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class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Lyra2</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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.mbox-text{padding:0!important;margin:0!important}.mw-parser-output .compact-ambox .ambox .mbox-text-span{display:list-item;line-height:1.5em;list-style-type:disc}body.skin-minerva .mw-parser-output .multiple-issues-text>.mw-collapsible-toggle,.mw-parser-output .compact-ambox .ambox .mbox-image,.mw-parser-output .compact-ambox .ambox .mbox-imageright,.mw-parser-output .compact-ambox .ambox .mbox-empty-cell,.mw-parser-output .compact-ambox .hide-when-compact{display:none}</style><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, 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alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>contains <a href="/wiki/Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_soapbox_or_means_of_promotion" title="Wikipedia:What Wikipedia is not">promotional content</a></b>.<span class="hide-when-compact"> Please help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Lyra2&action=edit">improve it</a> by removing <a href="/wiki/Wikipedia:Spam" title="Wikipedia:Spam">promotional language</a> and inappropriate <a href="/wiki/Wikipedia:External_links#Advertising_and_conflicts_of_interest" title="Wikipedia:External links">external links</a>, and by adding encyclopedic text written from a <a href="/wiki/Wikipedia:Neutral_point_of_view" title="Wikipedia:Neutral point of view">neutral point of view</a>.</span> <span class="date-container"><i>(<span class="date">October 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Primary_sources plainlinks metadata ambox ambox-content ambox-Primary_sources" 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 excessively on <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">references</a> to <a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research">primary sources</a></b>.<span class="hide-when-compact"> Please improve this article by adding <a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research">secondary or tertiary 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=%22Lyra2%22">"Lyra2"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Lyra2%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Lyra2%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=%22Lyra2%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Lyra2%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Lyra2%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">October 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" 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 alt="" 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>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Lyra2" title="Special:EditPage/Lyra2">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<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=%22Lyra2%22">"Lyra2"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Lyra2%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Lyra2%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=%22Lyra2%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Lyra2%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Lyra2%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">October 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p><b>Lyra2</b> is a <a href="/wiki/Password_hashing" class="mw-redirect" title="Password hashing">password hashing scheme</a> (PHS) that can also function as a <a href="/wiki/Key_derivation_function" title="Key derivation function">key derivation function</a> (KDF). It gained recognition during the <a href="/wiki/Password_Hashing_Competition" title="Password Hashing Competition">Password Hashing Competition</a> in July 2015,<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> which was won by <a href="/wiki/Argon2" title="Argon2">Argon2</a>. It is also used in proof-of-work algorithms such as Lyra2REv2,<sup id="cite_ref-Lyra2REv2_2-0" class="reference"><a href="#cite_note-Lyra2REv2-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> adopted by Vertcoin<sup id="cite_ref-vertcoin_3-0" class="reference"><a href="#cite_note-vertcoin-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and MonaCoin,<sup id="cite_ref-MonaCoin_4-0" class="reference"><a href="#cite_note-MonaCoin-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> among other cryptocurrencies.<sup id="cite_ref-lyra2ToC_5-0" class="reference"><a href="#cite_note-lyra2ToC-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Lyra2 was designed by Marcos A. Simplicio Jr., Leonardo C. Almeida, Ewerton R. Andrade, Paulo C. F. dos Santos, and <a href="/wiki/Paulo_S._L._M._Barreto" title="Paulo S. L. M. Barreto">Paulo S. L. M. Barreto</a> from <a href="/wiki/Polytechnic_School_of_the_University_of_S%C3%A3o_Paulo" title="Polytechnic School of the University of São Paulo">Escola Politécnica da Universidade de São Paulo</a>.<sup id="cite_ref-:0_6-0" class="reference"><a href="#cite_note-:0-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> It is based on Lyra,<sup id="cite_ref-:1_7-0" class="reference"><a href="#cite_note-:1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:8_8-0" class="reference"><a href="#cite_note-:8-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> which had been created by the same team. Lyra2 includes: </p> <ul><li>The ability to configure the desired amount of memory, processing time, and parallelism for the algorithm.