2012-02-14 18:45:18 +00:00
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<html>
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<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
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<title> RSA Interactive Simulator : Key Generation </title>
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<h1> RSA Interactive Simulator / Work Bench : Key Generation </h1>
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<h3>
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This RSA key generator, will lead you though making a key set.
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You may at anytime enter your own values into the forms, or
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use the ones calculated for you.
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</h3>
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<h3>
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Use the BACK button on your browser
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at your peril !
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</h3>
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<p>
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The first stage of RSA key generation is to choose two large
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prime numbers,
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p and q.
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A php utility to find prime numbers up to
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2 Billion (i.e. 2 000 000 000 ) is provided below.
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This is adequate for 56 bit RSA encryption simulations.
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This script has a 30 second processing time
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limitation which will interrupt the program if a
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very large range is given. Best to play with this a little...
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</p>
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<p>
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Pick some two of the prime numbers offered and cut and
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paste them into the form for further use.
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</p>
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<p>
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For full RSA simulations a <a href="bc.html"> bc </a>
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based prime number finder is provided as
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<a href="bc_primes.zip"> source code </a>
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and on-line <a href="bc_primes.php"> here </a>.
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</p>
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2012-02-17 13:18:51 +00:00
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<?
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// for php5 must do this to catch all the variables...
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$c = $_POST['c'];
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$m = $_POST['m'];
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$e = $_POST['e'];
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$e = $_POST['e'];
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$d = $_POST['d'];
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$p = $_POST['p'];
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$n = $_POST['n'];
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$q = $_POST['q'];
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$phi = $_POST['phi'];
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$mprivate = $_POST['mprivate'];
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?>
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2012-02-14 18:45:18 +00:00
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<br> <br> <A name="PRIME">
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<hr>
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<h2> FIND SUITABLE PRIMES </h2>
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<hr> <br> <br>
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<form enctype="multipart/form-data" method="post"
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action="primes.php">
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<strong>Prime Number Finder</strong>
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<small>Taken (and modified slightly) from
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<a href="http://www.planet-source-code.com/vb/scripts/ShowCode.asp?txtCodeId=1273&lngWId=8"> Prime Number finder 2 </a></small>
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<table border=2>
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<tr>
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<td>
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<strong>Min</strong>
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</td>
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<td>
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<input type=text name="x" size=120 value="100" colspan=2>
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</td>
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</tr>
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<tr>
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<td>
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<strong>max</strong>
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</td>
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<td>
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<input type=text name="i" size=120 value="1000" colspan=2>
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</td>
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</tr>
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<input type="hidden" name=p value=<? echo $p ?>>
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<input type="hidden" name=q value=<? echo $q ?>>
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<input type="hidden" name=phi value=<? echo $phi ?>>
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<input type="hidden" name=e value=<? echo $e ?>>
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<input type="hidden" name=n value=<? echo $n ?>>
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<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
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</table>
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</form>
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<br> <br><a name="MUL">
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<hr>
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<h2> FIND THE MODULUS OF THE PRIMES </h2>
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<hr>
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These when multiplied together,
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should be as large as the encryption
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key being used (for instance a 128 bit key has
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approx ln(2^128)/ln(10) == 39 decimal digits), note
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that this has already exceeded the 52 bits of
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precision of <b> double precision </b>
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maths as defined by the
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<a href="http://www.freesoft.org/CIE/RFC/1832/10.htm"> IEEE </a>
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<p>
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Test your values of P and Q here
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<form enctype="multipart/form-data" method="post"
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action="multiply.php">
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<strong>Multiply P and Q </strong>
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<table border=2>
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<tr>
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<td>
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<strong>Min</strong>
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</td>
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<td>
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<input type=text name="p" size=120 value="<? echo $p ?>" >
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</td>
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</tr>
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<tr>
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<td>
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<strong>max</strong>
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</td>
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<td>
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<input type=text name="q" size=120 value="<? echo $q ?>" >
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</td>
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</tr>
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<input type="hidden" name=phi value=<? echo $phi ?>>
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<input type="hidden" name=e value=<? echo $e ?>>
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<input type="hidden" name=n value=<? echo $n ?>>
