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112 lines
5.6 KiB
HTML
112 lines
5.6 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<html>
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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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the terms of the GNU Free Documentation License, Version 1.3 or any later
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version published by the Free Software Foundation; with no Invariant Sections,
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with the Front-Cover Texts being "A GNU Manual", and with the Back-Cover
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software". A copy of the license is included in
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GNU Free Documentation License. -->
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<head>
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<title>Integer Exponentiation (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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<meta name="keywords" content="Integer Exponentiation (GNU MP 6.1.0)">
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<link href="index.html#Top" rel="start" title="Top">
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<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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<link href="Integer-Functions.html#Integer-Functions" rel="up" title="Integer Functions">
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<link href="Integer-Roots.html#Integer-Roots" rel="next" title="Integer Roots">
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<link href="Integer-Division.html#Integer-Division" rel="prev" title="Integer Division">
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</head>
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<body lang="en">
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<a name="Integer-Exponentiation"></a>
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<div class="header">
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<p>
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Next: <a href="Integer-Roots.html#Integer-Roots" accesskey="n" rel="next">Integer Roots</a>, Previous: <a href="Integer-Division.html#Integer-Division" accesskey="p" rel="prev">Integer Division</a>, Up: <a href="Integer-Functions.html#Integer-Functions" accesskey="u" rel="up">Integer Functions</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="Exponentiation-Functions"></a>
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<h3 class="section">5.7 Exponentiation Functions</h3>
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<a name="index-Integer-exponentiation-functions"></a>
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<a name="index-Exponentiation-functions"></a>
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<a name="index-Powering-functions"></a>
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<dl>
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<dt><a name="index-mpz_005fpowm"></a>Function: <em>void</em> <strong>mpz_powm</strong> <em>(mpz_t <var>rop</var>, const mpz_t <var>base</var>, const mpz_t <var>exp</var>, const mpz_t <var>mod</var>)</em></dt>
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<dt><a name="index-mpz_005fpowm_005fui"></a>Function: <em>void</em> <strong>mpz_powm_ui</strong> <em>(mpz_t <var>rop</var>, const mpz_t <var>base</var>, unsigned long int <var>exp</var>, const mpz_t <var>mod</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em>(<var>base</var> raised to <var>exp</var>)
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modulo <var>mod</var></em>.
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</p>
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<p>Negative <var>exp</var> is supported if an inverse <em><var>base</var>^<span class="nolinebreak">-1</span><!-- /@w --> mod
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<var>mod</var></em> exists (see <code>mpz_invert</code> in <a href="Number-Theoretic-Functions.html#Number-Theoretic-Functions">Number Theoretic Functions</a>).
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If an inverse doesn’t exist then a divide by zero is raised.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpz_005fpowm_005fsec"></a>Function: <em>void</em> <strong>mpz_powm_sec</strong> <em>(mpz_t <var>rop</var>, const mpz_t <var>base</var>, const mpz_t <var>exp</var>, const mpz_t <var>mod</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em>(<var>base</var> raised to <var>exp</var>)
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modulo <var>mod</var></em>.
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</p>
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<p>It is required that <em><var>exp</var> > 0</em> and that <var>mod</var> is odd.
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</p>
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<p>This function is designed to take the same time and have the same cache access
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patterns for any two same-size arguments, assuming that function arguments are
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placed at the same position and that the machine state is identical upon
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function entry. This function is intended for cryptographic purposes, where
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resilience to side-channel attacks is desired.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpz_005fpow_005fui"></a>Function: <em>void</em> <strong>mpz_pow_ui</strong> <em>(mpz_t <var>rop</var>, const mpz_t <var>base</var>, unsigned long int <var>exp</var>)</em></dt>
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<dt><a name="index-mpz_005fui_005fpow_005fui"></a>Function: <em>void</em> <strong>mpz_ui_pow_ui</strong> <em>(mpz_t <var>rop</var>, unsigned long int <var>base</var>, unsigned long int <var>exp</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em><var>base</var> raised to <var>exp</var></em>. The case
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<em>0^0</em> yields 1.
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</p></dd></dl>
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</body>
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</html>
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