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rel="dns-prefetch" href="//login.wikimedia.org"/> 29 <link rel="dns-prefetch" href="//meta.wikimedia.org" /> 30 <!--[if lt IE 9]><script src="/w/load.php?debug=false&lang=en&modules=html5shiv&only=scripts&skin=vector&sync=1"></script><![endif]--> 31 </head> 32 <body class="mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Merkle_tree rootpage-Merkle_tree skin-vector action-view"> <div id="mw-page-base" class="noprint"></div> 33 <div id="mw-head-base" class="noprint"></div> 34 <div id="content" class="mw-body" role="main"> 35 <a id="top"></a> 36 <div id="siteNotice" class="mw-body-content"><!-- CentralNotice --></div><div class="mw-indicators mw-body-content"> 37 <div id="mw-indicator-spoken-icon" class="mw-indicator"><a href="/wiki/File:En-Merkle_Tree.ogg" title="Listen to this article"><img alt="Listen to this article" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/20px-Sound-icon.svg.png" width="20" height="15" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/30px-Sound-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/40px-Sound-icon.svg.png 2x" data-file-width="128" data-file-height="96" /></a></div> 38 </div> 39 <h1 id="firstHeading" class="firstHeading" lang="en">Merkle tree</h1> <div id="bodyContent" class="mw-body-content"> 40 <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> <div id="contentSub"></div> 41 <div id="jump-to-nav"></div> <a class="mw-jump-link" href="#mw-head">Jump to navigation</a> 42 <a class="mw-jump-link" href="#p-search">Jump to search</a> 43 <div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><div class="mw-parser-output"><div class="thumb tright"><div class="thumbinner" style="width:312px;"><a href="/wiki/File:Hash_Tree.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Hash_Tree.svg/310px-Hash_Tree.svg.png" width="310" height="197" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Hash_Tree.svg/465px-Hash_Tree.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/Hash_Tree.svg/620px-Hash_Tree.svg.png 2x" data-file-width="2200" data-file-height="1400" /></a> <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Hash_Tree.svg" class="internal" title="Enlarge"></a></div>An example of a binary hash tree. Hashes 0-0 and 0-1 are the hash values of data blocks L1 and L2, respectively, and hash 0 is the hash of the concatenation of hashes 0-0 and 0-1.</div></div></div> 44 <p>In <a href="/wiki/Cryptography" title="Cryptography">cryptography</a> and <a href="/wiki/Computer_science" title="Computer science">computer science</a>, a <b>hash tree</b> or <b>Merkle tree</b> is a <a href="/wiki/Tree_(data_structure)" title="Tree (data structure)">tree</a> in which every leaf node is labelled with the hash of a data block and every non-leaf node is labelled with the <a href="/wiki/Cryptographic_hash_function" title="Cryptographic hash function">cryptographic hash</a> of the labels of its child nodes. Hash trees allow efficient and secure verification of the contents of large data structures. Hash trees are a generalization of <a href="/wiki/Hash_list" title="Hash list">hash lists</a> and <a href="/wiki/Hash_chain" title="Hash chain">hash chains</a>. 45 </p><p>Demonstrating that a leaf node is a part of a given binary hash tree requires computing a number of hashes proportional to the <a href="/wiki/Logarithm" title="Logarithm">logarithm</a> of the number of leaf nodes of the tree;<sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup> this contrasts with hash lists, where the number is proportional to the number of leaf nodes itself. 46 </p><p>The concept of hash trees is named after <a href="/wiki/Ralph_Merkle" title="Ralph Merkle">Ralph Merkle</a> who patented it in 1979.