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<title>Message authentication code</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Message authentication code</span></span>

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<p>

In <a href="Cryptography" title="Cryptography">cryptography</a>, a <b>message authentication code</b> (<b>MAC</b>), sometimes known as an <b>authentication tag</b>, is a short piece of information used for <a href="Authentication" title="Authentication">authenticating</a> and <a href="Data_integrity" title="Data integrity">integrity</a>-checking a message. In other words, it is used to confirm that the message came from the stated sender (its authenticity) and has not been changed (its integrity). The MAC value allows verifiers (who also possess a secret key) to detect any changes to the message content.

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<div class="mw-heading mw-heading2"><h2 id="Terminology">Terminology</h2></div>

<p>The term <b>message integrity code</b> (<b>MIC</b>) is frequently substituted for the term <i>MAC</i>, especially in communications<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> to distinguish it from the use of the latter as <i><a href="Media_access_control_address" class="mw-redirect" title="Media access control address">media access control address</a></i> (<i>MAC address</i>). However, some authors<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> use MIC to refer to a <a href="Message_digest" class="mw-redirect" title="Message digest">message digest</a>, which aims only to uniquely but opaquely identify a single message. RFC 4949 recommends avoiding the term <i>message integrity code</i> (MIC), and instead using <i><a href="Checksum" title="Checksum">checksum</a></i>, <i><a href="Error_detection_code" class="mw-redirect" title="Error detection code">error detection code</a></i>, <i><a href="Hash_function" title="Hash function">hash</a></i>, <i>keyed hash</i>, <i>message authentication code</i>, or <i>protected checksum</i>.

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<div class="mw-heading mw-heading2"><h2 id="Definitions">Definitions</h2></div>

<p>Informally, a message authentication code system consists of three algorithms:

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<ul><li>A <a href="Key_generation" title="Key generation">key generation</a> algorithm selects a key from the key space uniformly at random.</li>

<li>A MAC generation algorithm efficiently returns a tag given the key and the message.</li>

<li>A verifying algorithm efficiently verifies the authenticity of the message given the same key and the tag. That is, return <i>accepted</i> when the message and tag are not tampered with or forged, and otherwise return <i>rejected</i>.</li></ul>

<p>A secure message authentication code must resist attempts by an adversary to <a href="Digital_signature_forgery" title="Digital signature forgery">forge tags, for arbitrary, selected, or all messages</a>, including under conditions of <a href="Digital_signature_forgery" title="Digital signature forgery">known-</a> or <a href="Digital_signature_forgery" title="Digital signature forgery">chosen-message</a>. It should be computationally infeasible to compute a valid tag of the given message without knowledge of the key, even if for the worst case, we assume the adversary knows the tag of any message but the one in question.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>Formally, a <b>message authentication code</b> (<b>MAC</b>) system is a triple of efficient<sup id="cite_ref-:1_4-0" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> algorithms (<i>G</i>, <i>S</i>, <i>V</i>) satisfying:

</p>

<ul><li><i>G</i> (key-generator) gives the key <i>k</i> on input <a href="Unary_numeral_system" title="Unary numeral system">1<sup><i>n</i></sup></a>, where <i>n</i> is the <a href="Security_parameter" title="Security parameter">security parameter</a>.</li>

<li><i>S</i> (signing) outputs a tag <i>t</i> on the key <i>k</i> and the input string <i>x</i>.</li>

<li><i>V</i> (verifying) outputs <i>accepted</i> or <i>rejected</i> on inputs: the key <i>k</i>, the string <i>x</i> and the tag <i>t</i>.</li></ul>

<p><i>S</i> and <i>V</i> must satisfy the following:

</p>

<dl><dd><span class="texhtml">Pr [ <i>k</i> ← <i>G</i>(1<sup><i>n</i></sup>), <i>V</i>( <i>k</i>, <i>x</i>, <i>S</i>(<i>k</i>, <i>x</i>) ) = <i>accepted</i> ] = 1</span>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></dd></dl>

