Document Zbl 1210.94090

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Codes Cryptography</a> <a href="/?q=in%3A261463" title="Articles in this Issue">55, No. 2-3, 189-200 (2010)</a>. </div> <div class="abstract">Summary: In this paper, we study the recently proposed encryption scheme MST$_3$, focusing on a concrete instantiation using Suzuki 2-groups. In a passive scenario, we argue that the one-wayness of this scheme may not, as claimed, be proven without the assumption that factoring group elements with respect to random covers for a subset of the group is hard. As a result, we conclude that for the proposed Suzuki 2-groups instantiation, impractical key sizes should be used in order to prevent more or less straightforward factorization attacks.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5709172">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A94A60" title="MSC2020">94A60</a> </td> <td class="space"> Cryptography </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A20F10" title="MSC2020">20F10</a> </td> <td class="space"> Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68P25" title="MSC2020">68P25</a> </td> <td class="space"> Data encryption (aspects in computer science) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apublic+key+cryptography">public key cryptography</a>; <a href="/?q=ut%3Acryptanalysis">cryptanalysis</a>; <a href="/?q=ut%3Agroup+factorizations">group factorizations</a>; <a href="/?q=ut%3Acovers">covers</a>; <a href="/?q=ut%3ASuzuki+2-groups">Suzuki 2-groups</a></div> <div class="software"> <h3>Software:</h3><a href="/software/320">GAP</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1210.94090" data-ciurl="/ci/05709172" data-biburl="/bibtex/05709172.bib" data-amsurl="/amsrefs/05709172.bib" data-xmlurl="/xml/05709172.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05709172.pdf" title="Zbl 1210.94090 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s10623-010-9373-0" aria-label="DOI for “A note on the security of $\text{MST} _{3}$”" title="10.1007/s10623-010-9373-0">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bellare M., Desai A., Pointcheval D., Rogaway P.: Relations among notions of security for public-key encryption schemes. In: CRYPTO’98: Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology, pp. 26–45. Springer-Verlag, London, UK (1998). · <a href="/0931.94014" class="nowrap">Zbl 0931.94014</a></td> </tr><tr> <td>[2]</td> <td class="space">Blackburn S.R., Cid C., Mullan C.: Cryptanalysis of the MST 3 Public Key Cryptosystem. Cryptology ePrint Archive: Report 2009/248. At the time of writing available electronically at http://www.eprint.iacr.org/2009/248 (2009). · <a href="/1185.94046" class="nowrap">Zbl 1185.94046</a></td> </tr><tr> <td>[3]</td> <td class="space">Bohli J.M., González Vasco M.I., Martínez C., Steinwandt R.: Weak keys in MST 1. Des. Codes Cryptogr. 37, 509–524 (2005) · <a href="/1114.94006" class="nowrap">Zbl 1114.94006</a> · <a href="https://doi.org/10.1007/s10623-004-4040-y" class="nowrap">doi:10.1007/s10623-004-4040-y</a></td> </tr><tr> <td>[4]</td> <td class="space">ElGamal T.: A public key cryptosystem and a signature scheme based on discrete logarithm. IEEE Trans. Info. Theory 31, 469–472 (1985) · <a href="/0571.94014" class="nowrap">Zbl 0571.94014</a> · <a href="https://doi.org/10.1109/TIT.1985.1057074" class="nowrap">doi:10.1109/TIT.1985.1057074</a></td> </tr><tr> <td>[5]</td> <td class="space">The GAP Group: GAP–Groups, Algorithms, and Programming, Version 4.4.10 http://www.gap-system.org (2007).</td> </tr><tr> <td>[6]</td> <td class="space">González Vasco M.I., Steinwandt R.: Obstacles in two public-key cryptosystems based on group factorizations. In: Nemoga, K., Grošek, O. (eds.) Cryptology, pp. 23–37. Tatra Mountains Mathematical Publications, Slovakia (2002). · <a href="/1049.94010" class="nowrap">Zbl 1049.94010</a></td> </tr><tr> <td>[7]</td> <td class="space">Huppert B., Blackburn N.: Finite Groups II. Springer, Berlin (1982) · <a href="/0477.20001" class="nowrap">Zbl 0477.20001</a></td> </tr><tr> <td>[8]</td> <td class="space">Lempken W., Magliveras S.S., van Trung T., Wei W.: A public key cryptosystem based on non-abelian finite groups. J. Cryptol. 22, 62–74 (2009) · <a href="/1168.94005" class="nowrap">Zbl 1168.94005</a> · <a href="https://doi.org/10.1007/s00145-008-9033-y" class="nowrap">doi:10.1007/s00145-008-9033-y</a></td> </tr><tr> <td>[9]</td> <td class="space">Magliveras S.S.: A cryptosystem from logarithmic signatures of finite groups. In: Proceedings of the 29th Midwest Symposium on Circuits and Systems, pp. 972–975. Elsevier Publishing Company, Amsterdam (1986).</td> </tr><tr> <td>[10]</td> <td class="space">Magliveras S.S., Memon N.D.: Linear complexity profile analysis of the PGM cryptosystem. Congresus Numerantium, Utilitas Mathematica 72, 51–60 (1989) · <a href="/0691.94003" class="nowrap">Zbl 0691.94003</a></td> </tr><tr> <td>[11]</td> <td class="space">Magliveras S.S., Memon N.D.: Properties of cryptosystem PGM. In: Advances in Cryptology. Proceedings of CRYPTO 1989, Lecture Notes on Computer Science, pp. 447–460. Springer-Verlag, Berlin (1989).</td> </tr><tr> <td>[12]</td> <td class="space">Magliveras S.S., Memon N.D.: Complexity tests for cryptosystem PGM. Congressus Numerantium, Utilitas Mathematica 79, 61–68 (1990) · <a href="/0860.94024" class="nowrap">Zbl 0860.94024</a></td> </tr><tr> <td>[13]</td> <td class="space">Magliveras S.S., Memon N.D.: Algebraic properties of cryptosystem PGM. J. Cryptol. 5, 167–183 (1992) · <a href="/0763.94014" class="nowrap">Zbl 0763.94014</a> · <a href="https://doi.org/10.1007/BF02451113" class="nowrap">doi:10.1007/BF02451113</a></td> </tr><tr> <td>[14]</td> <td class="space">Magliveras S.S., Stinson D.R., van Trung T.: New approaches to designing public key cryptosystems using one-way functions and trap-doors in finite groups. J. Cryptol. 15, 285–297 (2002) · <a href="/1020.94010" class="nowrap">Zbl 1020.94010</a> · <a href="https://doi.org/10.1007/s00145-001-0018-3" class="nowrap">doi:10.1007/s00145-001-0018-3</a></td> </tr><tr> <td>[15]</td> <td class="space">Magliveras S.S., Svaba P., van Trung T., Zajac P.: On the security of a realization of cryptosystem MST 3. Tatra Mt. Math. Publ. 41, 1–13 (2008) · <a href="/1240.94081" class="nowrap">Zbl 1240.94081</a></td> </tr><tr> <td>[16]</td> <td class="space">Motwani R., Raghavan P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995) · <a href="/0849.68039" class="nowrap">Zbl 0849.68039</a></td> </tr><tr> <td>[17]</td> <td class="space">Svaba P., Van Trung T.: On generation of random covers for finite groups. Tatra Mt. Math. Publ. 37, 105–112 (2007) · <a href="/1240.94092" class="nowrap">Zbl 1240.94092</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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