</li> <li>High memory usage with processing time similar to <a href="/wiki/Scrypt" title="Scrypt">scrypt</a>.</li></ul> <p>In addition, it:<sup id="cite_ref-lyra2ToC2_9-0" class="reference"><a href="#cite_note-lyra2ToC2-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Provides higher security against time-memory trade-offs.</li> <li>Allows legitimate users to better benefit from the parallelism capabilities of their own platforms.</li> <li>Increases the costs of creating dedicated hardware to attack the algorithm.</li> <li>Balances resistance against side-channel threats and attacks using cheaper, slower storage devices.</li></ul> <p>Lyra2 is released into the <a href="/wiki/Public_domain" title="Public domain">public domain</a>]<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. (September 2024)">citation needed</span></a></i>]</sup>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Design">Design</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lyra2&action=edit&section=1" title="Edit section: Design"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As any PHS, Lyra2 takes as input a <a href="/wiki/Salt_(cryptography)" title="Salt (cryptography)">salt</a> and a password, creating a <a href="/wiki/Pseudorandomness" title="Pseudorandomness">pseudorandom</a> output that can then be used as key material for cryptographic algorithms or as an <a href="/wiki/Authentication_protocol" title="Authentication protocol">authentication</a> string.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (December 2019)">failed verification</span></a></i>]</sup><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. (December 2019)">citation needed</span></a></i>]</sup> </p><p>Internally, the scheme's memory is organized as a matrix that is expected to remain in memory during the whole password hashing process. Since its cells are iteratively read and written, discarding a cell for saving memory leads to the need of recomputing it whenever it is accessed once again, until the point it was last modified.<sup id="cite_ref-lyra2ToC_5-1" class="reference"><a href="#cite_note-lyra2ToC-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>The construction and visitation of the matrix is done using a stateful combination of the absorbing, squeezing and duplexing operations of the underlying <a href="/wiki/Sponge_function" title="Sponge function">sponge</a> (i.e., its internal state is never reset to zero), ensuring the sequential nature of the whole process. </p><p>Also, the number of times the matrix's cells are revisited after initialization is defined by the user, allowing Lyra2's execution time to be fine-tuned according to the target platform's resources. </p> <div class="mw-heading mw-heading3"><h3 id="Inputs">Inputs</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lyra2&action=edit&section=2" title="Edit section: Inputs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">password</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">salt</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">t_cost</span> - execution time</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">m_cost</span> - memory required</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">outlen</span></li></ul> <p>The algorithm additionally enables parameterization in terms of:<sup id="cite_ref-lyra2RefGuide_11-0" class="reference"><a href="#cite_note-lyra2RefGuide-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <ul><li>degree of parallelism (number of <a href="/wiki/Thread_(computing)" title="Thread (computing)">threads</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span>)</li> <li>underlying permutation function (can be seen as the main cryptographic primitive)</li> <li>number of blocks used by the underlying permutation function (<i>bitrate</i>)</li> <li>number of rounds performed for the underlying permutation function (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>)</li> <li>number of bits to be used in rotations (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span>)</li> <li>output length(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>κ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \kappa }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54ddec2e922c5caea4e47d04feef86e782dc8e6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:1.676ex;" alt="{\displaystyle \kappa }"></span>)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Functions/symbols"><span id="Functions.2Fsymbols"></span>Functions/symbols</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lyra2&action=edit&section=3" title="Edit section: Functions/symbols"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt><code>||</code></dt> <dd>Concatenate two strings</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">^</code></dt> <dd>Bitwise XOR</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">[+]</code></dt> <dd>Word wise add operation (i.e., ignoring carries between words)</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">%</code></dt> <dd>Modulus</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">W</code></dt> <dd>The target machine's word size (usually, 32 or 64)</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">omega</code></dt> <dd>Number of bits to be used in rotations (recommended: a multiple of the machine's word size, W)</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">>>></code></dt> <dd>Right rotation</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">rho</code></dt> <dd>Number of rounds for reduced squeeze or duplexing operations</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">blen</code></dt> <dd>Sponge's