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<title>Extendable-output function</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Extendable-output function</span></span>

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<p><b>Extendable-output function</b> (<b>XOF</b>) is an extension<sup id="cite_ref-FOOTNOTEPeyrinWang20207_1-0" class="reference"><a href="#cite_note-FOOTNOTEPeyrinWang20207-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> of the <a href="Cryptographic_hash" class="mw-redirect" title="Cryptographic hash">cryptographic hash</a> that allows its output to be arbitrarily long. In particular, the <a href="Sponge_construction" class="mw-redirect" title="Sponge construction">sponge construction</a> makes any <a href="Sponge_hash" class="mw-redirect" title="Sponge hash">sponge hash</a> a natural XOF: the squeeze operation can be repeated, and the regular hash functions with a fixed-size result are obtained from a sponge mechanism by stopping the squeezing phase after obtaining the fixed number of bits).<sup id="cite_ref-FOOTNOTEMittelbachFischlin2021526_2-0" class="reference"><a href="#cite_note-FOOTNOTEMittelbachFischlin2021526-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>The genesis of a XOF makes it <a href="Collision_resistance" title="Collision resistance">collision</a>, <a href="Preimage_resistance" class="mw-redirect" title="Preimage resistance">preimage</a> and <a href="Second_preimage" class="mw-redirect" title="Second preimage">second preimage</a> resistant. Technically, any XOF can be turned into a cryptographic hash by truncating the result to a fixed length (in practice, hashes and XOFs are defined differently for <a href="Domain_separation_(cryptography)" class="mw-redirect" title="Domain separation (cryptography)">domain separation</a><sup id="cite_ref-FOOTNOTEDworkin20143_3-0" class="reference"><a href="#cite_note-FOOTNOTEDworkin20143-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>). The examples of XOF include the algorithms from the <a href="Keccak" class="mw-redirect" title="Keccak">Keccak</a> family: <a href="SHAKE128" class="mw-redirect" title="SHAKE128">SHAKE128</a>, <a href="SHAKE256" class="mw-redirect" title="SHAKE256">SHAKE256</a>, and a variant with higher efficiency, <a href="KangarooTwelve" class="mw-redirect" title="KangarooTwelve">KangarooTwelve</a>.<sup id="cite_ref-FOOTNOTEPeyrinWang20207_1-1" class="reference"><a href="#cite_note-FOOTNOTEPeyrinWang20207-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>XOFs are used as <a href="Key_derivation_function" title="Key derivation function">key derivation functions</a> (KDFs), <a href="Stream_cipher" title="Stream cipher">stream ciphers</a>,<sup id="cite_ref-FOOTNOTEPeyrinWang20207_1-2" class="reference"><a href="#cite_note-FOOTNOTEPeyrinWang20207-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="Mask_generation_function" title="Mask generation function">mask generation functions</a>.<sup id="cite_ref-FOOTNOTEPerlner20144_4-0" class="reference"><a href="#cite_note-FOOTNOTEPerlner20144-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Related-output_issues">Related-output issues</h2></div>

<p>By their nature, XOFs can produce related outputs (a longer result includes a shorter one as a prefix). The use of KDFs for key derivation can therefore cause related-output problems. As a "naïve" example, if the <a href="Triple_DES" title="Triple DES">Triple DES</a> keys are generated with a XOF, and there is a confusion in the implementation that causes some operations to be performed as 3TDEA (3x56 = 168-bit key), and some as 2TDEA (2x56 = 112 bit key), comparing the encryption results will lower the attack complexity to just 56 bits; similar problems can occur if hashes in the NIST SP 800-108 are naïvely replaced by the KDFs.<sup id="cite_ref-FOOTNOTEPerlner20145_5-0" class="reference"><a href="#cite_note-FOOTNOTEPerlner20145-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

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

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<li id="cite_note-FOOTNOTEPeyrinWang20207-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEPeyrinWang20207_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEPeyrinWang20207_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEPeyrinWang20207_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFPeyrinWang2020">Peyrin & Wang 2020</a>, p. 7.</span>

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<li id="cite_note-FOOTNOTEMittelbachFischlin2021526-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMittelbachFischlin2021526_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMittelbachFischlin2021">Mittelbach & Fischlin 2021</a>, p. 526.</span>

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<li id="cite_note-FOOTNOTEDworkin20143-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDworkin20143_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDworkin2014">Dworkin 2014</a>, p. 3.</span>

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<li id="cite_note-FOOTNOTEPerlner20144-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEPerlner20144_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPerlner2014">Perlner 2014</a>, p. 4.</span>

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<li id="cite_note-FOOTNOTEPerlner20145-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEPerlner20145_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPerlner2014">Perlner 2014</a>, p. 5.</span>

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

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</style><cite id="CITEREFMittelbachFischlin2021" class="citation book cs1">Mittelbach, Arno; Fischlin, Marc (2021). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Ly8WEAAAQBAJ&pg=PA526">"Extendable Output Functions (XOFs)"</a>. <i>The Theory of Hash Functions and Random Oracles: An Approach to Modern Cryptography</i>. Information Security and Cryptography. Springer International Publishing. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-030-63287-8</bdi><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-06-22</span></span>.</cite></li>

<li><cite id="CITEREFPeyrinWang2020" class="citation book cs1">Peyrin, Thomas; Wang, Haoyang (2020). <a rel="nofollow" class="external text" href="https://eprint.iacr.org/2020/986.pdf">"The MALICIOUS Framework: Embedding Backdoors into Tweakable Block Ciphers"</a> <span class="cs1-format">(PDF)</span>. <i>Advances in Cryptology – CRYPTO 2020</i>. Lecture Notes in Computer Science. Vol. 12172. Springer International Publishing. pp. <span class="nowrap">249–</span>278. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-030-56877-1_9">10.1007/978-3-030-56877-1_9</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-030-56876-4</bdi>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0302-9743">0302-9743</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:221107066">221107066</a>.</cite></li>

<li><cite id="CITEREFPerlner2014" class="citation web cs1">Perlner, Ray (August 22, 2014). <a rel="nofollow" class="external text" href="https://csrc.nist.gov/events/2014/sha-3-2014-workshop">"Extendable-Output Functions (XOFs)"</a>. <i>csrc.nist.gov</i>. <a href="NIST" class="mw-redirect" title="NIST">NIST</a><span class="reference-accessdate">. Retrieved <span class="nowrap">22 June</span> 2023</span>.</cite></li>

<li><cite id="CITEREFDworkin2014" class="citation web cs1">Dworkin, Morris (August 22, 2014). <a rel="nofollow" class="external text" href="https://csrc.nist.gov/events/2014/sha-3-2014-workshop">"Domain Extensions"</a>. <i>csrc.nist.gov</i>. <a href="NIST" class="mw-redirect" title="NIST">NIST</a><span class="reference-accessdate">. Retrieved <span class="nowrap">22 June</span> 2023</span>.</cite></li></ul>

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