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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Argon2</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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lang="de" hreflang="de" data-title="Argon2" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Argon2" title="Argon2 – Spanish" lang="es" hreflang="es" data-title="Argon2" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Argon2" title="Argon2 – French" lang="fr" hreflang="fr" data-title="Argon2" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/Argon2" title="Argon2 – Korean" lang="ko" hreflang="ko" data-title="Argon2" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Argon2" title="Argon2 – Italian" lang="it" hreflang="it" data-title="Argon2" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/Argon2" title="Argon2 – Japanese" lang="ja" hreflang="ja" data-title="Argon2" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/Argon2" title="Argon2 – Russian" lang="ru" hreflang="ru" data-title="Argon2" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Argon2" title="Argon2 – Turkish" lang="tr" hreflang="tr" data-title="Argon2" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/Argon2" title="Argon2 – Ukrainian" lang="uk" hreflang="uk" data-title="Argon2" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q21995362#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Password-based key derivation function created in 2015</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output 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.infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><caption class="infobox-title">Argon2</caption><tbody><tr><th colspan="2" class="infobox-header">General</th></tr><tr><th scope="row" class="infobox-label">Designers</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r979066050">.mw-parser-output ul.cslist,.mw-parser-output ul.sslist{margin:0;padding:0;display:inline-block;list-style:none}.mw-parser-output ul.cslist-embedded{display:inline}.mw-parser-output .cslist li,.mw-parser-output .sslist li{margin:0;padding:0 0.25em 0 0;display:inline-block}.mw-parser-output .cslist li:after{content:", "}.mw-parser-output .sslist li:after{content:"; "}.mw-parser-output .cslist li:last-child:after,.mw-parser-output .sslist li:last-child:after{content:none}</style><ul class="cslist"><li><a href="/wiki/Alex_Biryukov" title="Alex Biryukov">Alex Biryukov</a></li><li>Daniel Dinu</li><li><a href="/wiki/Dmitry_Khovratovich" title="Dmitry Khovratovich">Dmitry Khovratovich</a></li></ul></td></tr><tr><th scope="row" class="infobox-label">First published</th><td class="infobox-data">2015<span class="noprint">; 9 years ago</span><span style="display:none"> (<span class="bday dtstart published updated">2015</span>)</span></td></tr><tr><th colspan="2" class="infobox-header">Cipher detail</th></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Cryptographic_hash_function" title="Cryptographic hash function">Digest sizes</a></th><td class="infobox-data">variable</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Block_size_(cryptography)" title="Block size (cryptography)">Block sizes</a></th><td class="infobox-data">variable</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Round_(cryptography)" title="Round (cryptography)">Rounds</a></th><td class="infobox-data">variable</td></tr></tbody></table> <p><b>Argon2</b> is a <a href="/wiki/Key_derivation_function" title="Key derivation function">key derivation function</a> that was selected as the winner of the 2015 <a href="/wiki/Password_Hashing_Competition" title="Password Hashing Competition">Password Hashing Competition</a>.<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><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> It was designed by <a href="/wiki/Alex_Biryukov" title="Alex Biryukov">Alex Biryukov</a>, Daniel Dinu, and <a href="/wiki/Dmitry_Khovratovich" title="Dmitry Khovratovich">Dmitry Khovratovich</a> from the <a href="/wiki/University_of_Luxembourg" title="University of Luxembourg">University of Luxembourg</a>.<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> The reference implementation of Argon2 is released under a <a href="/wiki/Creative_Commons_CC0" class="mw-redirect" title="Creative Commons CC0">Creative Commons CC0</a> license (i.e. <a href="/wiki/Public_domain" title="Public domain">public domain</a>) or the <a href="/wiki/Apache_License" title="Apache License">Apache License 2.0</a>, and provides three related versions: </p> <ul><li>Argon2d maximizes resistance to GPU <a href="/wiki/Password_cracking" title="Password cracking">cracking attacks</a>. It accesses the memory array in a password dependent order, which reduces the possibility of <a href="/wiki/Time%E2%80%93memory_trade-off" class="mw-redirect" title="Time–memory trade-off">time–memory trade-off</a> (TMTO) attacks, but introduces possible <a href="/wiki/Side-channel_attack" title="Side-channel attack">side-channel attacks</a>.