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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Creating_public_key_fingerprints" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Creating_public_key_fingerprints"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Creating public key fingerprints</span> </div> </a> <ul id="toc-Creating_public_key_fingerprints-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Using_public_key_fingerprints_for_key_authentication" class="vector-toc-list-item vector-toc-level-1 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0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-One_source plainlinks metadata ambox ambox-content ambox-one_source" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>relies largely or entirely on a <a href="/wiki/Wikipedia:Articles_with_a_single_source" title="Wikipedia:Articles with a single source">single source</a></b>.<span class="hide-when-compact"> Relevant discussion may be found on the <a href="/wiki/Talk:Public_key_fingerprint" title="Talk:Public key fingerprint">talk page</a>. Please help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Public_key_fingerprint&action=edit">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">introducing citations to additional sources</a>.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Public+key+fingerprint%22">"Public key fingerprint"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Public+key+fingerprint%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Public+key+fingerprint%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Public+key+fingerprint%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Public+key+fingerprint%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Public+key+fingerprint%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">June 2014</span>)</i></span></div></td></tr></tbody></table> <p>In <a href="/wiki/Public-key_cryptography" title="Public-key cryptography">public-key cryptography</a>, a <b>public key fingerprint</b> is a short sequence of <a href="/wiki/Byte" title="Byte">bytes</a> used to identify a longer <a href="/wiki/Public_key" class="mw-redirect" title="Public key">public key</a>. Fingerprints are created by applying a <a href="/wiki/Cryptographic_hash_function" title="Cryptographic hash function">cryptographic hash function</a> to a public key. Since fingerprints are shorter than the keys they refer to, they can be used to simplify certain key management tasks. In <a href="/wiki/Microsoft" title="Microsoft">Microsoft</a> software, "thumbprint" is used instead of "fingerprint." </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Creating_public_key_fingerprints">Creating public key fingerprints</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Public_key_fingerprint&action=edit&section=1" title="Edit section: Creating public key fingerprints"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A public key fingerprint is typically created through the following steps: </p> <ol><li>A public key (and optionally some additional data) is encoded into a sequence of bytes. To ensure that the same fingerprint can be recreated later, the encoding must be deterministic, and any additional data must be exchanged and stored alongside the public key. The additional data is typically information which anyone using the public key should be aware of. Examples of additional data include: which protocol versions the key should be used with (in the case of <a href="/wiki/Pretty_Good_Privacy" title="Pretty Good Privacy">PGP</a> fingerprints); and the name of the key holder (in the case of <a href="/wiki/X.509" title="X.509">X.509</a> trust anchor fingerprints, where the additional data consists of an X.509 <a href="/wiki/Self-signed_certificate" title="Self-signed certificate">self-signed certificate</a>).</li> <li>The data produced in the previous step is hashed with a cryptographic hash function such as <a href="/wiki/SHA-1" title="SHA-1">SHA-1</a> or <a href="/wiki/SHA-2" title="SHA-2">SHA-2</a>.</li> <li>If desired, the hash function output can be truncated to provide a shorter, more convenient fingerprint.