<p>A MAC is <b>unforgeable</b> if for every efficient adversary <i>A</i>

</p>

<dl><dd><span class="texhtml">Pr [ <i>k</i> ← <i>G</i>(1<sup><i>n</i></sup>), (<i>x</i>, <i>t</i>) ← <i>A</i><sup><i>S</i>(<i>k</i>, · )</sup>(1<sup><i>n</i></sup>), <i>x</i> ∉ Query(<i>A</i><sup><i>S</i>(<i>k</i>, · )</sup>, 1<sup><i>n</i></sup>), <i>V</i>(<i>k</i>, <i>x</i>, <i>t</i>) = <i>accepted</i>] < negl(<i>n</i>)</span>,</dd></dl>

<p>where <i>A</i><sup><i>S</i>(<i>k</i>, · )</sup> denotes that <i>A</i> has access to the oracle <i>S</i>(<i>k</i>, · ), and Query(<i>A</i><sup><i>S</i>(<i>k</i>, · )</sup>, 1<sup><i>n</i></sup>) denotes the set of the queries on <i>S</i> made by <i>A</i>, which knows <i>n</i>. Clearly we require that any adversary cannot directly query the string <i>x</i> on <i>S</i>, since otherwise a valid tag can be easily obtained by that adversary.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Security">Security</h2></div>

<p>While MAC functions are similar to <a href="Cryptographic_hash_function" title="Cryptographic hash function">cryptographic hash functions</a>, they possess different security requirements. To be considered secure, a MAC function must resist <a href="Existential_forgery" class="mw-redirect" title="Existential forgery">existential forgery</a> under <a href="Digital_signature_forgery" title="Digital signature forgery">chosen-message attacks</a>. This means that even if an attacker has access to an <a href="Oracle_machine" title="Oracle machine">oracle</a> which possesses the secret key and generates MACs for messages of the attacker's choosing, the attacker cannot guess the MAC for other messages (which were not used to query the oracle) without performing infeasible amounts of computation.

</p><p>MACs differ from <a href="Digital_signature" title="Digital signature">digital signatures</a> as MAC values are both generated and verified using the same secret key. This implies that the sender and receiver of a message must agree on the same key before initiating communications, as is the case with <a href="Symmetric_encryption" class="mw-redirect" title="Symmetric encryption">symmetric encryption</a>. For the same reason, MACs do not provide the property of <a href="Non-repudiation" title="Non-repudiation">non-repudiation</a> offered by signatures specifically in the case of a network-wide <a href="Shared_secret" title="Shared secret">shared secret</a> key: any user who can verify a MAC is also capable of generating MACs for other messages. In contrast, a digital signature is generated using the private key of a key pair, which is public-key cryptography.<sup id="cite_ref-:1_4-1" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Since this private key is only accessible to its holder, a digital signature proves that a document was signed by none other than that holder. Thus, digital signatures do offer non-repudiation. However, non-repudiation can be provided by systems that securely bind key usage information to the MAC key; the same key is in the possession of two people, but one has a copy of the key that can be used for MAC generation while the other has a copy of the key in a <a href="Hardware_security_module" title="Hardware security module">hardware security module</a> that only permits MAC verification. This is commonly done in the finance industry.

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</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="Key_commitment" class="mw-redirect" title="Key commitment">Key commitment</a></div>

<p>While the primary goal of a MAC is to prevent forgery by adversaries without knowledge of the secret key, this is insufficient in certain scenarios. When an adversary is able to control the MAC key, stronger guarantees are needed, akin to <a href="Collision_resistance" title="Collision resistance">collision resistance</a> or <a href="Preimage_attack" title="Preimage attack">preimage security</a> in hash functions. For MACs, these concepts are known as <i>commitment</i> and <i>context-discovery</i> security.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Implementation">Implementation</h2></div>

