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<div align="center"><tt>Prof. Dr. Roberto Avanzi</tt><tt>,
Ruhr-Universität Bochum
<br>
<br>
</tt><tt>Montag 9. Juli 2007, 13:15 Uhr IC 4 / 39-41
<br>
<br>
</tt><tt><span class="ueber12pxinhalt"><a id="a10">Another Look at
Square Roots, Traces and Quadratic Equations in Fields of Even
Characteristic, with Applications to Elliptic Curve Cryptography</a></span><br>
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We discuss irreducible polynomials that can be used to speed up square
root<br>
extraction in fields of characteristic two. The obvious applications
are to <br>
point halving methods for elliptic curves and divisor halving methods
for <br>
hyperelliptic curves.
<br>
<br>
Irreducible polynomials <i>P(X)</i> such that the square root <i>ζ</i>
of a zero <i>x</i> of<br>
<i>P(X)</i> is a sparse polynomial are considered and those for which <i>ζ</i>
has<br>
minimal degree are characterized. We reveal a surprising connection<br>
between the minimality of this degree and the extremality of the the<br>
number of trace one elements in the polynomial base associated to <i>P(X)</i>.
<br>
<br>
We also show how to improve the speed of solving quadratic equations and<br>
that the increase in the time required to perform modular reduction is<br>
marginal and does not affect performance adversely. Experimental results<br>
confirm that the new polynomials mantain their promises; These results<br>
generalize work by Fong et al. to polynomials other than trinomials.<br>
Point halving gets a speed-up of 20% and the performance of scalar<br>
multiplication based on point halving is improved by at least 11%.<br>
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___________________________________________________________________________
<br>
Die Webseite des HGI-Seminars mit allen Informationen zu vergangenen und<br>
zukünftigen Vorträgen: <a class="moz-txt-link-freetext"
href="http://www.hgi.rub.de/deutsch/lehrangebot/seminar.html">http://www.hgi.rub.de/deutsch/lehrangebot/seminar.html</a>
<br>
<br>
<span class="moz-txt-tag">-- <br>
</span>Für das HGI, Michael Psarros <a class="moz-txt-link-rfc2396E"
href="mailto:michael.psarros@nds.rub.de"><michael.psarros@nds.rub.de></a>
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