</li> <li>Argon2i is optimized to resist side-channel attacks. It accesses the memory array in a password independent order.</li> <li>Argon2id is a hybrid version. It follows the Argon2i approach for the first half pass over memory and the Argon2d approach for subsequent passes. <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/RFC_(identifier)" class="mw-redirect" title="RFC (identifier)">RFC</a> <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc9106">9106</a> recommends using Argon2id if you do not know the difference between the types or you consider side-channel attacks to be a viable threat.<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></li></ul> <p>All three modes allow specification by three parameters that control: </p> <ul><li>execution time</li> <li>memory required</li> <li>degree of parallelism</li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Cryptanalysis">Cryptanalysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argon2&action=edit&section=1" title="Edit section: Cryptanalysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While there is no public <a href="/wiki/Cryptanalysis" title="Cryptanalysis">cryptanalysis</a> applicable to Argon2d, there are two published attacks on the Argon2i function. The first attack is applicable only to the old version of Argon2i, while the second has been extended to the latest version (1.3).<sup id="cite_ref-blocki_5-0" class="reference"><a href="#cite_note-blocki-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>The first attack shows that it is possible to compute a single-pass Argon2i function using between a quarter and a fifth of the desired space with no time penalty, and compute a multiple-pass Argon2i using only <span class="texhtml mvar" style="font-style:italic;">N</span>/<span class="texhtml mvar" style="font-style:italic;">e</span> (≈ <span class="texhtml mvar" style="font-style:italic;">N</span>/2.72) space with no time penalty.<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> According to the Argon2 authors, this attack vector was fixed in version 1.3.<sup id="cite_ref-:0_7-0" class="reference"><a href="#cite_note-:0-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The second attack shows that Argon2i can be computed by an algorithm which has complexity O(<span class="texhtml mvar" style="font-style:italic;">n</span><sup>7/4</sup> log(<span class="texhtml mvar" style="font-style:italic;">n</span>)) for all choices of parameters <span class="texhtml mvar" style="font-style:italic;">σ</span> (space cost), <span class="texhtml mvar" style="font-style:italic;">τ</span> (time cost), and thread-count such that <span class="texhtml mvar" style="font-style:italic;">n</span>=<span class="texhtml mvar" style="font-style:italic;">σ</span>∗<span class="texhtml mvar" style="font-style:italic;">τ</span>.<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> The Argon2 authors claim that this attack is not efficient if Argon2i is used with three or more passes.<sup id="cite_ref-:0_7-1" class="reference"><a href="#cite_note-:0-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> However, Joël Alwen and Jeremiah Blocki improved the attack and showed that in order for the attack to fail, Argon2i v1.3 needs more than 10 passes over memory.<sup id="cite_ref-blocki_5-1" class="reference"><a href="#cite_note-blocki-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>To address these concerns, RFC9106 recommends using Argon2id to largely mitigate such attacks. <sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Algorithm">Algorithm</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argon2&action=edit&section=2" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Source:<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> </p> <pre><span style="color:blue;"><b>Function</b></span> Argon2 <span style="color:blue;"><b>Inputs:</b></span> password (<b>P</b>): Bytes (0..2<sup>32</sup>-1) <span style="color:green;">Password (or message) to be hashed</span> salt (<b>S</b>): Bytes (8..2<sup>32</sup>-1) <span style="color:green;">Salt (16 bytes recommended for password hashing)</span> parallelism (<b>p</b>): Number (1..2<sup>24</sup>-1) <span style="color:green;">Degree of parallelism (i.e. number of threads)</span> tagLength (<b>T</b>): Number (4..2<sup>32</sup>-1) <span style="color:green;">Desired number of returned bytes</span> memorySizeKB (<b>m</b>): Number (8p..2<sup>32</sup>-1) <span style="color:green;">Amount of memory (in <a href="/wiki/Kibibyte" class="mw-redirect" title="Kibibyte">kibibytes</a>) to use</span> iterations (<b>t</b>): Number (1..2<sup>32</sup>-1) <span style="color:green;">Number of iterations to perform</span> version (<b>v</b>): Number (0x13)<sup> </sup> <span style="color:green;">The current version is 0x13 (19 decimal)</span> key (<b>K</b>): Bytes (0..2<sup>32</sup>-1) <span style="color:green;">Optional key (Errata: PDF says 0..32 bytes, RFC says 0..2<sup>32</sup> bytes)</span> associatedData (<b>X</b>): Bytes (0..2<sup>32</sup>-1) <span style="color:green;">Optional arbitrary extra data</span> hashType (<b>y</b>): Number (0=Argon2d, 1=Argon2i, 2=Argon2id) <span style="color:blue;"><b>Output:</b></span> tag: Bytes (tagLength)<sup> </sup> <span style="color:green;">The resulting generated bytes, tagLength bytes long</span> <span style="color:green;"><i>Generate initial 64-byte block H<sub>0</sub>.