<p>MAC algorithms can be constructed from other cryptographic primitives, like <a href="Cryptographic_hash_function" title="Cryptographic hash function">cryptographic hash functions</a> (as in the case of <a href="HMAC" title="HMAC">HMAC</a>) or from <a href="Block_cipher" title="Block cipher">block cipher</a> algorithms (<a href="OMAC_(cryptography)" class="mw-redirect" title="OMAC (cryptography)">OMAC</a>, <a href="CCM_mode" title="CCM mode">CCM</a>, <a href="Galois/Counter_mode" class="mw-redirect" title="Galois/Counter mode">GCM</a>, and <a href="PMAC_(cryptography)" title="PMAC (cryptography)">PMAC</a>). However many of the fastest MAC algorithms, like <a href="UMAC_(cryptography)" title="UMAC (cryptography)">UMAC</a>-<a href="VMAC" title="VMAC">VMAC</a> and <a href="Poly1305-AES" class="mw-redirect" title="Poly1305-AES">Poly1305-AES</a>, are constructed based on <a href="Universal_hashing" title="Universal hashing">universal hashing</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

</p><p>Intrinsically keyed hash algorithms such as <a href="SipHash" title="SipHash">SipHash</a> are also by definition MACs; they can be even faster than universal-hashing based MACs.<sup id="cite_ref-SipHash_9-0" class="reference"><a href="#cite_note-SipHash-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>

</p><p>Additionally, the MAC algorithm can deliberately combine two or more cryptographic primitives, so as to maintain protection even if one of them is later found to be vulnerable. For instance, in <a href="Transport_Layer_Security" title="Transport Layer Security">Transport Layer Security</a> (TLS) versions before 1.2, the <a href="Input_data" class="mw-redirect" title="Input data">input data</a> is split in halves that are each processed with a different hashing primitive (<a href="SHA-1" title="SHA-1">SHA-1</a> and <a href="SHA-2" title="SHA-2">SHA-2</a>) then <a href="Exclusive_or" title="Exclusive or">XORed</a> together to output the MAC.

</p>

<p><a href="Universal_hashing" title="Universal hashing">Universal hashing</a> and in particular <a href="Pairwise_independent" class="mw-redirect" title="Pairwise independent">pairwise independent</a> hash functions provide a secure message authentication code as long as the key is used at most once. This can be seen as the <a href="One-time_pad" title="One-time pad">one-time pad</a> for authentication.<sup id="cite_ref-:0_10-0" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p>The simplest such pairwise independent hash function is defined by the random key, <span class="nowrap"><i>key</i> = (<i>a</i>, <i>b</i>)</span>, and the MAC tag for a message <i>m</i> is computed as <span class="nowrap"><i>tag</i> = (<i>am</i> + <i>b</i>) mod <i>p</i></span>, where <i>p</i> is prime.

</p><p>More generally, <a href="K-independent_hashing" title="K-independent hashing"><i>k</i>-independent hashing</a> functions provide a secure message authentication code as long as the key is used less than <i>k</i> times for <i>k</i>-ways independent hashing functions.

</p><p>Message authentication codes and data origin authentication have been also discussed in the framework of <a href="Quantum_cryptography" title="Quantum cryptography">quantum cryptography</a>. By contrast to other cryptographic tasks, such as key distribution, for a rather broad class of quantum MACs it has been shown that quantum resources do not offer any advantage over unconditionally secure one-time classical MACs.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Standards">Standards</h2></div>

<p>Various standards exist that define MAC algorithms. These include:

</p>

<ul><li>FIPS PUB 113 <i>Computer Data Authentication</i>,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> withdrawn in 2002,<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> defines an algorithm based on <a href="Data_Encryption_Standard" title="Data Encryption Standard">DES</a>.</li>

<li>FIPS PUB 198-1 <i>The Keyed-Hash Message Authentication Code (HMAC)</i><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li>

<li>NIST SP800-185 <i>SHA-3 Derived Functions: cSHAKE, KMAC, TupleHash, and ParallelHash</i><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li>

<li><a href="ISO/IEC_9797-1" title="ISO/IEC 9797-1">ISO/IEC 9797-1</a> <i>Mechanisms using a block cipher</i><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></li>

<li><a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>/IEC 9797-2 <i>Mechanisms using a dedicated hash-function</i><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li>

<li><a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>/IEC 9797-3 <i>Mechanisms using a universal hash-function</i><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li>

<li><a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>/IEC 29192-6 <i>Lightweight cryptography - Message authentication codes</i><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li></ul>

<p>ISO/IEC 9797-1 and -2 define generic models and algorithms that can be used with any block cipher or hash function, and a variety of different parameters. These models and parameters allow more specific algorithms to be defined by nominating the parameters. For example, the FIPS PUB 113 algorithm is functionally equivalent to ISO/IEC 9797-1 MAC algorithm 1 with padding method 1 and a block cipher algorithm of DES.