</li></ol> <p>This process produces a short fingerprint which can be used to authenticate a much larger public key. For example, whereas a typical <a href="/wiki/RSA_(algorithm)" class="mw-redirect" title="RSA (algorithm)">RSA</a> public key will be 2048 bits in length or longer, typical <a href="/wiki/MD5" title="MD5">MD5</a> or <a href="/wiki/SHA-1" title="SHA-1">SHA-1</a> fingerprints are only 128 or 160 bits in length. </p><p>When displayed for human inspection, fingerprints are usually encoded into <a href="/wiki/Hexadecimal" title="Hexadecimal">hexadecimal</a> strings. These strings are then formatted into groups of characters for readability. For example, a 128-bit MD5 fingerprint for <a href="/wiki/Secure_Shell" title="Secure Shell">SSH</a> would be displayed as follows: </p> <pre> 43:51:43:a1:b5:fc:8b:b7:0a:3a:a9:b1:0f:66:73:a8 </pre> <div class="mw-heading mw-heading2"><h2 id="Using_public_key_fingerprints_for_key_authentication">Using public key fingerprints for key authentication</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Public_key_fingerprint&action=edit&section=2" title="Edit section: Using public key fingerprints for key authentication"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Key_authentication" title="Key authentication">key authentication</a></div> <p>When a public key is received over an untrusted channel, such as the <a href="/wiki/Internet" title="Internet">Internet</a>, the recipient often wishes to <a href="/wiki/Authentication" title="Authentication">authenticate</a> the public key. Fingerprints can help accomplish this, since their small size allows them to be passed over trusted channels where public keys won't easily fit. </p><p>For example, if Alice wishes to authenticate a public key as belonging to Bob, she can contact Bob over the phone or in person and ask him to read his fingerprint to her, or give her a scrap of paper with the fingerprint written down. Alice can then check that this trusted fingerprint matches the fingerprint of the public key. Exchanging and comparing values like this is much easier if the values are short fingerprints instead of long public keys. </p><p>Fingerprints can also be useful when automating the exchange or storage of key authentication data. For example, if key authentication data needs to be transmitted through a protocol or stored in a <a href="/wiki/Database" title="Database">database</a> where the size of a full public key is a problem, then exchanging or storing fingerprints may be a more viable solution. </p><p>In addition, fingerprints can be queried with search engines in order to ensure that the public key that a user just downloaded can be seen by third party search engines. If the search engine returns hits referencing the fingerprint linked to the proper site(s), one can feel more confident that the key is not being injected by an attacker, such as a <a href="/wiki/Man-in-the-middle_attack" title="Man-in-the-middle attack">Man-in-the-middle attack</a>. </p><p><a href="/wiki/Pretty_Good_Privacy" title="Pretty Good Privacy">PGP</a> developed the <a href="/wiki/PGP_word_list" title="PGP word list">PGP word list</a> to facilitate the exchange of public key fingerprints over voice channels. </p> <div class="mw-heading mw-heading2"><h2 id="Public_key_fingerprints_in_practice">Public key fingerprints in practice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Public_key_fingerprint&action=edit&section=3" title="Edit section: Public key fingerprints in practice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In systems such as SSH, users can exchange and check fingerprints manually to perform key authentication. Once a user has accepted another user's fingerprint, that fingerprint (or the key it refers to) will be stored locally along with a record of the other user's name or address, so that future communications with that user can be automatically authenticated. </p><p>In systems such as X.509-based <a href="/wiki/Public_key_infrastructure" title="Public key infrastructure">PKI</a>, fingerprints are primarily used to authenticate root keys. These root keys issue