block size in bytes</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">H or H_i</code></dt> <dd>Sponge with block size blen (in bytes) and underlying permutation f</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">H.absorb(input)</code></dt> <dd>Sponge's absorb operation on input</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">H.squeeze(len)</code></dt> <dd>Sponge's squeeze operation of len bytes</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">H.squeeze_{rho}(len)</code></dt> <dd>Sponge's squeeze operation of len bytes using rho rounds of f</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">H.duplexing(input,len)</code></dt> <dd>Sponge's duplexing operation on input, producing len bytes</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">H.duplexing_{rho}(input,len)</code></dt> <dd>Sponge's duplexing operation on input, using rho rounds of f, producing len bytes</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">pad(string)</code></dt> <dd>Pads a string to a multiple of blen bytes (padding rule: 10*1)</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">lsw(input)</code></dt> <dd>The least significant word of input</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">len(string)</code></dt> <dd>Length of a string, in bytes</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">syncThreads()</code></dt> <dd>Synchronize parallel threads</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">swap(input1,input2)</code></dt> <dd>Swap the value of two inputs</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">C</code></dt> <dd>Number of columns on the memory matrix (usually, 64, 128, 256, 512 or 1024)</dd> <dt><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">P</code></dt> <dd>Degree of parallelism (<code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">P >= 1</code> and <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">(m_cost/2) % P == 0</code>)</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Algorithm_without_parallelism">Algorithm without parallelism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lyra2&action=edit&section=4" title="Edit section: Algorithm without parallelism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1195917819">.mw-parser-output .pre-borderless{border:none}</style><pre class="pre">** Bootstrapping phase: Initializes the sponge's state and local variables # Byte representation of input parameters (others can be added) params = outlen || len(password) || len(salt) || t_cost || m_cost || C # Initializes the sponge's state (after that, password can be overwritten) H.absorb( pad(password || salt || params) ) # Initializes visitation step, window and first rows that will feed gap = 1 stp = 1 wnd = 2 sqrt = 2 prev0 = 2 row1 = 1 prev1 = 0 ** Setup phase: Initializes a (m_cost x C) memory matrix, its cells having blen-byte cells # Initializes M[0], M[1] and M[2] for col = 0 to C-1 M[0][C-1-col] = H.squeeze_{rho}(blen) for col = 0 to C-1 M[1][C-1-col] = H.duplexing_{rho}( M[0][col], blen) for col = 0 to C-1 M[2][C-1-col] = H.duplexing_{rho}( M[1][col], blen) # Filling Loop: initializes remainder rows for row0 = 3 to m_cost-1 # Columns Loop: M[row0] is initialized and M[row1] is updated for col = 0 to C-1 rand = H.duplexing_{rho}( M[row1][col] [+] M[prev0][col] [+] M[prev1][col], blen) M[row0][C-1-col] = M[prev0][col] ^ rand M[row1][col] = M[row1][col] ^ ( rand >>> omega ) # Rows to be revisited in next loop prev0 = row0 prev1 = row1 row1 = (row1 + stp) % wnd # Window fully revisited if (row1 = 0) # Doubles window and adjusts step wnd = 2 * wnd stp = sqrt + gap gap = -gap # Doubles sqrt every other iteration if (gap = -1) sqrt = 2 * sqrt ** Wandering phase: Iteratively overwrites pseudorandom cells of the memory matrix # Visitation Loop: (2 * m_cost * t_cost) rows revisited in pseudorandom fashion for wCount = 0 to ( (m_cost * t_cost) - 1) # Picks pseudorandom rows row0 = lsw(rand) % m_cost row1 = lsw( rand >>> omega ) % m_cost # Columns Loop: updates both M[row0] and M[row1] for col = 0 to C-1 # Picks pseudorandom columns col0 = lsw( ( rand >>> omega ) >>> omega ) % C col1 = lsw( ( ( rand >>> omega ) >>> omega ) >>> omega ) % C rand = H.duplexing_{rho}( M[row0][col] [+] M[row1][col] [+] M[prev0][col0] [+] M[prev1][col1], blen) M[row0][col] = M[row0][col] ^ rand M[row1][col] = M[row1][col] ^ ( rand >>> omega ) # Next iteration revisits most recently updated rows prev0 = row0 prev1 = row1 ** Wrap-up phase: output computation # Absorbs a final column with a full-round sponge H.absorb( M[row0][0] ) # Squeezes outlen bits with a full-round sponge output = H.squeeze(outlen) # Provides outlen-long bitstring as output return output</pre> <div class="mw-heading mw-heading3"><h3 id="Algorithm_with_parallelism">Algorithm with parallelism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lyra2&action=edit&section=5" title="Edit section: Algorithm with parallelism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <pre>for each i in [0..P] ** Bootstrapping phase: Initializes the sponge's state and local variables # Byte representation of input parameters (others can be added) params = outlen || len(password) || len(salt) || t_cost || m_cost || C || P || i # Initializes the sponge's state (after that, password can be overwritten) H_i.absorb( pad(password || salt || params) ) # Initializes visitation step, window and first rows that will feed gap = 1 stp = 1 wnd = 2 sqrt = 2 sync = 4 j = i prev0 = 2 rowP = 1 prevP = 0 ** Setup phase: Initializes a (m_cost x C) memory