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//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article includes a list of <a href="/wiki/Wikipedia:Citing_sources#General_references" title="Wikipedia:Citing sources">general references</a>, but <b>it lacks sufficient corresponding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a></b>.<span class="hide-when-compact"> Please help to <a href="/wiki/Wikipedia:WikiProject_Reliability" title="Wikipedia:WikiProject Reliability">improve</a> this article by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations.</span> <span class="date-container"><i>(<span class="date">January 2011</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> <p>An <b>adaptive chosen-ciphertext attack</b> (abbreviated as <b>CCA2</b>) is an interactive form of <a href="/wiki/Chosen-ciphertext_attack" title="Chosen-ciphertext attack">chosen-ciphertext attack</a> in which an attacker first sends a number of <a href="/wiki/Ciphertext" title="Ciphertext">ciphertexts</a> to be decrypted chosen adaptively, and then uses the results to distinguish a target ciphertext without consulting the oracle on the challenge ciphertext. In an adaptive attack, the attacker is further allowed adaptive queries to be asked after the target is revealed (but the target query is disallowed). It is extending the <a href="/wiki/Chosen-ciphertext_attack" title="Chosen-ciphertext attack">indifferent (non-adaptive) chosen-ciphertext attack</a> (CCA1) where the second stage of adaptive queries is not allowed. <a href="/wiki/Charles_Rackoff" title="Charles Rackoff">Charles Rackoff</a> and Dan Simon defined CCA2 and suggested a system building on the non-adaptive CCA1 definition and system of <a href="/wiki/Moni_Naor" title="Moni Naor">Moni Naor</a> and <a href="/wiki/Moti_Yung" title="Moti Yung">Moti Yung</a> (which was the first treatment of chosen ciphertext attack immunity of public key systems). </p><p>In certain practical settings, the goal of this attack is to gradually reveal information about an encrypted message, or about the decryption key itself. For <a href="/wiki/Public-key_cryptography" title="Public-key cryptography">public-key systems</a>, adaptive-chosen-ciphertexts are generally applicable only when they have the property of <a href="/wiki/Malleability_(cryptography)" title="Malleability (cryptography)">ciphertext malleability</a> — that is, a ciphertext can be modified in specific ways that will have a predictable effect on the decryption of that message. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Practical_attacks">Practical attacks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_chosen-ciphertext_attack&action=edit&section=1" title="Edit section: Practical attacks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Adaptive-chosen-ciphertext attacks were perhaps considered to be a theoretical concern, but not to have been be manifested in practice, until 1998, when <a href="/wiki/Daniel_Bleichenbacher" title="Daniel Bleichenbacher">Daniel Bleichenbacher</a> (then of <a href="/wiki/Bell_Laboratories" class="mw-redirect" title="Bell Laboratories">Bell Laboratories</a>) demonstrated a practical attack against systems using RSA encryption in concert with the <a href="/wiki/PKCS_1" title="PKCS 1">PKCS#1 v1.5</a> encoding function, including a version of the <a href="/wiki/Secure_Sockets_Layer" class="mw-redirect" title="Secure Sockets Layer">Secure Sockets Layer</a> (SSL) protocol used by thousands of <a href="/wiki/Web_server" title="Web server">web servers</a> at the time.<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> </p><p>The Bleichenbacher attacks, also known as the million message attack, took advantage of flaws within the PKCS #1 v1.5 padding function to gradually reveal the content of an RSA encrypted message. Under this padding function, padded plaintexts have a fixed format that it should follow. If the decryption device (e.g. SSL-equipped web server) somehow reveals whether the padding is valid, it also serves as an "oracle" that reveals information on the secret key. Finding the whole key requires sending several million test ciphertexts to the target.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In practical terms, this means that an SSL session key can be exposed in a reasonable amount of time, perhaps a day or less. </p><p>With slight variations, this vulnerability still exists in many modern servers, under the new name "Return Of Bleichenbacher's Oracle Threat" (ROBOT).