difficult to find two different messages {{math|''m''{{sub|1}}}} and {{math|''m''{{sub|2}}}} such that {{math|1=hash(''m''{{sub|1}}) = hash(''m''{{sub|2}})}}. Such a pair is called a cryptographic [[hash collision]]. This property is sometimes referred to as ''strong collision resistance''. It requires a hash value at least twice as long as that required for pre-image resistance; otherwise, collisions may be found by a [[birthday attack]].{{sfn|Katz|Lindell|2014|pp=155–157, 190, 232}}
Collision resistance implies second pre-image resistance but does not imply pre-image resistance.{{sfn|Rogaway|Shrimpton|2004|loc=in Sec. 5. Implications}} The weaker assumption is always preferred in theoretical cryptography, but in practice, a hash-function
Informally, these properties mean that a [[adversary (cryptography)|malicious adversary]] cannot replace or modify the input data without changing its digest. Thus, if two strings have the same digest, one can be very confident that they are identical. Second pre-image resistance prevents an attacker from crafting a document with the same hash as a document the attacker cannot control. Collision resistance prevents an attacker from creating two distinct documents with the same hash.
A function meeting these criteria may still have undesirable properties. Currently, popular cryptographic hash functions are vulnerable to [[Length extension attack|''length-extension'' attacks]]: given {{math|hash(''m'')}} and {{math|len(''m'')}} but not {{math|''m''}}, by choosing a suitable {{math|{{′|''m''}}}} an attacker can calculate {{math|hash(''m'' ∥ {{′|''m''}})}}, where {{math|∥}} denotes [[concatenation]].<ref name="Y0rF6">{{cite web|url=http://vnhacker.blogspot.com/2009/09/flickrs-api-signature-forgery.html|title=Flickr's API Signature Forgery Vulnerability|first1=Thai|last1=Duong|first2=Juliano|last2=Rizzo|access-date=2012-12-07|archive-date=2013-08-15|archive-url=https://web.archive.org/web/20130815164303/http://vnhacker.blogspot.com/2009/09/flickrs-api-signature-forgery.html|url-status=live}}</ref> This property can be used to break naive authentication schemes based on hash functions. The [[HMAC]] construction works around these problems.
In practice, collision resistance is insufficient for many practical uses. In addition to collision resistance, it should be impossible for an adversary to find two messages with substantially similar digests; or to infer any useful information about the data, given only its digest. In particular, a hash function should behave as much as possible like a [[random function]] (often called a [[random oracle]] in proofs of security) while still being deterministic and efficiently computable. This rules out functions like the [[SWIFFT]] function, which can be rigorously proven to be collision-resistant assuming that certain problems on ideal lattices are computationally difficult, but, as a linear function, does not satisfy these additional properties.{{sfn|Lyubashevsky|Micciancio|Peikert|Rosen|2008| pp=54–72}}
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Checksum algorithms, such as [[CRC32]] and other [[cyclic redundancy check]]s, are designed to meet much weaker requirements and are generally unsuitable as cryptographic hash functions. For example, a CRC was used for message integrity in the [[Wired Equivalent Privacy|WEP]] encryption standard, but an attack was readily discovered, which exploited the linearity of the checksum.
=== Degree of difficulty ===
In cryptographic practice, "difficult" generally means "almost certainly beyond the reach of any adversary who must be prevented from breaking the system for as long as the security of the system is deemed important". The meaning of the term is therefore somewhat dependent on the application since the effort that a malicious agent may put into the task is usually proportional to their expected gain. However, since the needed effort usually multiplies with the digest length, even a thousand-fold advantage in processing power can be neutralized by adding a dozen bits to the latter.
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In some [[Computational complexity theory|theoretical analyses]] "difficult" has a specific mathematical meaning, such as "not solvable in [[asymptotic computational complexity|asymptotic]] [[polynomial time]]". Such interpretations of ''difficulty'' are important in the study of [[provably secure cryptographic hash function]]s but do not usually have a strong connection to practical security. For example, an [[exponential time|exponential-time]] algorithm can sometimes still be fast enough to make a feasible attack. Conversely, a polynomial-time algorithm (e.g., one that requires {{math|''n''<sup>20</sup>}} steps for {{math|''n''}}-digit keys) may be too slow for any practical use.