matrix, its cells having blen-byte cells # Initializes M_i[0], M_i[1] and M_i[2] for col = 0 to C-1 M_i[0][C-1-col] = H_i.squeeze_{rho}(blen) for col = 0 to C-1 M_i[1][C-1-col] = H_i.duplexing_{rho}( M_i[0][col], blen) for col = 0 to C-1 M_i[2][C-1-col] = H_i.duplexing_{rho}( M_i[1][col], blen) # Filling Loop: initializes remainder rows for row0 = 3 to ( (m_cost / P) - 1 ) # Columns Loop: M_i[row0] is initialized and M_j[row1] is updated for col = 0 to C-1 rand = H_i.duplexing_{rho}( M_j[rowP][col] [+] M_i[prev0][col] [+] M_j[prevP][col], blen) M_i[row0][C-1-col] = M_i[prev0][col] ^ rand M_j[rowP][col] = M_j[rowP][col] ^ ( rand >>> omega ) # Rows to be revisited in next loop prev0 = row0 prevP = rowP rowP = (rowP + stp) % wnd # Window fully revisited if (rowP = 0) # Doubles window and adjusts step wnd = 2 * wnd stp = sqrt + gap gap = -gap # Doubles sqrt every other iteration if (gap = -1) sqrt = 2 * sqrt # Synchronize point if (row0 = sync) sync = sync + (sqrt / 2) j = (j + 1) % P syncThreads() syncThreads() ** Wandering phase: Iteratively overwrites pseudorandom cells of the memory matrix wnd = m_cost / (2 * P) sync = sqrt off0 = 0 offP = wnd # Visitation Loop: (2 * m_cost * t_cost / P) rows revisited in pseudorandom fashion for wCount = 0 to ( ( (m_cost * t_cost) / P) - 1) # Picks pseudorandom rows and slices (j) row0 = off0 + (lsw(rand) % wnd) rowP = offP + (lsw( rand >>> omega ) % wnd) j = lsw( ( rand >>> omega ) >>> omega ) % P # Columns Loop: update M_i[row0] for col = 0 to C-1 # Picks pseudorandom column col0 = lsw( ( ( rand >>> omega ) >>> omega ) >>> omega ) % C rand = H_i.duplexing_{rho}( M_i[row0][col] [+] M_i[prev0][col0] [+] M_j[rowP][col], blen) M_i[row0][col] = M_i[row0][col] ^ rand # Next iteration revisits most recently updated rows prev0 = row0 # Synchronize point if (wCount = sync) sync = sync + sqrt swap(off0,offP) syncThreads() syncThreads() ** Wrap-up phase: output computation # Absorbs a final column with a full-round sponge H_i.absorb( M_i[row0][0] ) # Squeezes outlen bits with a full-round sponge output_i = H_i.squeeze(outlen) # Provides outlen-long bitstring as output return output_0 ^ ... ^ output_{P-1} </pre> <div class="mw-heading mw-heading2"><h2 id="Security_analysis">Security analysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lyra2&action=edit&section=6" title="Edit section: Security analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Against Lyra2, the processing cost of attacks using <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/2^{n+2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/2^{n+2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccfe1012d970ce486b4269c9707dd1fc51eb49d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.806ex; height:3.176ex;" alt="{\displaystyle 1/2^{n+2}}"></span> of the amount of memory employed by a legitimate user is expected to be between <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(2^{2nT}R^{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mi>T</mi> </mrow> </msup> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(2^{2nT}R^{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a3037a64c1b2e741eb20c9390daca59d060fb9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.761ex; height:3.176ex;" alt="{\displaystyle O(2^{2nT}R^{3})}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(2^{2nT}R^{n+2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mi>T</mi> </mrow> </msup> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(2^{2nT}R^{n+2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14834bb704b2f8aec5aa2f56447b8d59b53dcc04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.026ex; height:3.176ex;" alt="{\displaystyle O(2^{2nT}R^{n+2})}"></span>, the latter being a better estimate for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\gg 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≫</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\gg 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f619e045ce20cf891dbdb9b57042c22ea5161d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.171ex; height:2.176ex;" alt="{\displaystyle n\gg 1}"></span>, instead of the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(R)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(R)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78dcf1dfcb9e7e9d62c1a9bab49329b4bdff1f9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.347ex; height:2.843ex;" alt="{\displaystyle O(R)}"></span> achieved when the amount of memory is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(R)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(R)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78dcf1dfcb9e7e9d62c1a9bab49329b4bdff1f9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.347ex; height:2.843ex;" alt="{\displaystyle O(R)}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> is a user-defined parameter to define a processing time. </p><p>This compares well to <a href="/wiki/Scrypt" title="Scrypt">Scrypt</a>, which displays a cost of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(R^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(R^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71ffc6a7e3a79ead67ccf93b771eaa18aa6ce78a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.401ex; height:3.176ex;" alt="{\displaystyle O(R^{2})}"></span> when the memory usage is high<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e66384bc40452c5452f33563fe0e27e803b0cc21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.745ex; height:2.843ex;" alt="{\displaystyle O(1)}"></span>,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> and with other solutions in the literature, for which the results are usually <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(R^{T+1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(R^{T+1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d29cb62f9ae042947b48f575b569eac6074794a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.836ex; height:3.176ex;" alt="{\displaystyle O(R^{T+1})}"></span>.