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup> 47 </p> 48 <div id="toc" class="toc"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2>Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> 49 <ul> 50 <li class="toclevel-1 tocsection-1"><a href="#Uses"><span class="tocnumber">1</span> <span class="toctext">Uses</span></a></li> 51 <li class="toclevel-1 tocsection-2"><a href="#Overview"><span class="tocnumber">2</span> <span class="toctext">Overview</span></a> 52 <ul> 53 <li class="toclevel-2 tocsection-3"><a href="#Second_preimage_attack"><span class="tocnumber">2.1</span> <span class="toctext">Second preimage attack</span></a></li> 54 <li class="toclevel-2 tocsection-4"><a href="#Tiger_tree_hash"><span class="tocnumber">2.2</span> <span class="toctext">Tiger tree hash</span></a> 55 <ul> 56 <li class="toclevel-3 tocsection-5"><a href="#Example"><span class="tocnumber">2.2.1</span> <span class="toctext">Example</span></a></li> 57 </ul> 58 </li> 59 </ul> 60 </li> 61 <li class="toclevel-1 tocsection-6"><a href="#See_also"><span class="tocnumber">3</span> <span class="toctext">See also</span></a></li> 62 <li class="toclevel-1 tocsection-7"><a href="#References"><span class="tocnumber">4</span> <span class="toctext">References</span></a></li> 63 <li class="toclevel-1 tocsection-8"><a href="#Further_reading"><span class="tocnumber">5</span> <span class="toctext">Further reading</span></a></li> 64 <li class="toclevel-1 tocsection-9"><a href="#External_links"><span class="tocnumber">6</span> <span class="toctext">External links</span></a></li> 65 </ul> 66 </div> 67 68 <h2><span class="mw-headline" id="Uses">Uses</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=1" title="Edit section: Uses">edit</a><span class="mw-editsection-bracket">]</span></span></h2> 69 <p>Hash trees can be used to verify any kind of data stored, handled and transferred in and between computers. They can help ensure that data blocks received from other peers in a <a href="/wiki/Peer-to-peer" title="Peer-to-peer">peer-to-peer network</a> are received undamaged and unaltered, and even to check that the other peers do not lie and send fake blocks. 70 </p><p>Hash trees are used in <a href="/wiki/Hash-based_cryptography" title="Hash-based cryptography">hash-based cryptography</a>. Hash trees are also used in the <a href="/wiki/InterPlanetary_File_System" title="InterPlanetary File System">IPFS</a>, <a href="/wiki/Btrfs" title="Btrfs">Btrfs</a> and <a href="/wiki/ZFS" title="ZFS">ZFS</a> file systems<sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[4]</a></sup> (to counter <a href="/wiki/Data_degradation" title="Data degradation">data degradation</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5">[5]</a></sup>); <a href="/wiki/Dat_(software)" title="Dat (software)">Dat</a> protocol; <a href="/wiki/Apache_Wave" title="Apache Wave">Apache Wave</a> protocol<sup id="cite_ref-6" class="reference"><a href="#cite_note-6">[6]</a></sup>; <a href="/wiki/Git_(software)" class="mw-redirect" title="Git (software)">Git</a> and <a href="/wiki/Mercurial" title="Mercurial">Mercurial</a> distributed revision control systems; the <a href="/wiki/Tahoe-LAFS" title="Tahoe-LAFS">Tahoe-LAFS</a> backup system; <a href="/wiki/Zeronet" class="mw-redirect" title="Zeronet">Zeronet</a>; the <a href="/wiki/Bitcoin" title="Bitcoin">Bitcoin</a> and <a href="/wiki/Ethereum" title="Ethereum">Ethereum</a> peer-to-peer networks<sup id="cite_ref-7" class="reference"><a href="#cite_note-7">[7]</a></sup>; the <a href="/wiki/Certificate_Transparency" title="Certificate Transparency">Certificate Transparency</a> framework; and a number of <a href="/wiki/NoSQL" title="NoSQL">NoSQL</a> systems such as <a href="/wiki/Apache_Cassandra" title="Apache Cassandra">Apache Cassandra</a>, <a href="/wiki/Riak" title="Riak">Riak</a>, and <a href="/wiki/Dynamo_(storage_system)" title="Dynamo (storage system)">Dynamo</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8">[8]</a></sup> 71 Suggestions have been made to use hash trees in <a href="/wiki/Trusted_computing" class="mw-redirect" title="Trusted computing">trusted computing</a> systems.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9">[9]</a></sup> 72 </p><p>The initial Bitcoin implementation of Merkle trees by <a href="/wiki/Satoshi_Nakamoto" title="Satoshi Nakamoto">Satoshi Nakamoto</a> applies the compression step of the hash function to an excessive degree, which is mitigated by using Fast Merkle Trees.