== Illustration ==
An illustration of the potential use of a cryptographic hash is as follows: [[Alice and Bob|Alice]] poses a tough math problem to [[Alice and Bob|Bob]] and claims that she has solved it. Bob would like to try it himself, but would yet like to be sure that Alice is not bluffing. Therefore, Alice writes down her solution, computes its hash, and tells Bob the hash value (whilst keeping the solution secret). Then, when Bob comes up with the solution himself a few days later, Alice can prove that she had the solution earlier by revealing it and having Bob hash it and check that it matches the hash value given to him before. (This is an example of a simple [[commitment scheme]]; in actual practice, Alice and Bob will often be computer programs, and the secret would be something less easily spoofed than a claimed puzzle solution.)
== Applications ==
=== Verifying the integrity of messages and files ===
{{ main | File verification }}
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[[MD5]], [[SHA-1]], or [[SHA-2]] hash digests are sometimes published on websites or forums to allow verification of integrity for downloaded files,<ref name="e87Bo">{{cite magazine | url=http://www.techrepublic.com/blog/security/use-md5-hashes-to-verify-software-downloads/374 | title=Use MD5 hashes to verify software downloads | magazine=TechRepublic | date=December 5, 2007 | access-date=March 2, 2013 | last=Perrin | first=Chad | archive-date=October 18, 2012 | archive-url=https://web.archive.org/web/20121018075308/http://www.techrepublic.com/blog/security/use-md5-hashes-to-verify-software-downloads/374 | url-status=live }}</ref> including files retrieved using [[file sharing]] such as [[Mirror website|mirroring]]. This practice establishes a [[chain of trust]] as long as the hashes are posted on a trusted site – usually the originating site – authenticated by [[HTTPS]]. Using a cryptographic hash and a chain of trust detects malicious changes to the file. Non-cryptographic [[error-detecting code]]s such as [[cyclic redundancy check]]s only prevent against ''non-malicious'' alterations of the file, since an intentional [[Spoofing attack|spoof]] can readily be crafted to have the [[Collision attack|colliding code]] value.
=== Signature generation and verification ===
{{ main | Digital signature }}
Almost all [[digital signature]] schemes require a cryptographic hash to be calculated over the message. This allows the signature calculation to be performed on the relatively small, statically sized hash digest. The message is considered authentic if the signature verification succeeds given the signature and recalculated hash digest over the message. So the message integrity property of the cryptographic hash is used to create secure and efficient digital signature schemes.
=== Password verification ===
{{main | Password hashing }}
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However, use of standard cryptographic hash functions, such as the SHA series, is no longer considered safe for password storage.<ref name="sp800-63B" />{{rp|5.1.1.2}} These algorithms are designed to be computed quickly, so if the hashed values are compromised, it is possible to try guessed passwords at high rates. Common [[graphics processing unit]]s can try billions of possible passwords each second. Password hash functions that perform [[key stretching]] – such as [[PBKDF2]], [[scrypt]] or [[Argon2]] – commonly use repeated invocations of a cryptographic hash to increase the time (and in some cases computer memory) required to perform [[brute-force attack]]s on stored password hash digests. For details, see {{section link||Attacks on hashed passwords}}.
A password hash also requires the use of a large random, non-secret [[Salt (cryptography)|salt]] value
=== Proof-of-work ===
{{ main | Proof of work }}
A proof-of-work system (or protocol, or function) is an economic measure to deter [[denial-of-service attack]]s and other service abuses such as spam on a network by requiring some work from the service requester, usually meaning processing time by a computer. A key feature of these schemes is their asymmetry: the work must be moderately hard (but feasible) on the requester side but easy to check for the service provider. One popular system – used in [[Bitcoin mining]] and [[Hashcash]] – uses partial hash inversions to prove that work was done, to unlock a mining reward in Bitcoin, and as a good-will token to send an e-mail in Hashcash. The sender is required to find a message whose hash value begins with a number of zero bits. The average work that the sender needs to perform in order to find a valid message is exponential in the number of zero bits required in the hash value, while the recipient can verify the validity of the message by executing a single hash function. For instance, in Hashcash, a sender is asked to generate a header whose 160-bit SHA-1 hash value has the first 20 bits as zeros. The sender will, on average, have to try {{math|2<sup>19</sup>}} times to find a valid header.