<sup id="cite_ref-:1_7-1" class="reference"><a href="#cite_note-:1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>Nonetheless, in practice these solutions usually involve a value of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> (memory usage) lower than those attained with the Lyra2 for the same processing time.<sup id="cite_ref-:3_16-0" class="reference"><a href="#cite_note-:3-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_17-0" class="reference"><a href="#cite_note-:4-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:5_18-0" class="reference"><a href="#cite_note-:5-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:6_19-0" class="reference"><a href="#cite_note-:6-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:7_20-0" class="reference"><a href="#cite_note-:7-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Performance">Performance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lyra2&action=edit&section=7" title="Edit section: Performance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Lyra2-Bench.pdf" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Lyra2-Bench.pdf/page1-1050px-Lyra2-Bench.pdf.jpg" decoding="async" width="1050" height="498" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Lyra2-Bench.pdf/page1-1575px-Lyra2-Bench.pdf.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Lyra2-Bench.pdf/page1-2100px-Lyra2-Bench.pdf.jpg 2x" data-file-width="7154" data-file-height="3393" /></a><figcaption>Performance of SSE-enabled Lyra2, for C = 256, ρ = 1, p = 1, and different T and R settings, compared with SSE-enabled <a href="/wiki/Scrypt" title="Scrypt">Scrypt</a> and memory-hard PHC finalists with minimum parameters.</figcaption></figure> <p>The processing time obtained with an SSE single-core implementation of Lyra2 is illustrated in the hereby shown figure. This figure was extracted from,<sup id="cite_ref-lyra2ToC2_9-1" class="reference"><a href="#cite_note-lyra2ToC2-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and is very similar to, third-party benchmarks performed during the PHC context.<sup id="cite_ref-:3_16-1" class="reference"><a href="#cite_note-:3-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_17-1" class="reference"><a href="#cite_note-:4-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:5_18-1" class="reference"><a href="#cite_note-:5-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:6_19-1" class="reference"><a href="#cite_note-:6-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:7_20-1" class="reference"><a href="#cite_note-:7-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>The results depicted correspond to the average execution time of Lyra2 configured with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C=256}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mn>256</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C=256}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b74a89bd6beece22634f3893748477be9d2188e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.352ex; height:2.176ex;" alt="{\displaystyle C=256}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho =1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho =1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6be1a852fccaddc2582e41b89a02b41b1ff4ffe7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.463ex; height:2.676ex;" alt="{\displaystyle \rho =1}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=768}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mn>768</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=768}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/038ca70988a61a6b427b131fb1efd893aa792099" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.583ex; height:2.176ex;" alt="{\displaystyle b=768}"></span> bits (i.e., the inner state has 256 bits), and different <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> settings, giving an overall idea of possible combinations of parameters and the corresponding usage of resources. </p><p>As shown in this figure, Lyra2 is able to execute in: less than 1 s while using up to 400 MB (with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=2^{14}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>14</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=2^{14}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20de54765cf8d74740e8150b07e6e996c91e0d9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.901ex; height:2.676ex;" alt="{\displaystyle R=2^{14}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T=5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14afc79da2d59a46580ab074c9f9eff341b4b8f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.897ex; height:2.176ex;" alt="{\displaystyle T=5}"></span>) or up to 1 GB of memory (with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R\approx 4.2\cdot 10^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>≈</mo> <mn>4.2</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R\approx 4.2\cdot 10^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8439c4843945ac0a6fdbd51c1667b80d86df64d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.892ex; height:2.676ex;" alt="{\displaystyle