certificates which can be used to authenticate user keys. This use of certificates eliminates the need for manual fingerprint verification between users. </p><p>In systems such as <a href="/wiki/Pretty_Good_Privacy" title="Pretty Good Privacy">PGP</a> or <a href="/wiki/Microsoft_Office_Groove" class="mw-redirect" title="Microsoft Office Groove">Groove</a>, fingerprints can be used for either of the above approaches: they can be used to authenticate keys belonging to other users, or keys belonging to certificate-issuing authorities. In PGP, normal users can issue certificates to each other, forming a <a href="/wiki/Web_of_trust" title="Web of trust">web of trust</a>, and fingerprints are often used to assist in this process (e.g., at <a href="/wiki/Key-signing_parties" class="mw-redirect" title="Key-signing parties">key-signing parties</a>). </p><p>In systems such as <a href="/wiki/Cryptographically_Generated_Addresses" class="mw-redirect" title="Cryptographically Generated Addresses">CGA</a> or <a href="/wiki/Self-certifying_File_System" title="Self-certifying File System">SFS</a> and most cryptographic <a href="/wiki/Peer-to-peer_network" class="mw-redirect" title="Peer-to-peer network">peer-to-peer networks</a>, fingerprints are embedded into pre-existing address and name formats (such as <a href="/wiki/IPv6" title="IPv6">IPv6</a> addresses, <a href="/wiki/File_name" class="mw-redirect" title="File name">file names</a> or other identification strings). If addresses and names are already being exchanged through trusted channels, this approach allows fingerprints to piggyback on them.<sup id="cite_ref-selfcert_1-0" class="reference"><a href="#cite_note-selfcert-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>In PGP, most keys are created in such a way that what is called the "key ID" is equal to the lower 32 or 64 bits respectively of a key fingerprint. PGP uses key IDs to refer to public keys for a variety of purposes. These are not, properly speaking, fingerprints, since their short length prevents them from being able to securely authenticate a public key. 32bit key ids should not be used as current hardware can generate a colliding 32bit key id in just 4 seconds.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Security_of_public_key_fingerprints">Security of public key fingerprints</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Public_key_fingerprint&action=edit&section=4" title="Edit section: Security of public key fingerprints"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The primary threat to the security of a fingerprint is a <a href="/wiki/Second-preimage_attack" class="mw-redirect" title="Second-preimage attack">second-preimage attack</a>, where an attacker constructs a key pair whose public key hashes to a fingerprint that matches the victim's fingerprint. The attacker could then present his public key in place of the victim's public key to masquerade as the victim. </p><p>A secondary threat to some systems is a <a href="/wiki/Collision_attack" title="Collision attack">collision attack</a>, where an attacker constructs multiple key pairs which hash to his own fingerprint. This may allow an attacker to repudiate signatures he has created, or cause other confusion. </p><p>To prevent preimage attacks, the cryptographic hash function used for a fingerprint should possess the property of second preimage resistance. If collision attacks are a threat, the hash function should also possess the property of collision-resistance. While it is acceptable to truncate hash function output for the sake of shorter, more usable fingerprints, the truncated fingerprints must be long enough to preserve the relevant properties of the hash function against <a href="/wiki/Brute-force_search" title="Brute-force search">brute-force search</a> attacks. </p><p>In practice, most fingerprints commonly used today are based on non-truncated MD5 or SHA-1 hashes. As of 2017, collisions but not preimages can be found in MD5 and SHA-1. The future is therefore likely to bring increasing use of newer hash functions such as <a href="/wiki/SHA-256" class="mw-redirect" title="SHA-256">SHA-256</a>. However, fingerprints