=== File or data identifier ===
A message digest can also serve as a means of reliably identifying a file; several [[Source Code Management|source code management]] systems, including [[Git (software)|Git]], [[Mercurial (software)|Mercurial]] and [[Monotone (software)|Monotone]], use the [[sha1sum]] of various types of content (file content, directory trees, ancestry information, etc.) to uniquely identify them. Hashes are used to identify files on [[peer-to-peer]] [[filesharing]] networks. For example, in an [[ed2k link]], an [[MD4]]-variant hash is combined with the file size, providing sufficient information for locating file sources, downloading the file, and verifying its contents. [[Magnet URI scheme|Magnet links]] are another example. Such file hashes are often the top hash of a [[hash list]] or a [[Merkle tree|hash tree]], which allows for additional benefits.
One of the main applications of a [[hash function]] is to allow the fast look-up of data in a [[hash table]]. Being hash functions of a particular kind, cryptographic hash functions lend themselves well to this application too.
However, compared with standard hash functions, cryptographic hash functions tend to be much more expensive computationally. For this reason, they tend to be used in contexts where it is necessary for users to protect themselves against the possibility of forgery (the creation of data with the same digest as the expected data) by potentially malicious participants.{{citation needed|date=May 2023}}
==== Content-addressable storage ====
{{excerpt|Content-addressable storage}}
== Hash functions based on block ciphers ==
There are several methods to use a [[block cipher]] to build a cryptographic hash function, specifically a [[one-way compression function]].
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A standard block cipher such as [[Advanced Encryption Standard|AES]] can be used in place of these custom block ciphers; that might be useful when an [[embedded system]] needs to implement both encryption and hashing with minimal code size or hardware area. However, that approach can have costs in efficiency and security. The ciphers in hash functions are built for hashing: they use large keys and blocks, can efficiently change keys every block, and have been designed and vetted for resistance to [[related-key attack]]s. General-purpose ciphers tend to have different design goals. In particular, AES has key and block sizes that make it nontrivial to use to generate long hash values; AES encryption becomes less efficient when the key changes each block; and related-key attacks make it potentially less secure for use in a hash function than for encryption.
== Hash function design ==
=== Merkle–Damgård construction ===
{{Main|Merkle–Damgård construction}}
[[Image:Merkle-Damgard hash big.svg|thumb|450px|right|The Merkle–Damgård hash construction]]
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The last block processed should also be unambiguously [[Padding (cryptography)|length padded]]; this is crucial to the security of this construction. This construction is called the [[Merkle–Damgård construction]]. Most common classical hash functions, including [[SHA-1]] and [[MD5]], take this form.
===
A straightforward application of the Merkle–Damgård construction, where the size of hash output is equal to the internal state size (between each compression step), results in a '''narrow-pipe''' hash design. This design causes many inherent flaws, including [[Length extension attack|length-extension]], multicollisions,<ref name="LkIref">{{Cite journal|last=Lucks|first=Stefan|date=2004|title=Design Principles for Iterated Hash Functions|url=https://eprint.iacr.org/2004/253|journal=Cryptology ePrint Archive|id=Report 2004/253|access-date=2017-07-18|archive-date=2017-05-21|archive-url=https://web.archive.org/web/20170521181207/http://eprint.iacr.org/2004/253|url-status=live}}</ref> long message attacks,{{sfn|Kelsey|Schneier|2005|pp=474–490}} generate-and-paste attacks,{{Citation needed|date=July 2017}} and also cannot be parallelized. As a result, modern hash functions are built on '''wide-pipe''' constructions that have a larger internal state size – which range from tweaks of the Merkle–Damgård construction<ref name="LkIref" /> to new constructions such as the [[sponge construction]] and [[HAIFA construction]].<ref name="EjaBK">{{Cite conference|last1=Biham|first1=Eli|last2=Dunkelman|first2=Orr|date=24 August 2006|title=A Framework for Iterative Hash Functions – HAIFA|url=https://eprint.iacr.org/2007/278|conference=Second NIST Cryptographic Hash Workshop|work=Cryptology ePrint Archive|id=Report 2007/278|access-date=18 July 2017|archive-date=28 April 2017|archive-url=https://web.archive.org/web/20170428160757/http://eprint.iacr.org/2007/278|url-status=live}}</ref> None of the entrants in the [[NIST hash function competition]] use a classical Merkle–Damgård construction.{{sfn|Nandi|Paul|2010}}
Meanwhile, truncating the output of a longer hash, such as used in SHA-512/256, also defeats many of these attacks.<ref name="ZY8I9">{{Cite report|last1=Dobraunig|first1=Christoph|last2=Eichlseder|first2=Maria|last3=Mendel|first3=Florian|date=February 2015|title=Security Evaluation of SHA-224, SHA-512/224, and SHA-512/256|url=http://www.cryptrec.go.jp/estimation/techrep_id2401.pdf|access-date=2017-07-18|archive-date=2016-12-27|archive-url=https://web.archive.org/web/20161227161240/http://cryptrec.go.jp/estimation/techrep_id2401.pdf|url-status=live}}</ref>
== Use in building other cryptographic primitives ==
Hash functions can be used to build other [[Cryptographic primitive|cryptographic primitives]]. For these other primitives to be cryptographically secure, care must be taken to build them correctly.