</i> All the input parameters are concatenated and input as a source of additional entropy. Errata: RFC says H<sub>0</sub> is 64-bits; PDF says H<sub>0</sub> is 64-bytes. Errata: RFC says the Hash is H^, the PDF says it's ℋ (but doesn't document what ℋ is). It's actually Blake2b. Variable length items are prepended with their length as 32-bit little-endian integers.</span> buffer ← parallelism ∥ tagLength ∥ memorySizeKB ∥ iterations ∥ version ∥ hashType ∥ Length(password) ∥ Password ∥ Length(salt) ∥ salt ∥ Length(key) ∥ key ∥ Length(associatedData) ∥ associatedData H<sub>0</sub> ← Blake2b(buffer, 64) <span style="color:green;"><i>//default hash size of Blake2b is 64-bytes</i></span> <span style="color:green;">Calculate number of 1 KB blocks by rounding down memorySizeKB to the nearest multiple of 4*parallelism <a href="/wiki/Kibibyte" class="mw-redirect" title="Kibibyte">kibibytes</a></span> blockCount ← Floor(memorySizeKB, 4*parallelism) <span style="color:green;">Allocate two-dimensional array of 1 KiB blocks (parallelism rows x columnCount columns)</span> columnCount ← blockCount / parallelism; <span style="color:green;">//In the RFC, columnCount is referred to as <b>q</b></span> <span style="color:green;">Compute the first and second block (i.e. column zero and one ) of each lane (i.e. row)</span> <b>for</b> i ← 0 <b>to</b> parallelism-1 <b>do</b> <span style="color:green;">for each row</span> B<sub>i</sub>[0] ← Hash(H<sub>0</sub> ∥ 0 ∥ i, 1024) <span style="color:green;"><i>//Generate a 1024-byte digest</i></span> B<sub>i</sub>[1] ← Hash(H<sub>0</sub> ∥ 1 ∥ i, 1024) <span style="color:green;"><i>//Generate a 1024-byte digest</i></span> <span style="color:green;">Compute remaining columns of each lane</span> <b>for</b> i ← 0 <b>to</b> parallelism-1 <b>do</b> <span style="color:green;">//for each row</span> <b>for</b> j ← 2 <b>to</b> columnCount-1 <b>do</b> <span style="color:green;">//for each subsequent column</span> <span style="color:green;">//i' and j' indexes depend if it's Argon2i, Argon2d, or Argon2id (See section 3.4)</span> i′, j′ ← GetBlockIndexes(i, j) <span style="color:green;">//the GetBlockIndexes function is not defined</span> B<sub>i</sub>[j] = G(B<sub>i</sub>[j-1], B<sub>i′</sub>[j′]) <span style="color:green;">//the G hash function is not defined</span> <span style="color:green;">Further passes when iterations > 1</span> <b>for</b> nIteration ← 2 <b>to</b> iterations <b>do</b> <b>for</b> i ← 0 <b>to</b> parallelism-1 <b>do</b> <span style="color:green;">for each row</span> <b>for</b> j ← 0 <b>to</b> columnCount-1 <b>do</b> <span style="color:green;">//for each subsequent column</span> <span style="color:green;">//i' and j' indexes depend if it's Argon2i, Argon2d, or Argon2id (See section 3.4)</span> i′, j′ ← GetBlockIndexes(i, j) <b>if</b> j == 0 <b>then</b> B<sub>i</sub>[0] = B<sub>i</sub>[0] xor G(B<sub>i</sub>[columnCount-1], B<sub>i′</sub>[j′]) <b>else</b> B<sub>i</sub>[j] = B<sub>i</sub>[j] xor G(B<sub>i</sub>[j-1], B<sub>i′</sub>[j′]) <span style="color:green;">Compute final block <b>C</b> as the XOR of the last column of each row</span> C ← B<sub>0</sub>[columnCount-1] <b>for</b> i ← 1 <b>to</b> parallelism-1 <b>do</b> C ← C <b>xor</b> B<sub>i</sub>[columnCount-1] <span style="color:green;">Compute output tag</span> <b>return</b> Hash(C, tagLength) </pre> <div class="mw-heading mw-heading3"><h3 id="Variable-length_hash_function">Variable-length hash function</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argon2&action=edit&section=3" title="Edit section: Variable-length hash function"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Argon2 makes use of a hash function capable of producing digests up to 2<sup>32</sup> bytes long. This hash function is internally built upon <a href="/wiki/Blake2" class="mw-redirect" title="Blake2">Blake2</a>. </p> <pre><span style="color:blue;"><b>Function</b></span> Hash(message, digestSize) <span style="color:blue;"><b>Inputs:</b></span> message: Bytes (0..2<sup>32</sup>-1) <span style="color:green;">Message to be hashed</span> digestSize: Integer (1..2<sup>32</sup>) <span style="color:green;">Desired number of bytes to be returned</span> <span style="color:blue;">Output:</span> digest: Bytes (digestSize)<sup> </sup> <span style="color:green;">The resulting generated bytes, digestSize bytes long</span> <span style="color:green;"><b>Hash</b> is a variable-length hash function, built using Blake2b, capable of generating digests up to 2<sup>32</sup> bytes.