based on SHA-256 and other hash functions with long output lengths are more likely to be truncated than (relatively short) MD5 or SHA-1 fingerprints. </p><p>In situations where fingerprint length must be minimized at all costs, fingerprint security can be boosted by increasing the cost of calculating the fingerprint. For example, in the context of <a href="/wiki/Cryptographically_Generated_Address" title="Cryptographically Generated Address">Cryptographically Generated Addresses</a>, this is called "Hash Extension" and requires anyone calculating a fingerprint to search for a <a href="/wiki/Hashsum" class="mw-redirect" title="Hashsum">hashsum</a> starting with a fixed number of zeroes,<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> which is assumed to be an expensive operation. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Public_key_fingerprint&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Fingerprint_(computing)" title="Fingerprint (computing)">Fingerprint (computing)</a></li> <li><a href="/wiki/PGP_word_list" title="PGP word list">PGP word list</a></li> <li><a href="/wiki/Public-key_cryptography" title="Public-key cryptography">Public-key cryptography</a></li> <li><a href="/wiki/Key_authentication" title="Key authentication">Key authentication</a></li> <li><a href="/wiki/Key_management" title="Key management">Key management</a></li> <li><a href="/wiki/Key_signing_party" title="Key signing party">Key signing party</a></li> <li><a href="/wiki/X.509" title="X.509">X.509</a></li> <li><a href="/wiki/Digital_signature" title="Digital signature">Digital signature</a></li> <li><a href="/wiki/Rabin_fingerprint" title="Rabin fingerprint">Rabin fingerprint</a></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=Public_key_fingerprint&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-selfcert-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-selfcert_1-0">^</a></b></span> <span class="reference-text"><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><cite id="CITEREFDavid_MazièresM._Frans_Kaashoek1998" class="citation conference cs1"><a href="/wiki/David_Mazi%C3%A8res" class="mw-redirect" title="David Mazières">David Mazières</a>; <a href="/wiki/Frans_Kaashoek" title="Frans Kaashoek">M. Frans Kaashoek</a> (September 1998). <a rel="nofollow" class="external text" href="http://cag.lcs.mit.edu/pub/dm/papers/mazieres:thesis.ps.gz"><i>Escaping the Evils of Centralized Control with self-certifying pathnames</i></a> <span class="cs1-format">(<a href="/wiki/PostScript" title="PostScript">PostScript</a>)</span>. Proceedings of the 8th <a href="/wiki/Association_for_Computing_Machinery" title="Association for Computing Machinery">ACM</a> SIGOPS European workshop: Support for composing distributed applications. Sintra, Portugal: MIT<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-12-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Escaping+the+Evils+of+Centralized+Control+with+self-certifying+pathnames&rft.place=Sintra%2C+Portugal&rft.pub=MIT&rft.date=1998-09&rft.au=David+Mazi%C3%A8res&rft.au=M.+Frans+Kaashoek&rft_id=http%3A%2F%2Fcag.lcs.mit.edu%2Fpub%2Fdm%2Fpapers%2Fmazieres%3Athesis.ps.gz&rfr_id=info%3Asid%2Fen.wikipedia.org%3APublic+key+fingerprint" class="Z3988"></span></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"><a rel="nofollow" class="external text" href="https://evil32.com/">Evil 32: Check Your GPG Fingerprints</a></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAura2005" class="citation cs1">Aura, Tumas (March 2005). <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc3972#section-7.2">"Hash Extension"</a>. <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc3972"><i>Cryptographically Generated Addresses (CGA)</i></a>. <a href="/wiki/Internet_Engineering_Task_Force" title="Internet Engineering Task Force">IETF</a>. sec. 7.2. <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%2FRFC3972">10.17487/RFC3972</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/rfc3972">3972</a><span class="reference-accessdate">. Retrieved <span class="nowrap">January 2,</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hash+Extension&rft.btitle=Cryptographically+Generated+Addresses+%28CGA%29&rft.pages=sec.