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README.html
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<!-- 2018-12-23 Sun 21:01 -->
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<div id="content">
<div id="outline-container-org0fca829" class="outline-2">
<h2 id="org0fca829"><span class="section-number-2">1</span> RSA-criptography-hs</h2>
<div class="outline-text-2" id="text-1">
<p>
The RSA criptography in haskell, made for learning purposes.
How to use:
</p>
</div>
<div id="outline-container-org37278ad" class="outline-3">
<h3 id="org37278ad"><span class="section-number-3">1.1</span> If you already have the public and private keys:</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Just call the functions encrypt m (e, n) and decript c (d, n ). d, n = private key; e,n = public key.
</p>
</div>
</div>
<div id="outline-container-org82d55a2" class="outline-3">
<h3 id="org82d55a2"><span class="section-number-3">1.2</span> If you do not have the keys:</h3>
<div class="outline-text-3" id="text-1-2">
<p>
Call the function rsaE m seed, and provide your number m - that you want to encript - and a random seed. To decript do the same
thing with rsaD m seed, providing your number and the same seed.
</p>
</div>
</div>
<div id="outline-container-org132e357" class="outline-3">
<h3 id="org132e357"><span class="section-number-3">1.3</span> Steps:</h3>
<div class="outline-text-3" id="text-1-3">
<ul class="org-ul">
<li>Choose two different prime numbers:
The easiest way to do this was with the method ramdomRIO (a,b), but, as this was made for learning purposes, I chose to use
randomR instead. The difference is that randomR needs a random number generator g, which is provided by the seed 'k'.</li>
<li><p>
Calculate the totient;
</p>
<p>
if x /= y then return ((x - 1) * (y -1))
</p></li>
</ul>
<ul class="org-ul">
<li><p>
Choose an integer e that is coprime to the totient. "e" is the public key exponent;
</p>
<p>
publicKey :: Integer -> Integer -> Int -> Integer -> IO Integer
publicKey m n k e = do
</p>
<p>
y <- calculateTotient m n k
if (gcd e y) == 1
then return e
else publicKey m n k (e + 1)
</p></li>
</ul>
<ul class="org-ul">
<li>Compute d = 1 + k*totient(n)."d" is kept as the private key exponent;</li>
<li><p>
Just encript or decript:
</p>
<p>
encrypt :: Integer -> (Integer, Integer) -> Integer
encrypt m (e, n) = ((m<sup>e</sup>) `mod` n)
</p>
<p>
decript :: Integer -> (Integer, Integer) -> Integer
decript c (d, n ) = (c<sup>d</sup> `mod` n)
</p></li>
</ul>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="date">Created: 2018-12-23 Sun 21:01</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>