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10">[10]</a></sup> 73 </p> 74 <h2><span class="mw-headline" id="Overview">Overview</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=2" title="Edit section: Overview">edit</a><span class="mw-editsection-bracket">]</span></span></h2> 75 <p>A hash tree is a <a href="/wiki/Binary_tree" title="Binary tree">tree</a> of <a href="/wiki/Hash_function" title="Hash function">hashes</a> in which the leaves are hashes of data blocks in, for instance, a file or set of files. Nodes further up in the tree are the hashes of their respective children. For example, in the picture <i>hash 0</i> is the result of hashing the <a href="/wiki/Concatenation" title="Concatenation">concatenation</a> of <i>hash 0-0</i> and <i>hash 0-1</i>. That is, <i>hash 0 = hash( hash 0-0 || hash 0-1 )</i> where <i>||</i> denotes concatenation. 76 </p><p>Most hash tree implementations are binary (two child nodes under each node) but they can just as well use many more child nodes under each node. 77 </p><p>Usually, a <a href="/wiki/Cryptographic_hash_function" title="Cryptographic hash function">cryptographic hash function</a> such as <a href="/wiki/SHA-2" title="SHA-2">SHA-2</a> is used for the hashing. If the hash tree only needs to protect against unintentional damage, unsecured <a href="/wiki/Checksum" title="Checksum">checksums</a> such as <a href="/wiki/Cyclic_redundancy_check" title="Cyclic redundancy check">CRCs</a> can be used. 78 </p><p>In the top of a hash tree there is a <i>top hash</i> (or <i>root hash</i> or <i>master hash</i>). Before downloading a file on a p2p network, in most cases the top hash is acquired from a trusted source, for instance a friend or a web site that is known to have good recommendations of files to download. When the top hash is available, the hash tree can be received from any non-trusted source, like any peer in the p2p network. Then, the received hash tree is checked against the trusted top hash, and if the hash tree is damaged or fake, another hash tree from another source will be tried until the program finds one that matches the top hash.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2016)">citation needed</span></a></i>]</sup> 79 </p><p>The main difference from a <a href="/wiki/Hash_list" title="Hash list">hash list</a> is that one branch of the hash tree can be downloaded at a time and the integrity of each branch can be checked immediately, even though the whole tree is not available yet. For example, in the picture, the integrity of <i>data block L2</i> can be verified immediately if the tree already contains <i>hash 0-0</i> and <i>hash 1</i> by hashing the data block and iteratively combining the result with <i>hash 0-0</i> and then <i>hash 1</i> and finally comparing the result with the <i>top hash</i>. Similarly, the integrity of <i>data block L3</i> can be verified if the tree already has <i>hash 1-1</i> and <i>hash 0</i>. This can be an advantage since it is efficient to split files up in very small data blocks so that only small blocks have to be re-downloaded if they get damaged. If the hashed file is very big, such a hash tree or hash list becomes fairly big. But if it is a tree, one small branch can be downloaded quickly, the integrity of the branch can be checked, and then the downloading of data blocks can start.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2016)">citation needed</span></a></i>]</sup> 80 </p> 81 <h3><span class="mw-headline" id="Second_preimage_attack">Second preimage attack</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=3" title="Edit section: Second preimage attack">edit</a><span class="mw-editsection-bracket">]</span></span></h3> 82 <p>The Merkle hash root does not indicate the tree depth, enabling a <a href="/wiki/Second-preimage_attack" class="mw-redirect" title="Second-preimage attack">second-preimage attack</a> in which an attacker creates a document other than the original that has the same Merkle hash root. For the example above, an attacker can create a new document containing two data blocks, where the first is hash 0-0 || hash 0-1, and the second is hash 1-0 || hash 1-1.