</p>

<div class="mw-heading mw-heading2"><h2 id="An_example_of_MAC_use">An example of MAC use</h2></div>

<p><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> In this example, the sender of a message runs it through a MAC algorithm to produce a MAC data tag. The message and the MAC tag are then sent to the receiver. The receiver in turn runs the message portion of the transmission through the same MAC algorithm using the same key, producing a second MAC data tag. The receiver then compares the first MAC tag received in the transmission to the second generated MAC tag. If they are identical, the receiver can safely assume that the message was not altered or tampered with during transmission (<a href="Data_integrity" title="Data integrity">data integrity</a>).

</p><p>However, to allow the receiver to be able to detect <a href="Replay_attack" title="Replay attack">replay attacks</a>, the message itself must contain data that assures that this same message can only be sent once (e.g. time stamp, <a href="Cryptographic_nonce" title="Cryptographic nonce">sequence number</a> or use of a <a href="#One-time_MAC">one-time MAC</a>). Otherwise an attacker could – without even understanding its content – record this message and play it back at a later time, producing the same result as the original sender.

</p>

<ul><li><a href="Checksum" title="Checksum">Checksum</a></li>

<li><a href="HMAC" title="HMAC">HMAC</a> (hash-based message authentication code)</li>

<li><a href="MMH-Badger_MAC" title="MMH-Badger MAC">MMH-Badger MAC</a></li>

<li><a href="Authenticated_encryption" title="Authenticated encryption">Authenticated encryption</a></li>

<li><a href="SipHash" title="SipHash">SipHash</a></li>

<div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2></div>

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</style><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20081013101112/http://standards.ieee.org/getieee802/download/802.11-2007.pdf"><i>IEEE Standard for Information Technology - Telecommunications and Information Exchange Between Systems - Local and Metropolitan Area Networks - Specific Requirements - Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications</i></a> <span class="cs1-format">(PDF)</span>. (2007 revision). <a href="IEEE-SA" class="mw-redirect" title="IEEE-SA">IEEE-SA</a>. 12 June 2007. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FIEEESTD.2007.373646">10.1109/IEEESTD.2007.373646</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7381-5656-9</bdi>. Archived from <a rel="nofollow" class="external text" href="http://standards.ieee.org/getieee802/download/802.11-2007.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 13 October 2008.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.cs.cornell.edu/courses/cs513/2005fa/NL20.hashing.html">"CS 513 System Security -- Hashes and Message Digests"</a>. <i>www.cs.cornell.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">20 December</span> 2023</span>.</cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">The strongest adversary is assumed to have access to the signing algorithm without knowing the key. However, her final forged message must be different from any message she chose to query the signing algorithm before. See Pass's discussions before def 134.2.</span>

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<li id="cite_note-:1-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Theoretically, an efficient algorithm runs within probabilistic polynomial time.</span>

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</li>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFBhaumikChakrabortyChoiDutta2024" class="citation book cs1">Bhaumik, Ritam; Chakraborty, Bishwajit; Choi, Wonseok; Dutta, Avijit; Govinden, Jérôme; Shen, Yaobin (2024). <a rel="nofollow" class="external text" href="https://link.springer.com/chapter/10.1007/978-3-031-68385-5_14">"The Committing Security of MACs with Applications to Generic Composition"</a>. In Reyzin, Leonid; Stebila, Douglas (eds.). <i>Advances in Cryptology – CRYPTO 2024</i>. Lecture Notes in Computer Science. Vol. 14923. Cham: Springer Nature Switzerland. pp. <span class="nowrap">425–</span>462. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-031-68385-5_14">10.1007/978-3-031-68385-5_14</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-031-68385-5</bdi>.</cite></span>