-7.2&rft.pub=IETF&rft.date=2005-03&rft_id=info%3Adoi%2F10.17487%2FRFC3972&rft.aulast=Aura&rft.aufirst=Tumas&rft_id=https%3A%2F%2Fdatatracker.ietf.org%2Fdoc%2Fhtml%2Frfc3972%26%23035%3Bsection-7.2&rfr_id=info%3Asid%2Fen.wikipedia.org%3APublic+key+fingerprint" class="Z3988"></span></span> </li> </ol></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline 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style="width:1%">Algorithms</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group wraplinks" style="width:1%"><a href="/wiki/Integer_factorization" title="Integer factorization">Integer factorization</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/Benaloh_cryptosystem" title="Benaloh cryptosystem">Benaloh</a></li> <li><a href="/wiki/Blum%E2%80%93Goldwasser_cryptosystem" title="Blum–Goldwasser cryptosystem">Blum–Goldwasser</a></li> <li><a href="/wiki/Cayley%E2%80%93Purser_algorithm" title="Cayley–Purser algorithm">Cayley–Purser</a></li> <li><a href="/wiki/Damg%C3%A5rd%E2%80%93Jurik_cryptosystem" title="Damgård–Jurik cryptosystem">Damgård–Jurik</a></li> <li><a href="/wiki/GMR_(cryptography)" title="GMR (cryptography)">GMR</a></li> <li><a href="/wiki/Goldwasser%E2%80%93Micali_cryptosystem" title="Goldwasser–Micali cryptosystem">Goldwasser–Micali</a></li> <li><a href="/wiki/Naccache%E2%80%93Stern_cryptosystem" title="Naccache–Stern cryptosystem">Naccache–Stern</a></li> <li><a href="/wiki/Paillier_cryptosystem" title="Paillier cryptosystem">Paillier</a></li> <li><a href="/wiki/Rabin_cryptosystem" title="Rabin cryptosystem">Rabin</a></li> <li><a href="/wiki/RSA_(cryptosystem)" title="RSA (cryptosystem)">RSA</a></li> <li><a href="/wiki/Okamoto%E2%80%93Uchiyama_cryptosystem" title="Okamoto–Uchiyama cryptosystem">Okamoto–Uchiyama</a></li> <li><a href="/wiki/Schmidt-Samoa_cryptosystem" title="Schmidt-Samoa cryptosystem">Schmidt–Samoa</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group wraplinks" style="width:1%"><a href="/wiki/Discrete_logarithm" title="Discrete logarithm">Discrete logarithm</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/Boneh%E2%80%93Lynn%E2%80%93Shacham" class="mw-redirect" title="Boneh–Lynn–Shacham">BLS</a></li> <li><a href="/wiki/Cramer%E2%80%93Shoup_cryptosystem" title="Cramer–Shoup cryptosystem">Cramer–Shoup</a></li> <li><a href="/wiki/Diffie%E2%80%93Hellman_key_exchange" title="Diffie–Hellman key exchange">DH</a></li> <li><a href="/wiki/Digital_Signature_Algorithm" title="Digital Signature Algorithm">DSA</a></li> <li><a href="/wiki/Elliptic-curve_Diffie%E2%80%93Hellman" title="Elliptic-curve Diffie–Hellman">ECDH</a> <ul><li><a href="/wiki/Curve25519" title="Curve25519">X25519</a></li> <li><a href="/wiki/Curve448" title="Curve448">X448</a></li></ul></li> <li><a href="/wiki/Elliptic_Curve_Digital_Signature_Algorithm" title="Elliptic Curve Digital Signature Algorithm">ECDSA</a></li> <li><a href="/wiki/EdDSA" title="EdDSA">EdDSA</a> <ul><li><a href="/wiki/EdDSA#Ed25519" title="EdDSA">Ed25519</a></li> <li><a href="/wiki/EdDSA#Ed448" title="EdDSA">Ed448</a></li></ul></li> <li><a href="/wiki/ECMQV" class="mw-redirect" title="ECMQV">ECMQV</a></li> <li><a href="/wiki/Encrypted_key_exchange" title="Encrypted key exchange">EKE</a></li> <li><a href="/wiki/ElGamal_encryption" title="ElGamal encryption">ElGamal</a> <ul><li><a href="/wiki/ElGamal_signature_scheme" title="ElGamal signature scheme">signature scheme</a></li></ul></li> <li><a href="/wiki/MQV" title="MQV">MQV</a></li> <li><a href="/wiki/Schnorr_signature" title="Schnorr signature">Schnorr</a></li> <li><a href="/wiki/SPEKE" title="SPEKE">SPEKE</a></li> <li><a href="/wiki/Secure_Remote_Password_protocol" title="Secure Remote Password protocol">SRP</a></li> <li><a href="/wiki/Station-to-Station_protocol" title="Station-to-Station protocol">STS</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group wraplinks" style="width:1%"><a href="/wiki/Lattice-based_cryptography" title="Lattice-based cryptography">Lattice/SVP/CVP</a>/<wbr /><a href="/wiki/Learning_with_errors" title="Learning