</span> <span style="color:green;">If the requested digestSize is 64-bytes or lower, then we use Blake2b directly</span> <b>if</b> (digestSize <= 64) <b>then</b> <b>return</b> Blake2b(digestSize ∥ message, digestSize) <span style="color:green;">//concatenate 32-bit little endian digestSize with the message bytes</span> <span style="color:green;">For desired hashes over 64-bytes (e.g. 1024 bytes for Argon2 blocks), we use Blake2b to generate twice the number of needed 64-byte blocks, and then only use 32-bytes from each block</span> <span style="color:green;">Calculate the number of whole blocks (knowing we're only going to use 32-bytes from each)</span> r ← Ceil(digestSize/32)-2; <span style="color:green;">Generate r whole blocks.</span> <span style="color:green;">Initial block is generated from message</span> V<sub>1</sub> ← Blake2b(digestSize ∥ message, 64); <span style="color:green;">Subsequent blocks are generated from previous blocks</span> <b>for</b> i ← 2 <b>to</b> r <b>do</b> V<sub>i</sub> ← Blake2b(V<sub>i-1</sub>, 64) <span style="color:green;">Generate the final (possibly partial) block</span> partialBytesNeeded ← digestSize – 32*r; V<sub>r+1</sub> ← Blake2b(V<sub>r</sub>, partialBytesNeeded) <span style="color:green;">Concatenate the first 32-bytes of each block V<sub>i</sub> (except the possibly partial last block, which we take the whole thing)</span> <span style="color:green;">Let A<sub>i</sub> represent the lower 32-bytes of block V<sub>i</sub></span> <b>return</b> A<sub>1</sub> ∥ A<sub>2</sub> ∥ ... ∥ A<sub>r</sub> ∥ V<sub>r+1</sub> </pre> <div class="mw-heading mw-heading2"><h2 id="Recommended_minimum_parameters">Recommended minimum parameters</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argon2&action=edit&section=4" title="Edit section: Recommended minimum parameters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As of May 2023, <a href="/wiki/OWASP" title="OWASP">OWASP</a>'s <i>Password Storage Cheat Sheet</i> recommends that people "use Argon2id with a minimum configuration of 19 MiB of memory, an iteration count of 2, and 1 degree of parallelism."<sup id="cite_ref-owasp_10-0" class="reference"><a href="#cite_note-owasp-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>OWASP recommends that Argon2id should be preferred over Argon2d and Argon2i because it provides a balanced resistance to both GPU-based attacks and side-channel attacks.<sup id="cite_ref-owasp_10-1" class="reference"><a href="#cite_note-owasp-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>OWASP further notes that the following Argon2id options provide equivalent cryptographic strength and simply trade off memory usage for compute workload:<sup id="cite_ref-owasp_10-2" class="reference"><a href="#cite_note-owasp-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Memory: 46 MiB, Iterations: 1, Parallelism: 1</li> <li>Memory: 19 MiB, Iterations: 2, Parallelism: 1</li> <li>Memory: 12 MiB, Iterations: 3, Parallelism: 1</li> <li>Memory: 9 MiB, Iterations: 4, Parallelism: 1</li> <li>Memory: 7 MiB, Iterations: 5, Parallelism: 1</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argon2&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://password-hashing.net/">"Password Hashing Competition"</a></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJos_Wetzels2016" class="citation arxiv cs1">Jos Wetzels (2016-02-08). "Open Sesame: The Password Hashing Competition and Argon2". <a href="/wiki/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/1602.03097">1602.03097</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/cs.CR">cs.CR</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Open+Sesame%3A+The+Password+Hashing+Competition+and+Argon2&rft.date=2016-02-08&rft_id=info%3Aarxiv%2F1602.03097&rft.au=Jos+Wetzels&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgon2" class="Z3988"></span></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"><a rel="nofollow" class="external text" href="https://password-hashing.net/argon2-specs.pdf">Argon2: the memory-hard function for password hashing and other applications</a>, Alex Biryukov, et al, October 1, 2015</span> </li> <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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBiryukovDinuKhovratovichJosefsson2021" class="citation web cs1">Biryukov, Alex; Dinu, Daniel; Khovratovich, Dmitry; Josefsson, Simon (September 2021). <a rel="nofollow" class="external text" href="https://www.rfc-editor.org/rfc/rfc9106.html">"Argon2 Memory-Hard Function for Password Hashing and Proof-of-Work Applications"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">September 9,</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Argon2+Memory-Hard+Function+for+Password+Hashing+and+Proof-of-Work+Applications&rft.date=2021-09&rft.aulast=Biryukov&rft.aufirst=Alex&rft.au=Dinu%2C+Daniel&rft.au=Khovratovich%2C+Dmitry&rft.au=Josefsson%2C+Simon&rft_id=https%3A%2F%2Fwww.rfc-editor.org%2Frfc%2Frfc9106.