R\approx 4.2\cdot 10^{4}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6664a95bcd54fdd09a9178e106bd05b1c849856" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.897ex; height:2.176ex;" alt="{\displaystyle T=1}"></span>); or in less than 5 s with 1.6 GB (with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=2^{16}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>16</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=2^{16}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e88ac5e5d100e072a4770da7116e8b27c49f149b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.901ex; height:2.676ex;" alt="{\displaystyle R=2^{16}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T=6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mn>6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e5a757f1bdecd5b3cc5e3edff01b69491c30733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.897ex; height:2.176ex;" alt="{\displaystyle T=6}"></span>). </p><p>All tests were performed on an <a href="/wiki/List_of_Intel_Xeon_microprocessors" class="mw-redirect" title="List of Intel Xeon microprocessors">Intel Xeon E5-2430</a> (2.20 GHz with 12 Cores, 64 bits) equipped with 48 GB of <a href="/wiki/Dynamic_random-access_memory" title="Dynamic random-access memory">DRAM</a>, running <a href="/wiki/Ubuntu_(operating_system)" class="mw-redirect" title="Ubuntu (operating system)">Ubuntu</a> 14.04 LTS 64 bits, and the source code was compiled using <a href="/wiki/GNU_Compiler_Collection" title="GNU Compiler Collection">GCC</a> 4.9.2.<sup id="cite_ref-lyra2ToC2_9-2" class="reference"><a href="#cite_note-lyra2ToC2-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Extensions">Extensions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lyra2&action=edit&section=8" title="Edit section: Extensions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lyra offers two main extensions:<sup id="cite_ref-lyra2RefGuide_11-1" class="reference"><a href="#cite_note-lyra2RefGuide-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <ul><li>**Lyra2-δ**: Provides more control over the algorithm's bandwidth usage.</li> <li>**Lyra2<i>p</i>**: Takes advantage of <a href="/wiki/Parallel_computing" title="Parallel computing">parallelism</a> capabilities on the user's platform.</li></ul> <p><br /> </p> <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=Lyra2&action=edit&section=9" 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 mw-references-columns"><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"><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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://password-hashing.net/">"Password Hashing Competition"</a>. <i>password-hashing.net</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=password-hashing.net&rft.atitle=Password+Hashing+Competition&rft_id=https%3A%2F%2Fpassword-hashing.net%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-Lyra2REv2-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lyra2REv2_2-0">^</a></b></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://en.bitcoinwiki.org/wiki/Lyra2REv2">"Lyra2REv2"</a>. <i>eprint.iacr.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=eprint.iacr.org&rft.atitle=Lyra2REv2&rft_id=https%3A%2F%2Fen.bitcoinwiki.org%2Fwiki%2FLyra2REv2&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-vertcoin-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-vertcoin_3-0">^</a></b></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="http://vertcoin.org">"Vertcoin"</a>. <i>vertcoin.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-10-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=vertcoin.org&rft.atitle=Vertcoin&rft_id=http%3A%2F%2Fvertcoin.org&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-MonaCoin-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-MonaCoin_4-0">^</a></b></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://monacoin.org">"MonaCoin"</a>. <i>monacoin.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-10-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=monacoin.org&rft.atitle=MonaCoin&rft_id=https%3A%2F%2Fmonacoin.org&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-lyra2ToC-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-lyra2ToC_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-lyra2ToC_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="CITEREFvan_BeirendonckTrudeauGiardBalatsoukas-Stimming2019" class="citation conference cs1">van Beirendonck, M.; Trudeau, L.; Giard, P.; Balatsoukas-Stimming, A. (2019-05-29). <i>A Lyra2 FPGA Core for Lyra2REv2-Based Cryptocurrencies</i>. IEEE International Symposium on Circuits and Systems (ISCAS). Sapporo, Japan: IEEE. pp. 1–5. <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/1807.05764">1807.05764</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FISCAS.2019.8702498">10.1109/ISCAS.2019.8702498</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=A+Lyra2+FPGA+Core+for+Lyra2REv2-Based+Cryptocurrencies&rft.place=Sapporo%2C+Japan&rft.pages=1-5&rft.pub=IEEE&rft.date=2019-05-29&rft_id=info%3Aarxiv%2F1807.05764&rft_id=info%3Adoi%2F10.1109%2FISCAS.2019.8702498&rft.aulast=van+Beirendonck&rft.aufirst=M.&rft.au=Trudeau%2C+L.&rft.au=Giard%2C+P.&rft.au=Balatsoukas-Stimming%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-:0-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_6-0">^</a></b></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://eprint.iacr.org/2015/136">"Cryptology ePrint Archive: Report 2015/136"</a>. <i>eprint.iacr.