<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Preventing_attacks">Preventing attacks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_chosen-ciphertext_attack&action=edit&section=2" title="Edit section: Preventing attacks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In order to prevent adaptive-chosen-ciphertext attacks, it is necessary to use an encryption or encoding scheme that limits ciphertext <a href="/wiki/Malleability_(cryptography)" title="Malleability (cryptography)">malleability</a> and a proof of security of the system. After the theoretical and foundation level development of CCA secure systems, a number of systems have been proposed in the Random Oracle model: the most common standard for RSA encryption is <a href="/wiki/Optimal_Asymmetric_Encryption_Padding" class="mw-redirect" title="Optimal Asymmetric Encryption Padding">Optimal Asymmetric Encryption Padding</a> (OAEP). Unlike improvised schemes such as the padding used in the early versions of PKCS#1, OAEP has been proven secure in the <a href="/wiki/Random_oracle" title="Random oracle">random oracle</a> model,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> OAEP was incorporated into PKCS#1 as of version 2.0 published in 1998 as the now-recommended encoding scheme, with the older scheme still supported but not recommended for new applications.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> However, the golden standard for security is to show the system secure without relying on the Random Oracle idealization.<sup id="cite_ref-katz_6-0" class="reference"><a href="#cite_note-katz-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_model">Mathematical model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_chosen-ciphertext_attack&action=edit&section=3" title="Edit section: Mathematical model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In complexity-theoretic cryptography, security against adaptive chosen-ciphertext attacks is commonly modeled using <a href="/wiki/Ciphertext_indistinguishability" title="Ciphertext indistinguishability">ciphertext indistinguishability</a> (IND-CCA2). </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=Adaptive_chosen-ciphertext_attack&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style 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Retrieved <span class="nowrap">2009-01-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Cryptology&rft.atitle=RSA-OAEP+Is+Secure+under+the+RSA+Assumption&rft.volume=17&rft.issue=2&rft.pages=81-104&rft.date=2004&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.11.7519%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A218582909%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs00145-002-0204-y&rft.aulast=Fujisaki&rft.aufirst=Eiichiro&rft.au=Okamoto%2C+Tatsuaki&rft.au=Pointcheval%2C+David&rft.au=Stern%2C+Jacques&rft_id=https%3A%2F%2Fwww.di.ens.fr%2F~pointche%2FDocuments%2FPapers%2F2004_joc.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAdaptive+chosen-ciphertext+attack" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaliskiStaddon1998" class="citation cs1">Kaliski, B.; Staddon, J. (October 1998). <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc2437"><i>PKCS #1: RSA Cryptography Specifications Version 2.0</i></a>. <a href="/wiki/Internet_Engineering_Task_Force" title="Internet Engineering Task Force">IETF</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.17487%2FRFC2437">10.17487/RFC2437</a></span>. <a href="/wiki/Request_for_Comments" title="Request for Comments">RFC</a> <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc2437">2437</a><span class="reference-accessdate">. Retrieved <span class="nowrap">February 20,</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=PKCS+%231%3A+RSA+Cryptography+Specifications+Version+2.0&rft.pub=IETF&rft.date=1998-10&rft_id=info%3Adoi%2F10.17487%2FRFC2437&rft.aulast=Kaliski&rft.aufirst=B.&rft.au=Staddon%2C+J.&rft_id=https%3A%2F%2Fdatatracker.ietf.org%2Fdoc%2Fhtml%2Frfc2437&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAdaptive+chosen-ciphertext+attack" class="Z3988"></span></span> </li> <li id="cite_note-katz-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-katz_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKatzLindell2015" class="citation book cs1">Katz, Jonathan; Lindell, Yehuda (2015). <i>Introduction to Modern Cryptography</i> (2 ed.). 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attack">Ciphertext-only</a></li> <li><a href="/wiki/Chosen-plaintext_attack" title="Chosen-plaintext attack">Chosen-plaintext</a> <ul><li><a href="/wiki/Adaptive_chosen-plaintext_attack" class="mw-redirect" title="Adaptive chosen-plaintext attack">Adaptive</a></li></ul></li> <li><a href="/wiki/Chosen-ciphertext_attack" title="Chosen-ciphertext attack">Chosen-ciphertext</a> <ul><li><a class="mw-selflink selflink">Adaptive</a></li> <li><a href="/wiki/Chosen-ciphertext_attack#Lunchtime_attacks" title="Chosen-ciphertext attack">Lunchtime</a></li></ul></li> <li><a href="/wiki/Known-plaintext_attack" title="Known-plaintext attack">Known-plaintext</a></li> <li><a href="/wiki/Side-channel_attack" title="Side-channel attack">Side-channel</a></li> <li>Open key models <ul><li><a href="/wiki/Related-key_attack" title="Related-key attack">Related-key</a></li> <li><a href="/wiki/Known-key_distinguishing_attack" title="Known-key distinguishing attack">Known-key</a></li></ul></li></ul> 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