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgon2" class="Z3988"></span></span> </li> <li id="cite_note-blocki-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-blocki_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-blocki_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJoël_AlwenJeremiah_Blocki2016" class="citation report cs1">Joël Alwen; Jeremiah Blocki (2016-08-05). <a rel="nofollow" class="external text" href="https://eprint.iacr.org/2016/759.pdf">Towards Practical Attacks on Argon2i and Balloon Hashing</a> <span class="cs1-format">(PDF)</span> (Report).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Towards+Practical+Attacks+on+Argon2i+and+Balloon+Hashing&rft.date=2016-08-05&rft.au=Jo%C3%ABl+Alwen&rft.au=Jeremiah+Blocki&rft_id=https%3A%2F%2Feprint.iacr.org%2F2016%2F759.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgon2" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHenryCorrigan-GibbsDan_BonehStuart_Schechter2016" class="citation report cs1">Henry; Corrigan-Gibbs; Dan Boneh; Stuart Schechter (2016-01-14). <a rel="nofollow" class="external text" href="https://eprint.iacr.org/2016/027.pdf">Balloon Hashing: Provably Space-Hard Hash Functions with Data-Independent Access Patterns</a> <span class="cs1-format">(PDF)</span> (Report).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Balloon+Hashing%3A+Provably+Space-Hard+Hash+Functions+with+Data-Independent+Access+Patterns&rft.date=2016-01-14&rft.au=Henry&rft.au=Corrigan-Gibbs&rft.au=Dan+Boneh&rft.au=Stuart+Schechter&rft_id=https%3A%2F%2Feprint.iacr.org%2F2016%2F027.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgon2" class="Z3988"></span></span> </li> <li id="cite_note-:0-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ietf.org/mail-archive/web/cfrg/current/msg07948.html">"[Cfrg] Argon2 v.1.3"</a>. <i>www.ietf.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-10-30</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.ietf.org&rft.atitle=%5BCfrg%5D+Argon2+v.1.3&rft_id=https%3A%2F%2Fwww.ietf.org%2Fmail-archive%2Fweb%2Fcfrg%2Fcurrent%2Fmsg07948.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgon2" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJoël_AlwenJeremiah_Blocki2016" class="citation report cs1">Joël Alwen; Jeremiah Blocki (2016-02-19). <a rel="nofollow" class="external text" href="https://eprint.iacr.org/2016/115.pdf">Efficiently Computing Data-Independent Memory-Hard Functions</a> <span class="cs1-format">(PDF)</span> (Report).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Efficiently+Computing+Data-Independent+Memory-Hard+Functions&rft.date=2016-02-19&rft.au=Jo%C3%ABl+Alwen&rft.au=Jeremiah+Blocki&rft_id=https%3A%2F%2Feprint.iacr.org%2F2016%2F115.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgon2" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs1"><a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc9106#section-7.4">"Recommendations"</a>. <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc9106"><i>Argon2 Memory-Hard Function for Password Hashing and Proof-of-Work Applications</i></a>. <a href="/wiki/Internet_Engineering_Task_Force" title="Internet Engineering Task Force">IETF</a>. September 2021. sec. 7.4. <a href="/wiki/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/10.17487%2FRFC9106">10.17487/RFC9106</a></span>. <a href="/wiki/Request_for_Comments" title="Request for Comments">RFC</a> <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc9106">9106</a><span class="reference-accessdate">. Retrieved <span class="nowrap">12 July</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Recommendations&rft.btitle=Argon2+Memory-Hard+Function+for+Password+Hashing+and+Proof-of-Work+Applications&rft.pages=sec.-7.4&rft.pub=IETF&rft.date=2021-09&rft_id=info%3Adoi%2F10.17487%2FRFC9106&rft_id=https%3A%2F%2Fdatatracker.ietf.org%2Fdoc%2Fhtml%2Frfc9106%26%23035%3Bsection-7.4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgon2" class="Z3988"></span></span> </li> <li id="cite_note-owasp-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-owasp_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-owasp_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-owasp_10-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://cheatsheetseries.owasp.org/cheatsheets/Password_Storage_Cheat_Sheet.html">"Password Storage Cheat Sheet"</a>. <i>OWASP Cheat Sheet Series</i>. OWASP<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-05-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=OWASP+Cheat+Sheet+Series&rft.atitle=Password+Storage+Cheat+Sheet&rft_id=https%3A%2F%2Fcheatsheetseries.owasp.org%2Fcheatsheets%2FPassword_Storage_Cheat_Sheet.