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11">[11]</a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12">[12]</a></sup> 83 </p><p>One simple fix is defined in <a href="/wiki/Certificate_Transparency" title="Certificate Transparency">Certificate Transparency</a>: when computing leaf node hashes, a 0x00 byte is prepended to the hash data, while 0x01 is prepended when computing internal node hashes. Limiting the hash tree size is a prerequisite of some <a href="/wiki/Linked_timestamping#Provable_security" title="Linked timestamping">formal security proofs</a>, and helps in making some proofs tighter. Some implementations limit the tree depth using hash tree depth prefixes before hashes, so any extracted hash chain is defined to be valid only if the prefix decreases at each step and is still positive when the leaf is reached. 84 </p> 85 <h3><span class="mw-headline" id="Tiger_tree_hash">Tiger tree hash</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=4" title="Edit section: Tiger tree hash">edit</a><span class="mw-editsection-bracket">]</span></span></h3> 86 <p>The Tiger tree hash is a widely used form of hash tree. It uses a binary hash tree (two child nodes under each node), usually has a data block size of 1024 <a href="/wiki/Byte" title="Byte">bytes</a> and uses the <a href="/wiki/Tiger_(hash)" class="mw-redirect" title="Tiger (hash)">Tiger hash</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13">[13]</a></sup> 87 </p><p>Tiger tree hashes are used in <a href="/wiki/Gnutella" title="Gnutella">Gnutella</a><sup id="cite_ref-14" class="reference"><a href="#cite_note-14">[14]</a></sup>, <a href="/wiki/Gnutella2" title="Gnutella2">Gnutella2</a>, and <a href="/wiki/Direct_Connect_(file_sharing)" class="mw-redirect" title="Direct Connect (file sharing)">Direct Connect</a> <a href="/wiki/Peer-to-peer" title="Peer-to-peer">P2P</a> file sharing protocols<sup id="cite_ref-15" class="reference"><a href="#cite_note-15">[15]</a></sup> and in <a href="/wiki/File_sharing" title="File sharing">file sharing</a> applications such as <a href="/wiki/Phex" title="Phex">Phex</a><sup id="cite_ref-16" class="reference"><a href="#cite_note-16">[16]</a></sup>, <a href="/wiki/BearShare" title="BearShare">BearShare</a>, <a href="/wiki/LimeWire" title="LimeWire">LimeWire</a>, <a href="/wiki/Shareaza" title="Shareaza">Shareaza</a>, <a href="/wiki/DCPlusPlus" class="mw-redirect" title="DCPlusPlus">DC++</a><sup id="cite_ref-17" class="reference"><a href="#cite_note-17">[17]</a></sup> and <a href="/wiki/Valknut_(software)" title="Valknut (software)">Valknut</a>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18">[18]</a></sup> 88 </p> 89 <h4><span class="mw-headline" id="Example">Example</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=5" title="Edit section: Example">edit</a><span class="mw-editsection-bracket">]</span></span></h4> 90 <p><a href="/wiki/Base32#RFC_4648_Base32_alphabet" title="Base32">Base32</a>: <code>R5T6Y8UYRYO5SUXGER5NMUOEZ5O6E4BHPP2MRFQ</code> 91 </p><p><a href="/wiki/Uniform_Resource_Name" title="Uniform Resource Name">URN</a>: <code><a rel="nofollow" class="external free" href="urn:tree:tiger:R5T6Y8UYRYO5SUXGER5NMUOEZ5O6E4BHPP2MRFQ">urn:tree:tiger:R5T6Y8UYRYO5SUXGER5NMUOEZ5O6E4BHPP2MRFQ</a></code> 92 </p><p><a href="/wiki/Magnet_URI_scheme" title="Magnet URI scheme">magnet</a>: <code><a rel="nofollow" class="external free" href="magnet:?xt=urn:tree:tiger:R5T6Y8UYRYO5SUXGER5NMUOEZ5O6E4BHPP2MRFQ">magnet:?xt=urn:tree:tiger:R5T6Y8UYRYO5SUXGER5NMUOEZ5O6E4BHPP2MRFQ</a></code> 93 </p> 94 <h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=6" title="Edit section: See also">edit</a><span class="mw-editsection-bracket">]</span></span></h2> 95 <div role="navigation" aria-label="Portals" class="noprint portal plainlist tright" style="margin:0.5em 0 0.5em 1em;border:solid #aaa 1px"> 96 <ul 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<li><a href="/wiki/Distributed_hash_table" title="Distributed hash