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<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="http://www.fastcrypto.org/vmac/draft-krovetz-vmac-01.txt">"VMAC: Message Authentication Code using Universal Hashing"</a>. <i>CFRG Working Group</i><span class="reference-accessdate">. Retrieved <span class="nowrap">16 March</span> 2010</span>.</cite></span>

</li>

<li id="cite_note-SipHash-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-SipHash_9-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFJean-Philippe_AumassonDaniel_J._Bernstein2012" class="citation web cs1">Jean-Philippe Aumasson & <a href="Daniel_J._Bernstein" title="Daniel J. Bernstein">Daniel J. Bernstein</a> (18 September 2012). <a rel="nofollow" class="external text" href="https://131002.net/siphash/siphash.pdf">"SipHash: a fast short-input PRF"</a> <span class="cs1-format">(PDF)</span>.</cite></span>

</li>

<li id="cite_note-:0-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_10-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFSimmons1985" class="citation book cs1"><a href="Gustavus_Simmons" title="Gustavus Simmons">Simmons, Gustavus</a> (1985). "Authentication theory/coding theory". <i>Advances in Cryptology – Proceedings of CRYPTO 84</i>. Berlin: Springer. pp. <span class="nowrap">411–</span>431.</cite></span>

</li>

<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite id="CITEREFNikolopoulosFischlin2020" class="citation journal cs1">Nikolopoulos, Georgios M.; Fischlin, Marc (2020). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fcryptography4040031">"Information-Theoretically Secure Data Origin Authentication with Quantum and Classical Resources"</a>. <i>Cryptography</i>. <b>4</b> (4): 31. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2011.06849">2011.06849</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fcryptography4040031">10.3390/cryptography4040031</a></span>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:226956062">226956062</a>.</cite></span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110927022556/http://www.itl.nist.gov/fipspubs/fip113.htm">"FIPS PUB 113 <i>Computer Data Authentication</i>"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.itl.nist.gov/fipspubs/fip113.htm">the original</a> on 27 September 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">10 October</span> 2010</span>.</cite></span>

</li>

<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100801020458/http://www.itl.nist.gov/fipspubs/withdraw.htm">"Federal Information Processing Standards Publications, Withdrawn FIPS Listed by Number"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.itl.nist.gov/fipspubs/withdraw.htm">the original</a> on 1 August 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">10 October</span> 2010</span>.</cite></span>

</li>

<li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://csrc.nist.gov/publications/fips/fips198-1/FIPS-198-1_final.pdf">"<i>The Keyed-Hash Message Authentication Code (HMAC)</i>"</a> <span class="cs1-format">(PDF)</span><span class="reference-accessdate">. Retrieved <span class="nowrap">20 December</span> 2023</span>.</cite></span>

</li>

<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-185.pdf">SHA-3 Derived Functions</a> nvlpubs.nist.gov</span>

</li>

<li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.iso.org/standard/50375.html">"ISO/IEC 9797-1:2011"</a>. <i>ISO</i><span class="reference-accessdate">. Retrieved <span class="nowrap">20 December</span> 2023</span>.</cite></span>

</li>

<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.iso.org/standard/51618.html">"ISO/IEC 9797-2:2011"</a>. <i>ISO</i><span class="reference-accessdate">. Retrieved <span class="nowrap">20 December</span> 2023</span>.</cite></span>

</li>

<li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.iso.org/standard/51619.html">"ISO/IEC 9797-3:2011"</a>. <i>ISO</i><span class="reference-accessdate">. Retrieved <span class="nowrap">20 December</span> 2023</span>.</cite></span>

</li>

<li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.iso.org/standard/71116.html">"ISO/IEC 29192-6:2019"</a>. <i>ISO</i><span class="reference-accessdate">. Retrieved <span class="nowrap">20 December</span> 2023</span>.</cite></span>

</li>

<li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><cite class="citation cs2">"Mac Security Overview", <i>Mac® Security Bible</i>, Wiley Publishing, Inc., 1 November 2011, pp. <span class="nowrap">1–</span>26, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F9781118257739.ch1">10.1002/9781118257739.ch1</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781118257739</bdi></cite></span>

