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    <div class="moz-forward-container">FYI...<br>
      <br>
      -------- Forwarded Message --------
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            <th align="RIGHT" nowrap="nowrap" valign="BASELINE">Subject:
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            <td>6.876 Advanced Topics in Cryptography: Lattices</td>
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            <th align="RIGHT" nowrap="nowrap" valign="BASELINE">Date: </th>
            <td>Tue, 8 Sep 2015 09:42:30 -0400</td>
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            <th align="RIGHT" nowrap="nowrap" valign="BASELINE">From: </th>
            <td>Vinod Vaikuntanathan <a class="moz-txt-link-rfc2396E" href="mailto:vinod.nathan@gmail.com">&lt;vinod.nathan@gmail.com&gt;</a></td>
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            <th align="RIGHT" nowrap="nowrap" valign="BASELINE">To: </th>
            <td>Csail <a class="moz-txt-link-rfc2396E" href="mailto:toc-faculty@csail.mit.edu">&lt;toc-faculty@csail.mit.edu&gt;</a>,
              <a class="moz-txt-link-abbreviated" href="mailto:toc-visitors@csail.mit.edu">toc-visitors@csail.mit.edu</a>, <a class="moz-txt-link-abbreviated" href="mailto:toc-students@csail.mit.edu">toc-students@csail.mit.edu</a>,
              <a class="moz-txt-link-abbreviated" href="mailto:theory-postdocs@csail.mit.edu">theory-postdocs@csail.mit.edu</a>,
              <a class="moz-txt-link-abbreviated" href="mailto:csail-announce@csail.mit.edu">csail-announce@csail.mit.edu</a></td>
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      <br>
      <div dir="ltr"><span style="font-size:12.8px">Dear all,</span><br
          style="font-size:12.8px">
        <br style="font-size:12.8px">
        <span style="font-size:12.8px">Please find below the
          announcement for a graduate course on lattices 6.876J that I
          am teaching this semester.</span><br style="font-size:12.8px">
        <br style="font-size:12.8px">
        <span style="font-size:12.8px">If you are interested in
          attending this </span><span class="" style="font-size:12.8px">class</span><span
          style="font-size:12.8px"> (either for credit or as a
          listener), </span><span style="font-size:12.8px">please drop
          me a line.</span><br style="font-size:12.8px">
        <br>
        Thanks, and best,<br style="font-size:12.8px">
        <span style="font-size:12.8px">Vinod</span>
        <div><span style="font-size:12.8px"><br>
          </span></div>
        <div><span style="font-size:12.8px"><br>
          </span></div>
        <div>
          <p class="MsoNormal"><span
style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif;background-image:initial;background-repeat:initial">6.876J
              ADVANCED TOPICS IN
              CRYPTOGRAPHY: LATTICES (3-0-9, H level)</span><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif"><br>
              <span
                style="background-image:initial;background-repeat:initial">Instructor:
Vinod
                Vaikuntanathan<br>
                <span
                  style="background-image:initial;background-repeat:initial">When:
                  MW<span class=""> </span><span class=""><span><span
                        tabindex="0">2:30-4 pm</span></span></span><span
                    class=""> (first
                    lecture: Wed 9/9)<br>
                    Where: 26-328</span><br>
                  <span
                    style="background-image:initial;background-repeat:initial">Class
website:
                    <a moz-do-not-send="true"
                      href="http://people.csail.mit.edu/vinodv/6876-Fall2015/index.html">http://people.csail.mit.edu/vinodv/6876-Fall2015/index.html</a><br>
                    <br>
                    <span
                      style="background-image:initial;background-repeat:initial"></span></span></span></span></span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif"><br>
              Integer Lattices are a formidable tool in mathematics
              and computer science, with many applications in
              (algebraic) number theory, in
              combinatorial optimization, and in breaking and building
              cryptosystems. Come to
              6.876 to learn about lattice algorithms, the complexity
              theory of lattice
              problems, and their use in cryptography.</span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif"><br>
            </span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif">A
              sample of topics we will cover include:</span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif"><br>
            </span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif">--
              Lattice Algorithms: Classical algorithms
              such as LLL and AKS for finding (approximate) shortest and
              closest vectors, as
              well as brand-new developments (from STOC and FOCS’15).<br>
              <br>
            </span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif">--
              Coppersmith’s Method and Using Lattices for Cryptanalysis:
              Breaking knapsack
              cryptosystems, low-exponent RSA and some stream ciphers.<br>
              <br>
            </span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif">--
              Complexity Theory of Lattice Problems: NP-hardness of
              approximation and AM
              protocols. We will discuss several open problems in this
              area.<br>
              <br>
            </span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif">--
              Cryptography: Ajtai’s worst-case to average-case reduction
              for lattice
              problems, one-way functions, public-key encryption,
              homomorphic encryption, you
              name it...</span></p>
          <p class="MsoNormal"><span
              style="font-size:9.5pt;line-height:107%;font-family:Arial,sans-serif"><br>
              <br>
              <span
                style="background-image:initial;background-repeat:initial">REGISTRATION:
Subscribe
                to the class mailing list at<span class=""> </span><a
                  moz-do-not-send="true"
                  href="http://lists.csail.mit.edu/mailman/listinfo/6876-f15"
                  target="_blank"><a class="moz-txt-link-freetext" href="http://lists.csail.mit.edu/mailman/listinfo/6876-f15">http://lists.csail.mit.edu/mailman/listinfo/6876-f15</a></a>
                if
                you would like to take the class for credit or as a
                listener.</span></span><br>
            <br>
            <span
              style="background-image:initial;background-repeat:initial">PREREQUISITES:
6.045
              and 6.046 (or equivalent) and basic linear algebra. If you
              do not have
              the prerequisites and would still like to take the class,
              come talk to me.<br>
              <br>
              <span
                style="background-image:initial;background-repeat:initial">GRADING:
The
                grade will be based on 1-2 problem sets, scribe notes
                and a final project.</span></span></p>
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