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgon2" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argon2&action=edit&section=6" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://github.com/p-h-c/phc-winner-argon2">Argon2 source code repository on Github</a></li> <li><a rel="nofollow" class="external text" href="https://www.cryptolux.org/images/0/0d/Argon2.pdf">Argon2 specification</a></li> <li><a rel="nofollow" class="external text" href="https://password-hashing.net/">Password Hashing Competition</a></li> <li><a rel="nofollow" class="external text" href="https://www.cryptolux.org/index.php/Argon2">Uni.Lu Argon2 Page</a></li> <li><a rel="nofollow" class="external text" href="https://eprint.iacr.org/2016/027.pdf">Balloon Hashing: A Memory-Hard Function Providing Provable Protection Against Sequential Attacks</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222">RFC <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc9106">9106</a> Argon2 Memory-Hard Function for Password Hashing and Proof-of-Work Applications</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist 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style="font-size:114%;margin:0 4em"><a href="/wiki/Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash functions</a> and <a href="/wiki/Message_authentication_code" title="Message authentication code">message authentication codes</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/List_of_hash_functions" title="List of hash functions">List</a></li> <li><a href="/wiki/Comparison_of_cryptographic_hash_functions" title="Comparison of cryptographic hash functions">Comparison</a></li> <li><a href="/wiki/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="/wiki/MD5" title="MD5">MD5</a> (compromised)</li> <li><a href="/wiki/SHA-1" title="SHA-1">SHA-1</a> (compromised)</li> <li><a href="/wiki/SHA-2" title="SHA-2">SHA-2</a></li> <li><a href="/wiki/SHA-3" title="SHA-3">SHA-3</a></li> <li><a href="/wiki/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="/wiki/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="/wiki/BLAKE_(hash_function)" title="BLAKE (hash function)">BLAKE</a></li> <li><a href="/wiki/Gr%C3%B8stl" title="Grøstl">Grøstl</a></li> <li><a href="/wiki/JH_(hash_function)" title="JH (hash function)">JH</a></li> <li><a href="/wiki/Skein_(hash_function)" title="Skein (hash function)">Skein</a></li> <li><a href="/wiki/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="/wiki/BLAKE3" class="mw-redirect" title="BLAKE3">BLAKE3</a></li> <li><a href="/wiki/CubeHash" title="CubeHash">CubeHash</a></li> <li><a href="/wiki/Elliptic_curve_only_hash" title="Elliptic curve only hash">ECOH</a></li> <li><a href="/wiki/Fast_syndrome-based_hash" title="Fast syndrome-based hash">FSB</a></li> <li><a href="/wiki/Fugue_(hash_function)" title="Fugue (hash function)">Fugue</a></li> <li><a href="/wiki/GOST_(hash_function)" title="GOST (hash function)">GOST</a></li> <li><a href="/wiki/HAS-160" title="HAS-160">HAS-160</a></li> <li><a href="/wiki/HAVAL" title="HAVAL">HAVAL</a></li> <li><a href="/wiki/Kupyna" title="Kupyna">Kupyna</a></li> <li><a href="/wiki/LSH_(hash_function)" title="LSH (hash function)">LSH</a></li> <li><a href="/wiki/Lane_(hash_function)" title="Lane (hash function)">Lane</a></li> <li><a href="/wiki/MASH-1" title="MASH-1">MASH-1</a></li> <li><a href="/wiki/MASH-1#MASH2" title="MASH-1">MASH-2</a></li> <li><a href="/wiki/MD2_(hash_function)" title="MD2 (hash function)">MD2</a></li> <li><a href="/wiki/MD4" title="MD4">MD4</a></li> <li><a href="/wiki/MD6" title="MD6">MD6</a></li> <li><a href="/wiki/MDC-2" title="MDC-2">MDC-2</a></li> <li><a href="/wiki/N-hash" title="N-hash">N-hash</a></li> <li><a href="/wiki/RIPEMD" title="RIPEMD">RIPEMD</a></li> <li><a href="/wiki/RadioGat%C3%BAn" title="RadioGatún">RadioGatún</a></li> <li><a href="/wiki/SIMD_(hash_function)" title="SIMD (hash function)">SIMD</a></li> <li><a href="/wiki/SM3_(hash_function)" title="SM3 (hash function)">SM3</a></li> <li><a href="/wiki/SWIFFT" title="SWIFFT">SWIFFT</a></li> <li><a href="/wiki/Shabal" title="Shabal">Shabal</a></li> <li><a href="/wiki/Snefru" title="Snefru">Snefru</a></li> <li><a href="/wiki/Streebog" title="Streebog">Streebog</a></li> <li><a href="/wiki/Tiger_(hash_function)" title="Tiger (hash function)">Tiger</a></li> <li><a href="/wiki/Very_smooth_hash" title="Very smooth hash">VSH</a></li> <li><a href="/wiki/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="/wiki/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 class="mw-selflink selflink">Argon2</a></li> <li><a href="/wiki/Balloon_hashing" title="Balloon hashing">Balloon</a></li> <li><a href="/wiki/Bcrypt" title="Bcrypt">bcrypt</a></li> <li><a href="/wiki/Catena_(cryptography)" class="mw-redirect" title="Catena (cryptography)">Catena</a></li> <li><a href="/wiki/Crypt_(C)" title="Crypt (C)">crypt</a></li> <li><a href="/wiki/LAN_Manager#LM_hash_details" title="LAN Manager">LM hash</a></li> <li><a href="/wiki/Lyra2" title="Lyra2">Lyra2</a></li> <li><a href="/wiki/Makwa_(cryptography)" class="mw-redirect" title="Makwa (cryptography)">Makwa</a></li> <li><a href="/wiki/PBKDF2" title="PBKDF2">PBKDF2</a></li> <li><a href="/wiki/Scrypt" title="Scrypt">scrypt</a></li> <li><a href="/wiki/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="/wiki/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"> <ul><li><a href="/wiki/HKDF" title="HKDF">HKDF</a></li> <li>KDF1/KDF2</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Message_authentication_code" title="Message