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Some hash functions, such as [[Skein (hash function)|Skein]], [[Keccak]], and [[RadioGatún]], output an arbitrarily long stream and can be used as a [[stream cipher]], and stream ciphers can also be built from fixed-length digest hash functions. Often this is done by first building a [[cryptographically secure pseudorandom number generator]] and then using its stream of random bytes as [[keystream]]. [[SEAL (cipher)|SEAL]] is a stream cipher that uses [[SHA-1]] to generate internal tables, which are then used in a keystream generator more or less unrelated to the hash algorithm. SEAL is not guaranteed to be as strong (or weak) as SHA-1. Similarly, the key expansion of the [[HC-256|HC-128 and HC-256]] stream ciphers makes heavy use of the [[SHA-256]] hash function.
== Concatenation ==
[[Concatenation|Concatenating]] outputs from multiple hash functions provide collision resistance as good as the strongest of the algorithms included in the concatenated result.{{Citation needed|date=May 2016}} For example, older versions of [[Transport Layer Security|Transport Layer Security (TLS) and Secure Sockets Layer (SSL)]] used concatenated [[MD5]] and [[SHA-1]] sums.{{sfn|Mendel|Rechberger|Schläffer|2009|p=145|ps= :Concatenating ... is often used by implementors to "hedge bets" on hash functions. A combiner of the form MD5|SHA-1 as used in SSL3.0/TLS1.0 ... is an example of such a strategy.}}{{sfn|Harnik|Kilian|Naor|Reingold|2005|p=99|ps=: the concatenation of hash functions as suggested in the TLS... is guaranteed to be as secure as the candidate that remains secure.}} This ensures that a method to find collisions in one of the hash functions does not defeat data protected by both hash functions.{{Citation needed|date=May 2016}}
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For [[Merkle–Damgård construction]] hash functions, the concatenated function is as collision-resistant as its strongest component, but not more collision-resistant.{{Citation needed|date=May 2016}} [[Antoine Joux]] observed that 2-collisions lead to {{math|''n''}}-collisions: if it is feasible for an attacker to find two messages with the same MD5 hash, then they can find as many additional messages with that same MD5 hash as they desire, with no greater difficulty.{{sfn|Joux|2004}} Among those {{math|''n''}} messages with the same MD5 hash, there is likely to be a collision in SHA-1. The additional work needed to find the SHA-1 collision (beyond the exponential birthday search) requires only [[polynomial time]].<ref name="urlGmane">{{cite web |url=http://article.gmane.org/gmane.comp.encryption.general/5154 |title=More Problems with Hash Functions |first=Hal |last=Finney |author-link=Hal Finney (computer scientist) |date=August 20, 2004 |work=The Cryptography Mailing List |access-date=May 25, 2016 |archive-url=https://web.archive.org/web/20160409095104/http://article.gmane.org/gmane.comp.encryption.general/5154 |archive-date=April 9, 2016 |url-status=dead}}</ref>{{sfn|Hoch|Shamir|2008|pp=616–630}}
== Cryptographic hash algorithms ==
There are many cryptographic hash algorithms; this section lists a few algorithms that are referenced relatively often. A more extensive list can be found on the page containing a [[comparison of cryptographic hash functions]].
=== MD5 ===
{{ Main | MD5 }}
MD5 was designed by [[Ronald Rivest]] in 1991 to replace an earlier hash function, MD4, and was specified in 1992 as RFC 1321. Collisions against MD5 can be calculated within seconds, which makes the algorithm unsuitable for most use cases where a cryptographic hash is required. MD5 produces a digest of 128 bits (16 bytes).
=== SHA-1 ===
{{ Main | SHA-1 }}
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Documents may refer to SHA-1 as just "SHA", even though this may conflict with the other Secure Hash Algorithms such as SHA-0, SHA-2, and SHA-3.