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=eprint.iacr.org&rft.atitle=Cryptology+ePrint+Archive%3A+Report+2015%2F136&rft_id=https%3A%2F%2Feprint.iacr.org%2F2015%2F136&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-:1-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_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 id="CITEREFAlmeidaAndradeBarretoSimplicio_Jr2014" class="citation journal cs1">Almeida, Leonardo C.; Andrade, Ewerton R.; Barreto, Paulo S. L. M.; Simplicio Jr, Marcos A. (2014-01-04). "Lyra: password-based key derivation with tunable memory and processing costs". <i>Journal of Cryptographic Engineering</i>. <b>4</b> (2): 75–89. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.642.8519">10.1.1.642.8519</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs13389-013-0063-5">10.1007/s13389-013-0063-5</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2190-8508">2190-8508</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:5245769">5245769</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Cryptographic+Engineering&rft.atitle=Lyra%3A+password-based+key+derivation+with+tunable+memory+and+processing+costs&rft.volume=4&rft.issue=2&rft.pages=75-89&rft.date=2014-01-04&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.642.8519%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A5245769%23id-name%3DS2CID&rft.issn=2190-8508&rft_id=info%3Adoi%2F10.1007%2Fs13389-013-0063-5&rft.aulast=Almeida&rft.aufirst=Leonardo+C.&rft.au=Andrade%2C+Ewerton+R.&rft.au=Barreto%2C+Paulo+S.+L.+M.&rft.au=Simplicio+Jr%2C+Marcos+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-:8-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-:8_8-0">^</a></b></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://eprint.iacr.org/2014/030">"Cryptology ePrint Archive: Report 2014/030"</a>. <i>eprint.iacr.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=eprint.iacr.org&rft.atitle=Cryptology+ePrint+Archive%3A+Report+2014%2F030&rft_id=https%3A%2F%2Feprint.iacr.org%2F2014%2F030&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-lyra2ToC2-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-lyra2ToC2_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-lyra2ToC2_9-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-lyra2ToC2_9-2"><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 id="CITEREFAndradeSimplicio_JrBarretoSantos2016" class="citation journal cs1">Andrade, E.; Simplicio Jr, M.; Barreto, P.; Santos, P. (2016-01-01). "Lyra2: efficient password hashing with high security against time-memory trade-offs". <i>IEEE Transactions on Computers</i>. <b>PP</b> (99): 3096–3108. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTC.2016.2516011">10.1109/TC.2016.2516011</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0018-9340">0018-9340</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:37232444">37232444</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Computers&rft.atitle=Lyra2%3A+efficient+password+hashing+with+high+security+against+time-memory+trade-offs&rft.volume=PP&rft.issue=99&rft.pages=3096-3108&rft.date=2016-01-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A37232444%23id-name%3DS2CID&rft.issn=0018-9340&rft_id=info%3Adoi%2F10.1109%2FTC.2016.2516011&rft.aulast=Andrade&rft.aufirst=E.&rft.au=Simplicio+Jr%2C+M.&rft.au=Barreto%2C+P.&rft.au=Santos%2C+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChen2009" class="citation journal cs1">Chen, Lily (2009). <a rel="nofollow" class="external text" href="http://csrc.nist.gov/publications/nistpubs/800-108/sp800-108.pdf">"Recommendation for Key Derivation Using Pseudorandom Functions (Revised)"</a> <span class="cs1-format">(PDF)</span>. <i>Computer Security</i>. NIST. <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/10.6028%2FNIST.SP.800-108">10.6028/NIST.SP.800-108</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computer+Security&rft.atitle=Recommendation+for+Key+Derivation+Using+Pseudorandom+Functions+%28Revised%29&rft.date=2009&rft_id=info%3Adoi%2F10.6028%2FNIST.SP.800-108&rft.aulast=Chen&rft.aufirst=Lily&rft_id=http%3A%2F%2Fcsrc.nist.gov%2Fpublications%2Fnistpubs%2F800-108%2Fsp800-108.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-lyra2RefGuide-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-lyra2RefGuide_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-lyra2RefGuide_11-1"><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="CITEREFSimplicio_JrAlmeidaAndradeSantos" class="citation web cs1">Simplicio Jr, Marcos A.; Almeida, Leonardo C.; Andrade, Ewerton R.; Santos, Paulo C.; Barreto, Paulo S. L. M. <a rel="nofollow" class="external text" href="https://password-hashing.net/submissions/specs/Lyra2-v3.pdf">"The Lyra2 reference guide"</a> <span class="cs1-format">(PDF)</span>. <i>PHC</i>. The Password Hashing Competition.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=PHC&rft.atitle=The+Lyra2+reference+guide&rft.aulast=Simplicio+Jr&rft.aufirst=Marcos+A.&rft.au=Almeida%2C+Leonardo+C.&rft.au=Andrade%2C+Ewerton+R.&rft.au=Santos%2C+Paulo+C.&rft.au=Barreto%2C+Paulo+S.+L.+M.&rft_id=https%3A%2F%2Fpassword-hashing.net%2Fsubmissions%2Fspecs%2FLyra2-v3.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPercival" class="citation web cs1">Percival, Colin. <a rel="nofollow" class="external text" href="https://www.tarsnap.com/scrypt/scrypt.pdf">"Stronger Key Derivation via Sequential Memory-Hard Functions"</a> <span class="cs1-format">(PDF)</span>. <i>TARSNAP</i>. The Technical BSD Conference.