table">Distributed hash table</a></li> 102 <li><a href="/wiki/Hash_table" title="Hash table">Hash table</a></li> 103 <li><a href="/wiki/Hash_trie" title="Hash trie">Hash trie</a></li> 104 <li><a href="/wiki/Linked_timestamping" title="Linked timestamping">Linked timestamping</a></li> 105 <li><a href="/wiki/Radix_tree" title="Radix tree">Radix tree</a></li></ul> 106 <h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=7" title="Edit section: References">edit</a><span class="mw-editsection-bracket">]</span></span></h2> 107 <div class="reflist columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> 108 <ol class="references"> 109 <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation web">Becker, Georg (2008-07-18). <a rel="nofollow" class="external text" href="http://www.emsec.rub.de/media/crypto/attachments/files/2011/04/becker_1.pdf">"Merkle Signature Schemes, Merkle Trees and Their Cryptanalysis"</a> <span class="cs1-format">(PDF)</span>. Ruhr-Universität Bochum. p. 16<span class="reference-accessdate">. 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Archived from <a rel="nofollow" class="external text" href="http://open-content.net/specs/draft-jchapweske-thex-02.html">the original</a> on 2009-08-03.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Tree+Hash+EXchange+format+%28THEX%29&rft.date=2003-03-04&rft.aulast=Chapweske&rft.aufirst=J.&rft.au=Mohr%2C+G.&rft_id=http%3A%2F%2Fopen-content.net%2Fspecs%2Fdraft-jchapweske-thex-02.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMerkle+tree" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r861714446"/></span> 134 </li> 135 <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://gtk-gnutella.sourceforge.net/doxygen/tigertree_8c.html">"tigertree.c File Reference"</a>. <i>Gtk-Gnutella</i><span class="reference-accessdate">. Retrieved <span class="nowrap">23 September</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Gtk-Gnutella&rft.atitle=tigertree.c+File+Reference&rft_id=http%3A%2F%2Fgtk-gnutella.sourceforge.net%2Fdoxygen%2Ftigertree_8c.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMerkle+tree" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r861714446"/></span> 136 </li> 137 <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://www.symantec.com/security_response/attacksignatures/detail.jsp?asid=21587">"Audit: P2P DirectConnect Application"</a>. <i>Symantec</i><span class="reference-accessdate">. Retrieved <span class="nowrap">23 September</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Symantec&rft.atitle=Audit%3A+P2P+DirectConnect+Application&rft_id=https%3A%2F%2Fwww.symantec.com%2Fsecurity_response%2Fattacksignatures%2Fdetail.jsp%3Fasid%3D21587&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMerkle+tree" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r861714446"/></span> 138 </li> 139 <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><cite class="citation web">Arne Babenhauserheide (7 Jan 2007). <a rel="nofollow" class="external text" href="http://www.phex.org/mambo/content/view/80/2/">"Phex 3.0.0 released"</a>. <i>Phex</i><span class="reference-accessdate">. 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Retrieved <span class="nowrap">23 September</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GTK-Gnutella&rft.atitle=Development&rft_id=http%3A%2F%2Fgtk-gnutella.sourceforge.net%2Fen%2F%3Fpage%3Ddevel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMerkle+tree" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r861714446"/></span> 144 </li> 145 </ol></div> 146 <h2><span class="mw-headline" id="Further_reading">Further reading</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=8" title="Edit section: Further reading">edit</a><span class="mw-editsection-bracket">]</span></span></h2> 147 <ul><li><span><a rel="nofollow" class="external text" href="//www.google.com/patents/US4309569">Merkle tree patent 4,309,569</a></span> –  explains both the hash tree structure and the use of it to handle many one-time signatures</li> 148 <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080316033726/http://www.open-content.net/specs/draft-jchapweske-thex-02.html">Tree Hash EXchange format (THEX)</a> –  a detailed description of Tiger trees</li></ul> 149 <h2><span class="mw-headline" id="External_links">External links</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Merkle_tree&action=edit&section=9" title="Edit section: External links">edit</a><span class="mw-editsection-bracket">]</span></span></h2> 150 <div id="section_SpokenWikipedia" class="infobox sisterproject plainlinks haudio"><div style="text-align: center; white-space:nowrap"><b>Listen to this article</b> (<a href="/wiki/File:En-Merkle_Tree.ogg" title="File:En-Merkle Tree.ogg">info/dl</a>) 151 <div class="center"><div class="floatnone"><div class="mediaContainer" style="width:200px"><audio id="mwe_player_0" controls="" preload="none" style="width:200px" class="kskin" data-durationhint="285.27437641723" data-startoffset="0" data-mwtitle="En-Merkle_Tree.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/5/5b/En-Merkle_Tree.ogg" type="audio/ogg; codecs="vorbis"" data-title="Original Ogg file (61 kbps)" data-shorttitle="Ogg source" data-width="0" data-height="0" data-bandwidth="60800" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5b/En-Merkle_Tree.ogg/En-Merkle_Tree.ogg.mp3" type="audio/mpeg" data-title="MP3" data-shorttitle="MP3" data-transcodekey="mp3" data-width="0" data-height="0" data-bandwidth="127608" /></audio></div></div></div> 152 </div> 153 <p><br /> 154 </p> 155 <div style="float: left; margin-left: 5px;"><div class="floatnone"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/45px-Sound-icon.svg.png" title="Spoken Wikipedia" width="45" height="34" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/68px-Sound-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/90px-Sound-icon.svg.png 2x" data-file-width="128" data-file-height="96" /></div></div> 156 <div style="font-size: xx-small; line-height: 1.6em; margin-left: 60px;">This audio file was created from a revision of the article "<span class="fn">Merkle tree</span>" dated 2013-09-17, and does not reflect subsequent edits to the article. (<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help">Audio help</a>)</div> 157 <div style="text-align: center; clear: both"><b><a href="/wiki/Wikipedia:Spoken_articles" title="Wikipedia:Spoken articles">More spoken articles</a></b></div> 158 </div> 159 <ul><li><a rel="nofollow" class="external text" href="https://github.com/IAIK/merkle-tree">A C implementation of a dynamically re-sizeable binary SHA-256 hash tree (Merkle Tree)</a></li> 160 <li><a rel="nofollow" class="external text" href="https://github.com/richpl/merkletree">Merkle Tree implementation in Java</a></li> 161 <li><a rel="nofollow" class="external text" href="https://www.codeproject.com/articles/9336/thexcs-tth-tiger-tree-hash-maker-in-c">Tiger Tree Hash (TTH) source code in C#</a>, by Gil Schmidt</li> 162 <li><a rel="nofollow" class="external text" href="http://sourceforge.net/projects/tigertree/">Tiger Tree Hash (TTH) implementations in C and Java</a></li> 163 <li><a rel="nofollow" class="external text" href="http://rhash.sourceforge.net/">RHash</a>, an open source command-line tool, which can calculate TTH and magnet links with TTH</li></ul> 164 <div role="navigation" class="navbox" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks collapsible collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Template:Cryptography_navbox" title="Template:Cryptography navbox"><abbr title="View this template" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">v</abbr></a></li><li class="nv-talk"><a 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title="Cryptanalysis">Cryptanalysis</a></li> 167 <li><a href="/wiki/Outline_of_cryptography" title="Outline of cryptography">Outline of cryptography</a></li></ul> 168 </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> 169 <ul><li><a href="/wiki/Symmetric-key_algorithm" title="Symmetric-key algorithm">Symmetric-key algorithm</a></li> 170 <li><a href="/wiki/Block_cipher" title="Block cipher">Block cipher</a></li> 171 <li><a