authentication code">MAC functions</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="/wiki/CBC-MAC" title="CBC-MAC">CBC-MAC</a></li> <li><a href="/wiki/Data_Authentication_Algorithm" title="Data Authentication Algorithm">DAA</a></li> <li><a href="/wiki/Galois_Message_Authentication_Code" class="mw-redirect" title="Galois Message Authentication Code">GMAC</a></li> <li><a href="/wiki/HMAC" title="HMAC">HMAC</a></li> <li><a href="/wiki/NMAC" class="mw-redirect" title="NMAC">NMAC</a></li> <li><a href="/wiki/One-key_MAC" title="One-key MAC">OMAC</a>/<a href="/wiki/One-key_MAC" title="One-key MAC">CMAC</a></li> <li><a href="/wiki/PMAC_(cryptography)" title="PMAC (cryptography)">PMAC</a></li> <li><a href="/wiki/Poly1305" title="Poly1305">Poly1305</a></li> <li><a href="/wiki/SipHash" title="SipHash">SipHash</a></li> <li><a href="/wiki/UMAC_(cryptography)" title="UMAC (cryptography)">UMAC</a></li> <li><a href="/wiki/VMAC" title="VMAC">VMAC</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/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"> <ul><li><a href="/wiki/CCM_mode" title="CCM mode">CCM</a></li> <li><a href="/wiki/ChaCha20-Poly1305" title="ChaCha20-Poly1305">ChaCha20-Poly1305</a></li> <li><a href="/wiki/CWC_mode" title="CWC mode">CWC</a></li> <li><a href="/wiki/EAX_mode" title="EAX mode">EAX</a></li> <li><a href="/wiki/Galois/Counter_Mode" title="Galois/Counter Mode">GCM</a></li> <li><a href="/wiki/IAPM_(mode)" title="IAPM (mode)">IAPM</a></li> <li><a href="/wiki/OCB_mode" title="OCB mode">OCB</a></li></ul> </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="/wiki/Collision_attack" title="Collision attack">Collision attack</a></li> <li><a href="/wiki/Preimage_attack" title="Preimage attack">Preimage attack</a></li> <li><a href="/wiki/Birthday_attack" title="Birthday attack">Birthday attack</a></li> <li><a href="/wiki/Brute-force_attack" title="Brute-force attack">Brute-force attack</a></li> <li><a href="/wiki/Rainbow_table" title="Rainbow table">Rainbow table</a></li> <li><a href="/wiki/Side-channel_attack" title="Side-channel attack">Side-channel attack</a></li> <li><a href="/wiki/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="/wiki/Avalanche_effect" title="Avalanche effect">Avalanche effect</a></li> <li><a href="/wiki/Hash_collision" title="Hash collision">Hash collision</a></li> <li><a href="/wiki/Merkle%E2%80%93Damg%C3%A5rd_construction" title="Merkle–Damgård construction">Merkle–Damgård construction</a></li> <li><a href="/wiki/Sponge_function" title="Sponge function">Sponge function</a></li> <li><a href="/wiki/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="/wiki/CAESAR_Competition" title="CAESAR Competition">CAESAR Competition</a></li> <li><a href="/wiki/CRYPTREC" title="CRYPTREC">CRYPTREC</a></li> <li><a href="/wiki/NESSIE" title="NESSIE">NESSIE</a></li> <li><a href="/wiki/NIST_hash_function_competition" title="NIST hash function competition">NIST hash function competition</a></li> <li><a href="/wiki/Password_Hashing_Competition" title="Password Hashing Competition">Password Hashing Competition</a></li> <li><a href="/wiki/NSA_Suite_B_Cryptography" title="NSA Suite B Cryptography">NSA Suite B</a></li> <li><a href="/wiki/Commercial_National_Security_Algorithm_Suite" title="Commercial National Security Algorithm Suite">CNSA</a></li></ul> </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="/wiki/Post-quantum_cryptography#Hash-based_cryptography" title="Post-quantum cryptography">Hash-based cryptography</a></li> <li><a href="/wiki/Merkle_tree" title="Merkle tree">Merkle tree</a></li> <li><a href="/wiki/Message_authentication" title="Message authentication">Message authentication</a></li> <li><a href="/wiki/Proof_of_work" title="Proof of work">Proof of work</a></li> <li><a href="/wiki/Salt_(cryptography)" title="Salt (cryptography)">Salt</a></li> <li><a href="/wiki/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 class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Cryptography_navbox" title="Template:Cryptography navbox"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Cryptography_navbox" title="Template talk:Cryptography navbox"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Cryptography_navbox" title="Special:EditPage/Template:Cryptography navbox"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Cryptography" style="font-size:114%;margin:0 4em"><a href="/wiki/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="/wiki/History_of_cryptography" title="History of cryptography">History of cryptography</a></li> <li><a href="/wiki/Outline_of_cryptography" title="Outline of cryptography">Outline of cryptography</a></li> <li><a href="/wiki/Classical_cipher" title="Classical cipher">Classical cipher</a></li> <li><a href="/wiki/Cryptographic_protocol" title="Cryptographic protocol">Cryptographic protocol</a> <ul><li><a href="/wiki/Authentication_protocol" title="Authentication protocol">Authentication protocol</a></li></ul></li> <li><a