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89 lines
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HTML
89 lines
4.0 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<!-- This manual describes how to install and use the GNU multiple precision
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arithmetic library, version 6.1.0.
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Copyright 1991, 1993-2015 Free Software Foundation, Inc.
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Permission is granted to copy, distribute and/or modify this document under
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<title>Modular Powering Algorithm (GNU MP 6.1.0)</title>
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<meta name="description" content="How to install and use the GNU multiple precision arithmetic library, version 6.1.0.">
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<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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<link href="Powering-Algorithms.html#Powering-Algorithms" rel="up" title="Powering Algorithms">
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<link href="Root-Extraction-Algorithms.html#Root-Extraction-Algorithms" rel="next" title="Root Extraction Algorithms">
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<link href="Normal-Powering-Algorithm.html#Normal-Powering-Algorithm" rel="prev" title="Normal Powering Algorithm">
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<a name="Modular-Powering-Algorithm"></a>
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<div class="header">
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<p>
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Previous: <a href="Normal-Powering-Algorithm.html#Normal-Powering-Algorithm" accesskey="p" rel="prev">Normal Powering Algorithm</a>, Up: <a href="Powering-Algorithms.html#Powering-Algorithms" accesskey="u" rel="up">Powering Algorithms</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<a name="Modular-Powering"></a>
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<h4 class="subsection">15.4.2 Modular Powering</h4>
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<p>Modular powering is implemented using a <em>2^k</em>-ary sliding window
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algorithm, as per “Handbook of Applied Cryptography” algorithm 14.85
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(see <a href="References.html#References">References</a>). <em>k</em> is chosen according to the size of the
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exponent. Larger exponents use larger values of <em>k</em>, the choice being
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made to minimize the average number of multiplications that must supplement
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the squaring.
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</p>
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<p>The modular multiplies and squarings use either a simple division or the REDC
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method by Montgomery (see <a href="References.html#References">References</a>). REDC is a little faster,
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essentially saving N single limb divisions in a fashion similar to an exact
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remainder (see <a href="Exact-Remainder.html#Exact-Remainder">Exact Remainder</a>).
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</p>
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