href="/wiki/Stream_cipher" title="Stream cipher">Stream cipher</a></li> 172 <li><a href="/wiki/Public-key_cryptography" title="Public-key cryptography">Public-key cryptography</a></li> 173 <li><a href="/wiki/Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li> 174 <li><a href="/wiki/Message_authentication_code" title="Message authentication code">Message authentication code</a></li> 175 <li><a 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title="Portal" width="16" height="14" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/fd/Portal-puzzle.svg/24px-Portal-puzzle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/fd/Portal-puzzle.svg/32px-Portal-puzzle.svg.png 2x" data-file-width="32" data-file-height="28" /> <a href="/wiki/Portal:Cryptography" title="Portal:Cryptography">Portal</a></li> 180 <li><img alt="WikiProject" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" title="WikiProject" width="16" height="16" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /> <a href="/wiki/Wikipedia:WikiProject_Cryptography" title="Wikipedia:WikiProject Cryptography">WikiProject</a></li></ul> 181 </div></td></tr></tbody></table><div></div></td></tr></tbody></table></div> 182 <div role="navigation" class="navbox" aria-labelledby="Tree_data_structures" style="padding:3px"><table class="nowraplinks collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Template:CS_trees" title="Template:CS trees"><abbr title="View this template" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:CS_trees" title="Template talk:CS trees"><abbr title="Discuss this template" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="//en.wikipedia.org/w/index.php?title=Template:CS_trees&action=edit"><abbr title="Edit this template" 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title="AA tree">AA</a></li> 186 <li><a href="/wiki/(a,b)-tree" title="(a,b)-tree">(a,b)</a></li> 187 <li><a href="/wiki/AVL_tree" title="AVL tree">AVL</a></li> 188 <li><a href="/wiki/B-tree" title="B-tree">B</a></li> 189 <li><a href="/wiki/B%2B_tree" title="B+ tree">B+</a></li> 190 <li><a href="/wiki/B*-tree" class="mw-redirect" title="B*-tree">B*</a></li> 191 <li><a href="/wiki/Bx-tree" title="Bx-tree">B<sup>x</sup></a></li> 192 <li>(<a href="/wiki/Optimal_binary_search_tree" title="Optimal binary search tree">Optimal</a>) <a href="/wiki/Binary_search_tree" title="Binary search tree">Binary search</a></li> 193 <li><a href="/wiki/Dancing_tree" title="Dancing tree">Dancing</a></li> 194 <li><a href="/wiki/HTree" title="HTree">HTree</a></li> 195 <li><a href="/wiki/Interval_tree" title="Interval tree">Interval</a></li> 196 <li><a href="/wiki/Order_statistic_tree" title="Order statistic tree">Order statistic</a></li> 197 <li>(<a href="/wiki/Left-leaning_red%E2%80%93black_tree" title="Left-leaning red–black tree">Left-leaning</a>) <a href="/wiki/Red%E2%80%93black_tree" title="Red–black tree">Red-black</a></li> 198 <li><a href="/wiki/Scapegoat_tree" title="Scapegoat tree">Scapegoat</a></li> 199 <li><a href="/wiki/Splay_tree" title="Splay tree">Splay</a></li> 200 <li><a href="/wiki/T-tree" title="T-tree">T</a></li> 201 <li><a href="/wiki/Treap" title="Treap">Treap</a></li> 202 <li><a href="/wiki/UB-tree" title="UB-tree">UB</a></li> 203 <li><a href="/wiki/Weight-balanced_tree" title="Weight-balanced tree">Weight-balanced</a></li></ul> 204 </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Heap_(data_structure)" title="Heap (data structure)">Heaps</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> 205 <ul><li><a href="/wiki/Binary_heap" title="Binary heap">Binary</a></li> 206 <li><a href="/wiki/Binomial_heap" title="Binomial heap">Binomial</a></li> 207 <li><a href="/wiki/Brodal_queue" title="Brodal queue">Brodal</a></li> 208 <li><a href="/wiki/Fibonacci_heap" title="Fibonacci heap">Fibonacci</a></li> 209 <li><a href="/wiki/Leftist_tree" title="Leftist tree">Leftist</a></li> 210 <li><a href="/wiki/Pairing_heap" title="Pairing heap">Pairing</a></li> 211 <li><a href="/wiki/Skew_heap" title="Skew heap">Skew</a></li> 212 <li><a href="/wiki/Van_Emde_Boas_tree" title="Van