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=TARSNAP&rft.atitle=Stronger+Key+Derivation+via+Sequential+Memory-Hard+Functions&rft.aulast=Percival&rft.aufirst=Colin&rft_id=https%3A%2F%2Fwww.tarsnap.com%2Fscrypt%2Fscrypt.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://eprint.iacr.org/2013/525">"Cryptology ePrint Archive: Report 2013/525"</a>. <i>eprint.iacr.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=eprint.iacr.org&rft.atitle=Cryptology+ePrint+Archive%3A+Report+2013%2F525&rft_id=https%3A%2F%2Feprint.iacr.org%2F2013%2F525&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmidt" class="citation web cs1">Schmidt, Sascha. <a rel="nofollow" class="external text" href="https://www.uni-weimar.de/fileadmin/user/fak/medien/professuren/Mediensicherheit/Research/Theses/sascha-schmidt-master-thesis-catena.pdf">"Implementation of the Catena Password-Scrambling Framework"</a> <span class="cs1-format">(PDF)</span>. <i>Bauhaus-Universität Weimar</i>. Faculty of Media.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Bauhaus-Universit%C3%A4t+Weimar&rft.atitle=Implementation+of+the+Catena+Password-Scrambling+Framework&rft.aulast=Schmidt&rft.aufirst=Sascha&rft_id=https%3A%2F%2Fwww.uni-weimar.de%2Ffileadmin%2Fuser%2Ffak%2Fmedien%2Fprofessuren%2FMediensicherheit%2FResearch%2FTheses%2Fsascha-schmidt-master-thesis-catena.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/P-H-C/phc-winner-argon2/blob/master/argon2-specs.pdf">"P-H-C/phc-winner-argon2"</a> <span class="cs1-format">(PDF)</span>. <i>GitHub</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=P-H-C%2Fphc-winner-argon2&rft_id=https%3A%2F%2Fgithub.com%2FP-H-C%2Fphc-winner-argon2%2Fblob%2Fmaster%2Fargon2-specs.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-:3-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_16-1"><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="http://article.gmane.org/gmane.comp.security.phc/2237">"Gmane -- Another PHC candidates mechanical tests"</a>. <i>article.gmane.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=article.gmane.org&rft.atitle=Gmane+--+Another+PHC+candidates+mechanical+tests&rft_id=http%3A%2F%2Farticle.gmane.org%2Fgmane.comp.security.phc%2F2237&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-:4-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-:4_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:4_17-1"><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="http://article.gmane.org/gmane.comp.security.phc/1992">"Gmane -- A review per day Lyra2"</a>. <i>article.gmane.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=article.gmane.org&rft.atitle=Gmane+--+A+review+per+day+Lyra2&rft_id=http%3A%2F%2Farticle.gmane.org%2Fgmane.comp.security.phc%2F1992&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-:5-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-:5_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:5_18-1"><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="http://article.gmane.org/gmane.comp.security.phc/1596">"Gmane -- Lyra2 initial review"</a>. <i>article.gmane.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=article.gmane.org&rft.atitle=Gmane+--+Lyra2+initial+review&rft_id=http%3A%2F%2Farticle.gmane.org%2Fgmane.comp.security.phc%2F1596&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-:6-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-:6_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:6_19-1"><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="http://article.gmane.org/gmane.comp.security.phc/1849">"Gmane -- Memory performance and ASIC attacks"</a>. <i>article.gmane.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=article.gmane.org&rft.atitle=Gmane+--+Memory+performance+and+ASIC+attacks&rft_id=http%3A%2F%2Farticle.gmane.org%2Fgmane.comp.security.phc%2F1849&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" class="Z3988"></span></span> </li> <li id="cite_note-:7-20"><span class="mw-cite-backlink">^ <a href="#cite_ref-:7_20-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:7_20-1"><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="http://article.gmane.org/gmane.comp.security.phc/1830">"Gmane -- Quick analysis of Argon"</a>. <i>article.gmane.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-03-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=article.gmane.org&rft.atitle=Gmane+--+Quick+analysis+of+Argon&rft_id=http%3A%2F%2Farticle.gmane.org%2Fgmane.comp.security.phc%2F1830&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALyra2" 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=Lyra2&action=edit&section=10" 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="http://lyra-2.net/">Lyra2's website</a></li> <li><a rel="nofollow" class="external text" href="https://github.com/leocalm/Lyra/">Lyra2 source code repository on Github</a></li></ul> <div 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class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Cryptography_hash" title="Template:Cryptography hash"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Cryptography_hash" title="Template talk:Cryptography hash"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Cryptography_hash" title="Special:EditPage/Template:Cryptography hash"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Cryptographic_hash_functions_and_message_authentication_codes" 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 href="/wiki/Argon2" title="Argon2">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 class="mw-selflink selflink">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" 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