</li>

</ol></div>

</div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

<ul><li><cite id="CITEREFGoldreich2001" class="citation cs2">Goldreich, Oded (2001), <i>Foundations of cryptography I: Basic Tools</i>, Cambridge: Cambridge University Press, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-511-54689-1</bdi></cite></li>

<li><cite id="CITEREFGoldreich2004" class="citation cs2">Goldreich, Oded (2004), <i>Foundations of cryptography II: Basic Applications</i> (1. publ. ed.), Cambridge [u.a.]: Cambridge Univ. Press, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-83084-3</bdi></cite></li>

<li><cite id="CITEREFPass" class="citation cs2">Pass, Rafael, <a rel="nofollow" class="external text" href="https://www.cs.cornell.edu/courses/cs4830/2010fa/lecnotes.pdf"><i>A Course in Cryptography</i></a> <span class="cs1-format">(PDF)</span><span class="reference-accessdate">, retrieved <span class="nowrap">31 December</span> 2015</span></cite><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20061020212439/http://www.rsasecurity.com/rsalabs/node.asp?id=2177">RSA Laboratories entry on MACs</a></li>

<li><a rel="nofollow" class="external text" href="http://web.mit.edu/6.857/OldStuff/Fall97/lectures/lecture3.pdf">Ron Rivest lecture on MACs</a></li></ul>

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</style></div><div role="navigation" class="navbox" aria-label="Navbox0" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Cryptographic_hash_functions_and_message_authentication_codes539" style="font-size:114%;margin:0 4em"><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash functions</a> and </div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<li><a href="Comparison_of_cryptographic_hash_functions" title="Comparison of cryptographic hash functions">Comparison</a></li>

<li><a href="Hash_function_security_summary" title="Hash function security summary">Known attacks</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Common functions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="MD5" title="MD5">MD5</a> (compromised)</li>

<li><a href="SHA-1" title="SHA-1">SHA-1</a> (compromised)</li>

<li><a href="BLAKE_(hash_function)#BLAKE2" title="BLAKE (hash function)">BLAKE2</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="NIST_hash_function_competition" title="NIST hash function competition">SHA-3 finalists</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="BLAKE_(hash_function)" title="BLAKE (hash function)">BLAKE</a></li>

<li><a href="Gr%C3%B8stl" title="Grøstl">Grøstl</a></li>

<li><a href="Skein_(hash_function)" title="Skein (hash function)">Skein</a></li>

<li><a href="SHA-3" title="SHA-3">Keccak</a> (winner)</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other functions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="BLAKE3" class="mw-redirect" title="BLAKE3">BLAKE3</a></li>

<li><a href="CubeHash" title="CubeHash">CubeHash</a></li>

<li><a href="Fugue_(hash_function)" title="Fugue (hash function)">Fugue</a></li>

<li><a href="HAVAL" title="HAVAL">HAVAL</a></li>

<li><a href="Kupyna" title="Kupyna">Kupyna</a></li>

<li><a href="RIPEMD" title="RIPEMD">RIPEMD</a></li>

<li><a href="RadioGat%C3%BAn" title="RadioGatún">RadioGatún</a></li>

<li><a href="SWIFFT" title="SWIFFT">SWIFFT</a></li>

<li><a href="Shabal" title="Shabal">Shabal</a></li>

<li><a href="Snefru" title="Snefru">Snefru</a></li>

<li><a href="Streebog" title="Streebog">Streebog</a></li>

<li><a href="Tiger_(hash_function)" title="Tiger (hash function)">Tiger</a></li>

<li><a href="Whirlpool_(hash_function)" title="Whirlpool (hash function)">Whirlpool</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Password hashing/<br><a href="Key_stretching" title="Key stretching">key stretching</a> functions</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Argon2" title="Argon2">Argon2</a></li>

<li><a href="Balloon_hashing" title="Balloon hashing">Balloon</a></li>

<li><a href="Bcrypt" title="Bcrypt">bcrypt</a></li>

<li><a href="Catena_(cryptography)" class="mw-redirect" title="Catena (cryptography)">Catena</a></li>