href="/wiki/Cryptographic_primitive" title="Cryptographic primitive">Cryptographic primitive</a></li> <li><a href="/wiki/Cryptanalysis" title="Cryptanalysis">Cryptanalysis</a></li> <li><a href="/wiki/Cryptocurrency" title="Cryptocurrency">Cryptocurrency</a></li> <li><a href="/wiki/Cryptosystem" title="Cryptosystem">Cryptosystem</a></li> <li><a href="/wiki/Cryptographic_nonce" title="Cryptographic nonce">Cryptographic nonce</a></li> <li><a href="/wiki/Cryptovirology" title="Cryptovirology">Cryptovirology</a></li> <li><a href="/wiki/Hash_function" title="Hash function">Hash function</a> <ul><li><a href="/wiki/Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li> <li><a href="/wiki/Key_derivation_function" title="Key derivation function">Key derivation function</a></li> <li><a href="/wiki/Secure_Hash_Algorithms" title="Secure Hash Algorithms">Secure Hash Algorithms</a></li></ul></li> <li><a href="/wiki/Digital_signature" title="Digital signature">Digital signature</a></li> <li><a href="/wiki/Kleptography" title="Kleptography">Kleptography</a></li> <li><a href="/wiki/Key_(cryptography)" title="Key (cryptography)">Key (cryptography)</a></li> <li><a href="/wiki/Key_exchange" title="Key exchange">Key exchange</a></li> <li><a href="/wiki/Key_generator" title="Key generator">Key generator</a></li> <li><a href="/wiki/Key_schedule" title="Key schedule">Key schedule</a></li> <li><a href="/wiki/Key_stretching" title="Key stretching">Key stretching</a></li> <li><a href="/wiki/Keygen" title="Keygen">Keygen</a></li> <li><a href="/wiki/Template:Cryptography_machines" title="Template:Cryptography machines">Machines</a></li> <li><a href="/wiki/Cryptojacking_malware" class="mw-redirect" title="Cryptojacking malware">Cryptojacking malware</a></li> <li><a href="/wiki/Ransomware" title="Ransomware">Ransomware</a></li> <li><a href="/wiki/Random_number_generation" title="Random number generation">Random number generation</a> <ul><li><a href="/wiki/Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Cryptographically secure pseudorandom number generator</a> (CSPRNG)</li></ul></li> <li><a href="/wiki/Pseudorandom_noise" title="Pseudorandom noise">Pseudorandom noise</a> (PRN)</li> <li><a href="/wiki/Secure_channel" title="Secure channel">Secure channel</a></li> <li><a href="/wiki/Insecure_channel" class="mw-redirect" title="Insecure channel">Insecure channel</a></li> <li><a href="/wiki/Subliminal_channel" title="Subliminal channel">Subliminal channel</a></li> <li><a href="/wiki/Encryption" title="Encryption">Encryption</a></li> <li><a href="/wiki/Decryption" class="mw-redirect" title="Decryption">Decryption</a></li> <li><a href="/wiki/End-to-end_encryption" title="End-to-end encryption">End-to-end encryption</a></li> <li><a href="/wiki/Harvest_now,_decrypt_later" title="Harvest now, decrypt later">Harvest now, decrypt later</a></li> <li><a href="/wiki/Information-theoretic_security" title="Information-theoretic security">Information-theoretic security</a></li> <li><a href="/wiki/Plaintext" title="Plaintext">Plaintext</a></li> <li><a href="/wiki/Codetext" class="mw-redirect" title="Codetext">Codetext</a></li> <li><a href="/wiki/Ciphertext" title="Ciphertext">Ciphertext</a></li> <li><a href="/wiki/Shared_secret" title="Shared secret">Shared secret</a></li> <li><a href="/wiki/Trapdoor_function" title="Trapdoor function">Trapdoor function</a></li> <li><a href="/wiki/Trusted_timestamping" title="Trusted timestamping">Trusted timestamping</a></li> <li><a href="/wiki/Key-based_routing" title="Key-based routing">Key-based routing</a></li> <li><a href="/wiki/Onion_routing" title="Onion routing">Onion routing</a></li> <li><a href="/wiki/Garlic_routing" title="Garlic routing">Garlic routing</a></li> <li><a href="/wiki/Kademlia" title="Kademlia">Kademlia</a></li> <li><a href="/wiki/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="/wiki/Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li> <li><a href="/wiki/Block_cipher" title="Block cipher">Block cipher</a></li> <li><a href="/wiki/Stream_cipher" title="Stream cipher">Stream cipher</a></li> <li><a href="/wiki/Symmetric-key_algorithm" title="Symmetric-key algorithm">Symmetric-key algorithm</a></li> <li><a href="/wiki/Authenticated_encryption" title="Authenticated encryption">Authenticated encryption</a></li> <li><a href="/wiki/Public-key_cryptography" title="Public-key cryptography">Public-key cryptography</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li> <li><a href="/wiki/Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li> <li><a href="/wiki/Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li> <li><a href="/wiki/Message_authentication_code" title="Message authentication code">Message authentication code</a></li> <li><a href="/wiki/Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Random numbers</a></li> <li><a href="/wiki/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"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" 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