with errors">LWE</a>/<wbr /><a href="/wiki/Short_integer_solution_problem" title="Short integer solution problem">SIS</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/BLISS_signature_scheme" title="BLISS signature scheme">BLISS</a></li> <li><a href="/wiki/Kyber" title="Kyber">Kyber</a></li> <li><a href="/wiki/NewHope" title="NewHope">NewHope</a></li> <li><a href="/wiki/NTRUEncrypt" title="NTRUEncrypt">NTRUEncrypt</a></li> <li><a href="/wiki/NTRUSign" title="NTRUSign">NTRUSign</a></li> <li><a href="/wiki/RLWE-KEX" class="mw-redirect" title="RLWE-KEX">RLWE-KEX</a></li> <li><a href="/wiki/RLWE-SIG" class="mw-redirect" title="RLWE-SIG">RLWE-SIG</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group wraplinks" style="width:1%">Others</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/Algebraic_Eraser" title="Algebraic Eraser">AE</a></li> <li><a href="/wiki/CEILIDH" title="CEILIDH">CEILIDH</a></li> <li><a href="/wiki/Efficient_Probabilistic_Public-Key_Encryption_Scheme" title="Efficient Probabilistic Public-Key Encryption Scheme">EPOC</a></li> <li><a href="/wiki/Hidden_Field_Equations" title="Hidden Field Equations">HFE</a></li> <li><a href="/wiki/Integrated_Encryption_Scheme" title="Integrated Encryption Scheme">IES</a></li> <li><a href="/wiki/Lamport_signature" title="Lamport signature">Lamport</a></li> <li><a href="/wiki/McEliece_cryptosystem" title="McEliece cryptosystem">McEliece</a></li> <li><a href="/wiki/Merkle%E2%80%93Hellman_knapsack_cryptosystem" title="Merkle–Hellman knapsack cryptosystem">Merkle–Hellman</a></li> <li><span class="wraplinks"><a href="/wiki/Naccache%E2%80%93Stern_knapsack_cryptosystem" title="Naccache–Stern knapsack cryptosystem">Naccache–Stern knapsack cryptosystem</a></span></li> <li><a href="/wiki/Three-pass_protocol" title="Three-pass protocol">Three-pass protocol</a></li> <li><a href="/wiki/XTR" title="XTR">XTR</a></li> <li><a href="/wiki/SQIsign" title="SQIsign">SQIsign</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discrete_logarithm#Cryptography" title="Discrete logarithm">Discrete logarithm cryptography</a></li> <li><a href="/wiki/Elliptic-curve_cryptography" title="Elliptic-curve cryptography">Elliptic-curve cryptography</a></li> <li><a href="/wiki/Hash-based_cryptography" title="Hash-based cryptography">Hash-based cryptography</a></li> <li><a href="/wiki/Non-commutative_cryptography" title="Non-commutative cryptography">Non-commutative cryptography</a></li> <li><a href="/wiki/RSA_problem" title="RSA problem">RSA problem</a></li> <li><a href="/wiki/Trapdoor_function" title="Trapdoor function">Trapdoor function</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 hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/CRYPTREC" title="CRYPTREC">CRYPTREC</a></li> <li><a href="/wiki/IEEE_P1363" title="IEEE P1363">IEEE P1363</a></li> <li><a href="/wiki/NESSIE" title="NESSIE">NESSIE</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> <li><a href="/wiki/NIST_Post-Quantum_Cryptography_Standardization" title="NIST Post-Quantum Cryptography Standardization">Post-Quantum Cryptography</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Digital_signature" title="Digital signature">Digital signature</a></li> <li><a href="/wiki/Optimal_asymmetric_encryption_padding" title="Optimal asymmetric encryption padding">OAEP</a></li> <li><a class="mw-selflink selflink">Fingerprint</a></li> <li><a href="/wiki/Public_key_infrastructure" title="Public key infrastructure">PKI</a></li> <li><a href="/wiki/Web_of_trust" title="Web of trust">Web of trust</a></li> <li><a href="/wiki/Key_size" title="Key size">Key size</a></li> <li><a href="/wiki/Identity-based_cryptography" title="Identity-based cryptography">Identity-based cryptography</a></li> <li><a href="/wiki/Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li> <li><a href="/wiki/OpenPGP_card" title="OpenPGP card">OpenPGP card</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="Cryptography149" 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" data-file-width="180" data-file-height="185" /></span></span> <a 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