<li><a href="Crypt_(C)" title="Crypt (C)">crypt</a></li>

<li><a href="Makwa_(cryptography)" class="mw-redirect" title="Makwa (cryptography)">Makwa</a></li>

<li><a href="PBKDF2" title="PBKDF2">PBKDF2</a></li>

<li><a href="Scrypt" title="Scrypt">scrypt</a></li>

<li><a href="Yescrypt" title="Yescrypt">yescrypt</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">General purpose<br><a href="Key_derivation_function" title="Key derivation function">key derivation functions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="SipHash" title="SipHash">SipHash</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Authenticated_encryption" title="Authenticated encryption">Authenticated<br>encryption</a> modes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="ChaCha20-Poly1305" title="ChaCha20-Poly1305">ChaCha20-Poly1305</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Attacks</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Collision_attack" title="Collision attack">Collision attack</a></li>

<li><a href="Preimage_attack" title="Preimage attack">Preimage attack</a></li>

<li><a href="Birthday_attack" title="Birthday attack">Birthday attack</a></li>

<li><a href="Brute-force_attack" title="Brute-force attack">Brute-force attack</a></li>

<li><a href="Rainbow_table" title="Rainbow table">Rainbow table</a></li>

<li><a href="Side-channel_attack" title="Side-channel attack">Side-channel attack</a></li>

<li><a href="Length_extension_attack" title="Length extension attack">Length extension attack</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Design</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Avalanche_effect" title="Avalanche effect">Avalanche effect</a></li>

<li><a href="Hash_collision" title="Hash collision">Hash collision</a></li>

<li><a href="Merkle%E2%80%93Damg%C3%A5rd_construction" title="Merkle–Damgård construction">Merkle–Damgård construction</a></li>

<li><a href="Sponge_function" title="Sponge function">Sponge function</a></li>

<li><a href="HAIFA_construction" title="HAIFA construction">HAIFA construction</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Standardization</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="CAESAR_Competition" title="CAESAR Competition">CAESAR Competition</a></li>

<li><a href="CRYPTREC" title="CRYPTREC">CRYPTREC</a></li>

<li><a href="NESSIE" title="NESSIE">NESSIE</a></li>

<li><a href="NIST_hash_function_competition" title="NIST hash function competition">NIST hash function competition</a></li>

<li><a href="Password_Hashing_Competition" title="Password Hashing Competition">Password Hashing Competition</a></li>

<li><a href="NSA_Suite_B_Cryptography" title="NSA Suite B Cryptography">NSA Suite B</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Utilization</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Post-quantum_cryptography#Hash-based_cryptography" title="Post-quantum cryptography">Hash-based cryptography</a></li>

<li><a href="Merkle_tree" title="Merkle tree">Merkle tree</a></li>

<li><a href="Message_authentication" title="Message authentication">Message authentication</a></li>

<li><a href="Proof_of_work" title="Proof of work">Proof of work</a></li>

<li><a href="Pepper_(cryptography)" title="Pepper (cryptography)">Pepper</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Cryptography149" style="font-size:114%;margin:0 4em"><a href="Cryptography" title="Cryptography">Cryptography</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="History_of_cryptography" title="History of cryptography">History of cryptography</a></li>

<li><a href="Outline_of_cryptography" title="Outline of cryptography">Outline of cryptography</a></li>

<li><a href="Classical_cipher" title="Classical cipher">Classical cipher</a></li>

<li><a href="Cryptographic_protocol" title="Cryptographic protocol">Cryptographic protocol</a>

<ul><li><a href="Authentication_protocol" title="Authentication protocol">Authentication protocol</a></li></ul></li>

<li><a href="Cryptographic_primitive" title="Cryptographic primitive">Cryptographic primitive</a></li>

<li><a href="Cryptanalysis" title="Cryptanalysis">Cryptanalysis</a></li>

<li><a href="Cryptocurrency" title="Cryptocurrency">Cryptocurrency</a></li>

<li><a href="Cryptosystem" title="Cryptosystem">Cryptosystem</a></li>

<li><a href="Cryptographic_nonce" title="Cryptographic nonce">Cryptographic nonce</a></li>