=== RIPEMD-160 ===
{{ Main | RIPEMD-160 }}
RIPEMD (RACE Integrity Primitives Evaluation Message Digest) is a family of cryptographic hash functions developed in Leuven, Belgium, by Hans Dobbertin, Antoon Bosselaers, and Bart Preneel at the COSIC research group at the Katholieke Universiteit Leuven, and first published in 1996. RIPEMD was based upon the design principles used in MD4 and is similar in performance to the more popular SHA-1. RIPEMD-160 has, however, not been broken. As the name implies, RIPEMD-160 produces a hash digest of 160 bits (20 bytes).
=== Whirlpool ===
{{ Main | Whirlpool (hash function) }}
Whirlpool is a cryptographic hash function designed by Vincent Rijmen and Paulo S. L. M. Barreto, who first described it in 2000. Whirlpool is based on a substantially modified version of the Advanced Encryption Standard (AES). Whirlpool produces a hash digest of 512 bits (64 bytes).
=== SHA-2 ===
{{ Main | SHA-2 }}
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The output size in bits is given by the extension to the "SHA" name, so SHA-224 has an output size of 224 bits (28 bytes); SHA-256, 32 bytes; SHA-384, 48 bytes; and SHA-512, 64 bytes.
=== SHA-3 ===
{{ Main | SHA-3 }}
SHA-3 (Secure Hash Algorithm 3) was released by NIST on August 5, 2015. SHA-3 is a subset of the broader cryptographic primitive family Keccak. The Keccak algorithm is the work of Guido Bertoni, Joan Daemen, Michael Peeters, and Gilles Van Assche. Keccak is based on a sponge construction, which can also be used to build other cryptographic primitives such as a stream cipher. SHA-3 provides the same output sizes as SHA-2: 224, 256, 384, and 512 bits.
Configurable output sizes can also be obtained using the SHAKE-128 and SHAKE-256 functions. Here the -128 and -256 extensions to the name imply the [[security strength]] of the function rather than the output size in bits.
=== BLAKE2 ===
{{ Main | BLAKE2 }}
BLAKE2, an improved version of BLAKE, was announced on December 21, 2012. It was created by Jean-Philippe Aumasson, Samuel Neves, [[Zooko Wilcox-O'Hearn]], and Christian Winnerlein with the goal of replacing the widely used but broken MD5 and SHA-1 algorithms. When run on 64-bit x64 and ARM architectures, BLAKE2b is faster than SHA-3, SHA-2, SHA-1, and MD5. Although BLAKE and BLAKE2 have not been standardized as SHA-3 has, BLAKE2 has been used in many protocols including the [[Argon2]] password hash, for the high efficiency that it offers on modern CPUs. As BLAKE was a candidate for SHA-3, BLAKE and BLAKE2 both offer the same output sizes as SHA-3 – including a configurable output size.
=== BLAKE3 ===
{{ Main | BLAKE3 }}
BLAKE3, an improved version of BLAKE2, was announced on January 9, 2020. It was created by Jack O'Connor, Jean-Philippe Aumasson, Samuel Neves, and Zooko Wilcox-O'Hearn. BLAKE3 is a single algorithm, in contrast to BLAKE and BLAKE2, which are algorithm families with multiple variants. The BLAKE3 compression function is closely based on that of BLAKE2s, with the biggest difference being that the number of rounds is reduced from 10 to 7. Internally, BLAKE3 is a [[Merkle tree]], and it supports higher degrees of parallelism than BLAKE2.
== Attacks on cryptographic hash algorithms ==
There is a long list of cryptographic hash functions but many have been found to be vulnerable and should not be used. For instance, NIST selected 51 hash functions<ref name="UNudB">Andrew Regenscheid, Ray Perlner, Shu-Jen Chang, John Kelsey, Mridul Nandi, Souradyuti Paul, [https://nvlpubs.nist.gov/nistpubs/Legacy/IR/nistir7620.pdf Status Report on the First Round of the SHA-3 Cryptographic Hash Algorithm Competition] {{Webarchive|url=https://web.archive.org/web/20180605095224/https://nvlpubs.nist.gov/nistpubs/Legacy/IR/nistir7620.pdf |date=2018-06-05 }}</ref> as candidates for round 1 of the SHA-3 hash competition, of which 10 were considered broken and 16 showed significant weaknesses and therefore did not make it to the next round; more information can be found on the main article about the [[NIST hash function competition]]s.
