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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Crypto-Number-ModArithmetic.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">cryptonite-0.20: Cryptography Primitives sink</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>License</th><td>BSD-style</td></tr><tr><th>Maintainer</th><td>Vincent Hanquez <vincent@snarc.org></td></tr><tr><th>Stability</th><td>experimental</td></tr><tr><th>Portability</th><td>Good</td></tr><tr><th>Safe Haskell</th><td>None</td></tr><tr><th>Language</th><td>Haskell2010</td></tr></table><p class="caption">Crypto.Number.ModArithmetic</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">exponentiation</a></li><li><a href="#g:2">inverse computing</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc empty"> </div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><a href="#v:expSafe">expSafe</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></li><li class="src short"><a href="#v:expFast">expFast</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></li><li class="src short"><a href="#v:inverse">inverse</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></li><li class="src short"><a href="#v:inverseCoprimes">inverseCoprimes</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></li></ul></div><div id="interface"><h1 id="g:1">exponentiation</h1><div class="top"><p class="src"><a id="v:expSafe" class="def">expSafe</a> <a href="src/Crypto-Number-ModArithmetic.html#expSafe" class="link">Source</a> <a href="#v:expSafe" class="selflink">#</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></td><td class="doc"><p>base</p></td></tr><tr><td class="src">-> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></td><td class="doc"><p>exponant</p></td></tr><tr><td class="src">-> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></td><td class="doc"><p>modulo</p></td></tr><tr><td class="src">-> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></td><td class="doc"><p>result</p></td></tr></table></div><div class="doc"><p>Compute the modular exponentiation of base^exponant using
algorithms design to avoid side channels and timing measurement</p><p>Modulo need to be odd otherwise the normal fast modular exponentiation
is used.</p><p>When used with integer-simple, this function is not different
from expFast, and thus provide the same unstudied and dubious
timing and side channels claims.</p><p>with GHC 7.10, the powModSecInteger is missing from integer-gmp
(which is now integer-gmp2), so is has the same security as old
ghc version.</p></div></div><div class="top"><p class="src"><a id="v:expFast" class="def">expFast</a> <a href="src/Crypto-Number-ModArithmetic.html#expFast" class="link">Source</a> <a href="#v:expFast" class="selflink">#</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></td><td class="doc"><p>base</p></td></tr><tr><td class="src">-> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></td><td class="doc"><p>exponant</p></td></tr><tr><td class="src">-> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></td><td class="doc"><p>modulo</p></td></tr><tr><td class="src">-> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a></td><td class="doc"><p>result</p></td></tr></table></div><div class="doc"><p>Compute the modular exponentiation of base^exponant using
the fastest algorithm without any consideration for
hiding parameters.</p><p>Use this function when all the parameters are public,
otherwise <code><a href="Crypto-Number-ModArithmetic.html#v:expSafe">expSafe</a></code> should be prefered.</p></div></div><h1 id="g:2">inverse computing</h1><div class="top"><p class="src"><a id="v:inverse" class="def">inverse</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> <a href="src/Crypto-Number-ModArithmetic.html#inverse" class="link">Source</a> <a href="#v:inverse" class="selflink">#</a></p><div class="doc"><p>inverse computes the modular inverse as in g^(-1) mod m</p></div></div><div class="top"><p class="src"><a id="v:inverseCoprimes" class="def">inverseCoprimes</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> <a href="src/Crypto-Number-ModArithmetic.html#inverseCoprimes" class="link">Source</a> <a href="#v:inverseCoprimes" class="selflink">#</a></p><div class="doc"><p>Compute the modular inverse of 2 coprime numbers.
This is equivalent to inverse except that the result
is known to exists.</p><p>if the numbers are not defined as coprime, this function
will raise a CoprimesAssertionError.</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.2</p></div></body></html>
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