<li><a href="Cryptovirology" title="Cryptovirology">Cryptovirology</a></li>

<li><a href="Hash_function" title="Hash function">Hash function</a>

<ul><li><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li>

<li><a href="Key_derivation_function" title="Key derivation function">Key derivation function</a></li>

<li><a href="Secure_Hash_Algorithms" title="Secure Hash Algorithms">Secure Hash Algorithms</a></li></ul></li>

<li><a href="Digital_signature" title="Digital signature">Digital signature</a></li>

<li><a href="Kleptography" title="Kleptography">Kleptography</a></li>

<li><a href="Key_(cryptography)" title="Key (cryptography)">Key (cryptography)</a></li>

<li><a href="Key_exchange" title="Key exchange">Key exchange</a></li>

<li><a href="Key_generator" title="Key generator">Key generator</a></li>

<li><a href="Key_schedule" title="Key schedule">Key schedule</a></li>

<li><a href="Key_stretching" title="Key stretching">Key stretching</a></li>

<li><a href="Keygen" title="Keygen">Keygen</a></li>

<li>Machines</li>

<li><a href="Cryptojacking_malware" class="mw-redirect" title="Cryptojacking malware">Cryptojacking malware</a></li>

<li><a href="Ransomware" title="Ransomware">Ransomware</a></li>

<li><a href="Random_number_generation" title="Random number generation">Random number generation</a>

<ul><li><a href="Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Cryptographically secure pseudorandom number generator</a> (CSPRNG)</li></ul></li>

<li><a href="Pseudorandom_noise" title="Pseudorandom noise">Pseudorandom noise</a> (PRN)</li>

<li><a href="Secure_channel" title="Secure channel">Secure channel</a></li>

<li><a href="Insecure_channel" class="mw-redirect" title="Insecure channel">Insecure channel</a></li>

<li><a href="Subliminal_channel" title="Subliminal channel">Subliminal channel</a></li>

<li><a href="Encryption" title="Encryption">Encryption</a></li>

<li><a href="Decryption" class="mw-redirect" title="Decryption">Decryption</a></li>

<li><a href="End-to-end_encryption" title="End-to-end encryption">End-to-end encryption</a></li>

<li><a href="Harvest_now%2C_decrypt_later" title="Harvest now, decrypt later">Harvest now, decrypt later</a></li>

<li><a href="Information-theoretic_security" title="Information-theoretic security">Information-theoretic security</a></li>

<li><a href="Plaintext" title="Plaintext">Plaintext</a></li>

<li><a href="Codetext" class="mw-redirect" title="Codetext">Codetext</a></li>

<li><a href="Ciphertext" title="Ciphertext">Ciphertext</a></li>

<li><a href="Shared_secret" title="Shared secret">Shared secret</a></li>

<li><a href="Trapdoor_function" title="Trapdoor function">Trapdoor function</a></li>

<li><a href="Trusted_timestamping" title="Trusted timestamping">Trusted timestamping</a></li>

<li><a href="Key-based_routing" title="Key-based routing">Key-based routing</a></li>

<li><a href="Onion_routing" title="Onion routing">Onion routing</a></li>

<li><a href="Garlic_routing" title="Garlic routing">Garlic routing</a></li>

<li><a href="Kademlia" title="Kademlia">Kademlia</a></li>

<li><a href="Mix_network" title="Mix network">Mix network</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li>

<li><a href="Block_cipher" title="Block cipher">Block cipher</a></li>

<li><a href="Stream_cipher" title="Stream cipher">Stream cipher</a></li>

<li><a href="Symmetric-key_algorithm" title="Symmetric-key algorithm">Symmetric-key algorithm</a></li>

<li><a href="Authenticated_encryption" title="Authenticated encryption">Authenticated encryption</a></li>

<li><a href="Public-key_cryptography" title="Public-key cryptography">Public-key cryptography</a></li>

<li><a href="Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li>

<li><a href="Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li>

<li><a href="Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li>

<li><a href="Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Random numbers</a></li>

<li><a href="Steganography" title="Steganography">Steganography</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Category</li></ul>

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