Emde Boas tree">Van Emde Boas</a></li> 213 <li><a href="/wiki/Weak_heap" title="Weak heap">Weak</a></li></ul> 214 </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Trie" title="Trie">Tries</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> 215 <ul><li><a href="/wiki/Ctrie" title="Ctrie">Ctrie</a></li> 216 <li><a href="/wiki/C-trie" title="C-trie">C-trie (compressed ADT)</a></li> 217 <li><a href="/wiki/Hash_tree_(persistent_data_structure)" title="Hash tree (persistent data structure)">Hash</a></li> 218 <li><a href="/wiki/Radix_tree" title="Radix tree">Radix</a></li> 219 <li><a href="/wiki/Suffix_tree" title="Suffix tree">Suffix</a></li> 220 <li><a href="/wiki/Ternary_search_tree" title="Ternary search tree">Ternary search</a></li> 221 <li><a href="/wiki/X-fast_trie" title="X-fast trie">X-fast</a></li> 222 <li><a href="/wiki/Y-fast_trie" title="Y-fast trie">Y-fast</a></li></ul> 223 </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Spatial_index" class="mw-redirect" title="Spatial index">Spatial</a> data partitioning trees</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> 224 <ul><li><a href="/wiki/Ball_tree" title="Ball tree">Ball</a></li> 225 <li><a href="/wiki/BK-tree" title="BK-tree">BK</a></li> 226 <li><a href="/wiki/BSP_tree" class="mw-redirect" title="BSP tree">BSP</a></li> 227 <li><a href="/wiki/Cartesian_tree" title="Cartesian tree">Cartesian</a></li> 228 <li><a href="/wiki/Hilbert_R-tree" title="Hilbert R-tree">Hilbert R</a></li> 229 <li><a href="/wiki/K-d_tree" title="K-d tree"><i>k</i>-d</a> (<a href="/wiki/Implicit_k-d_tree" title="Implicit k-d tree">implicit <i>k</i>-d</a>)</li> 230 <li><a href="/wiki/M-tree" title="M-tree">M</a></li> 231 <li><a href="/wiki/Metric_tree" title="Metric tree">Metric</a></li> 232 <li><a href="/wiki/MVP_tree" class="mw-redirect" title="MVP tree">MVP</a></li> 233 <li><a href="/wiki/Octree" title="Octree">Octree</a></li> 234 <li><a href="/wiki/Priority_R-tree" title="Priority R-tree">Priority R</a></li> 235 <li><a href="/wiki/Quadtree" title="Quadtree">Quad</a></li> 236 <li><a href="/wiki/R-tree" title="R-tree">R</a></li> 237 <li><a href="/wiki/R%2B_tree" title="R+ tree">R+</a></li> 238 <li><a href="/wiki/R*_tree" title="R* tree">R*</a></li> 239 <li><a href="/wiki/Segment_tree" title="Segment tree">Segment</a></li> 240 <li><a href="/wiki/Vantage-point_tree" title="Vantage-point tree">VP</a></li> 241 <li><a href="/wiki/X-tree" title="X-tree">X</a></li></ul> 242 </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other trees</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> 243 <ul><li><a href="/wiki/Cover_tree" title="Cover tree">Cover</a></li> 244 <li><a href="/wiki/Exponential_tree" title="Exponential tree">Exponential</a></li> 245 <li><a href="/wiki/Fenwick_tree" title="Fenwick tree">Fenwick</a></li> 246 <li><a href="/wiki/Finger_tree" title="Finger tree">Finger</a></li> 247 <li><a href="/wiki/Fractal_tree_index" title="Fractal tree index">Fractal tree index</a></li> 248 <li><a href="/wiki/Fusion_tree" title="Fusion tree">Fusion</a></li> 249 <li><a href="/wiki/Hash_calendar" title="Hash calendar">Hash calendar</a></li> 250 <li><a href="/wiki/IDistance" title="IDistance">iDistance</a></li> 251 <li><a href="/wiki/K-ary_tree" title="K-ary tree">K-ary</a></li> 252 <li><a href="/wiki/Left-child_right-sibling_binary_tree" title="Left-child right-sibling binary tree">Left-child right-sibling</a></li> 253 <li><a href="/wiki/Link/cut_tree" title="Link/cut tree">Link/cut</a></li> 254 <li><a href="/wiki/Log-structured_merge-tree" title="Log-structured merge-tree">Log-structured merge</a></li> 255 <li><a class="mw-selflink selflink">Merkle</a></li> 256 <li><a href="/wiki/PQ_tree" title="PQ tree">PQ</a></li> 257 <li><a href="/wiki/Range_tree" title="Range tree">Range</a></li> 258 <li><a href="/wiki/SPQR_tree" title="SPQR tree">SPQR</a></li> 259 <li><a href="/wiki/Top_tree" title="Top tree">Top</a></li></ul> 260 </div></td></tr></tbody></table></div> 261 262 <!-- 263 NewPP limit report 264 Parsed by mw1330 265 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