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Many cryptographic hashes are based on the [[Merkle–Damgård construction]]. All cryptographic hashes that directly use the full output of a Merkle–Damgård construction are vulnerable to [[length extension attack]]s. This makes the MD5, SHA-1, RIPEMD-160, Whirlpool, and the SHA-256 / SHA-512 hash algorithms all vulnerable to this specific attack. SHA-3, BLAKE2, BLAKE3, and the truncated SHA-2 variants are not vulnerable to this type of attack.{{cit|date=April 2020}}
== Attacks on hashed passwords ==
{{main|Password cracking}}
Rather than store plain user passwords, controlled-access systems frequently store the hash of each user's password in a file or database. When someone requests access, the password they submit is hashed and compared with the stored value. If the database is stolen (an all-too-frequent occurrence<ref name="jjUS1">{{cite news|url=https://www.csoonline.com/article/2130877/the-biggest-data-breaches-of-the-21st-century.html|title=The 15 biggest data breaches of the 21st century|first=Dan|last=Swinhoe|first2=Michael|last2=Hill|publisher=CSO Magazine|date=April 17, 2020|access-date=November 25, 2020|archive-date=November 24, 2020|archive-url=https://web.archive.org/web/20201124152328/https://www.csoonline.com/article/2130877/the-biggest-data-breaches-of-the-21st-century.html|url-status=live}}</ref>), the thief will only have the hash values, not the passwords.
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The United States [[National Institute of Standards and Technology]] recommends storing passwords using special hashes called [[key derivation function]]s (KDFs) that have been created to slow brute force searches.<ref name="sp800-63B">{{cite book | title = SP 800-63B-3 – Digital Identity Guidelines, Authentication and Lifecycle Management | publisher = NIST | date = June 2017 | doi=10.6028/NIST.SP.800-63b | author=Grassi Paul A.}}</ref>{{rp|5.1.1.2}} Slow hashes include [[pbkdf2]], [[bcrypt]], [[scrypt]], [[argon2]], [[Balloon hashing|Balloon]] and some recent modes of [[crypt (C)|Unix crypt]]. For KDFs that perform multiple hashes to slow execution, NIST recommends an iteration count of 10,000 or more.<ref name="sp800-63B" />{{rp|5.1.1.2}}
== See also ==
{{div col|colwidth=23em}}
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== References ==
=== Citations ===
{{reflist}}
=== Sources ===
{{refbegin}}
* {{cite book|last1=Harnik|first1=Danny|last2=Kilian|first2=Joe|last3=Naor|first3=Moni|last4=Reingold |first4=Omer|last5=Rosen|first5=Alon|title=Advances in Cryptology – EUROCRYPT 2005|chapter=On Robust Combiners for Oblivious Transfer and Other Primitives|series=Lecture Notes in Computer Science|volume=3494 |year=2005|pages=96–113|issn=0302-9743|doi=10.1007/11426639_6|isbn=978-3-540-25910-7}}
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* {{cite book | first1 = Jean-Philippe | last1 = Aumasson | date = 6 November 2017 | title = Serious Cryptography: A Practical Introduction to Modern Encryption | publisher = No Starch Press | pages = | isbn = 978-1-59327-826-7 | oclc = 1012843116 | url = https://books.google.com/books?id=W1v6DwAAQBAJ}}
== External links ==
* {{cite book | first1 = Christof | last1 = Paar | first2 = Jan | last2 = Pelzl | chapter-url = http://wiki.crypto.rub.de/Buch/movies.php | chapter = 11: Hash Functions | title = Understanding Cryptography, A Textbook for Students and Practitioners | publisher = [[Springer Science+Business Media|Springer]] | date = 2009 | url-status = dead | archive-url = https://archive.today/20121208212741/http://wiki.crypto.rub.de/Buch/movies.php | archive-date = 2012-12-08 }} (companion web site contains online cryptography course that covers hash functions)
* {{cite web | url = http://ehash.iaik.tugraz.at/wiki/The_eHash_Main_Page | title = The ECRYPT Hash Function Website }}
* {{cite web | url = http://www.guardtime.com/educational-series-on-hashes/ | title = Series of mini-lectures about cryptographic hash functions | first = A. | last = Buldas | date = 2011 | url-status = dead | archive-url = https://archive.today/20121206020054/http://www.guardtime.com/educational-series-on-hashes/ | archive-date = 2012-12-06 }}
* [https://github.com/CRPrinzler/HASH-verify Open source python based application with GUI used to verify downloads.]
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