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<input type="hidden" name=mprivate value=<? echo $mprivate ?>>
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<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
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</table>
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</form>
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</p>
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<br> <br> <A NAME="PHI">
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<hr>
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<h2> FIND PHI</h2>
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<hr>
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<p>
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When you have chosen your two prime numbers.....we need to find <strong> phi == (p-1)(q-1) </strong>
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</p>
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<form enctype="multipart/form-data" method="post"
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action="find_phi.php">
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<strong>RSA p and q</strong>
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<table border=2>
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<tr>
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<td>
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<strong>p</strong>
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</td>
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<td>
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<input type=text name="p" size=120 value="<? echo $p ?>" >
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</td>
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</tr>
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<tr>
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<td>
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<strong>q</strong>
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</td>
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<td>
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<input type=text name="q" size=120 value="<? echo $q ?>" >
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</td>
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</tr>
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<input type="hidden" name=phi value=<? echo $phi ?>>
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<input type="hidden" name=e value=<? echo $e ?>>
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<input type="hidden" name=n value=<? echo $n ?>>
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<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
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</table>
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</table>
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</form>
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<br> <br> <A name="GCD">
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<hr>
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<h2> GREATEST COMMON DENOMINATOR </h2>
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<hr>
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<p>
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We now need to find a small number 'e' which is co-prime to phi.
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This number may therefore be any number you choose, (except 1, which would be unsafe cryptographically) as long as it is <b> co-prime to phi </b>.
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This number forms the second part of your public key.
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Hints to <a href="hints_to_choosing_e.html"> choosing e </a>.
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</p>
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<p>
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Note that this calls the gcd (greatest common denominator) function
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which returns 1 when co-prime values are entered.
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</p>
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<form enctype="multipart/form-data" method="post"
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action="gcd.php">
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<strong>RSA e and phi </strong>
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<table border=2>
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<tr>
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<td>
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<strong>e</strong>
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</td>
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<td>
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<input type=text name="e" size=120 value="<? echo $e ?>">
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</td>
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</tr>
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<tr>
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<td>
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<strong>phi</strong>
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</td>
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<td>
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<input type=text name="phi" size=120 value="<? echo $phi ?>">
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</td>
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</tr>
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<input type="hidden" name=p value=<? echo $p ?>>
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<input type="hidden" name=q value=<? echo $q ?>>
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<input type="hidden" name=n value=<? echo $n ?>>
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<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
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</table>
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</form>
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<br> <br>
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<hr>
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<h2> FIND D </h2>
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<hr>
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<p>
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We now need to find a number 'd' so that <strong> d.e % phi == 1 </strong>
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This number will be your private key.</p>
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Enter a seed value for D or calculate it yourself.
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If the number typed obeys <strong> d.e % phi == 1 </strong>
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it will be used, otherwise it will be used as a start seed value.
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Leave blank to iterate to find lowest d value.
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Note on the algorithm used are <a href="find_d.html"> here </a>
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<A name="D">
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<form enctype="multipart/form-data" method="post"
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action="find_d.php">
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<strong>RSA find 'd'</strong>
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<table border=2>
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<tr>
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<td>
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<strong>d</strong>
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</td>
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<td>
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<input type=text name="d" size=120 value="<? echo $d ?>" >
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</td>
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</tr>
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<tr>
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<td>
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<strong>phi</strong>
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</td>
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<td width>
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<input type=text name="phi" size=120 value="<? echo $phi ?>">
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</td>
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</tr>
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<input type="hidden" name=e value=<? echo $e ?>>
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<input type="hidden" name=p value=<? echo $p ?>>
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<input type="hidden" name=q value=<? echo $q ?>>
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<input type="hidden" name=n value=<? echo $n ?>>
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<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
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</table>
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</table>
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</form>
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<br> <br> <A name="KEYS">
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<hr>
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<h2> RSA KEYSET </h2>
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<hr>
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<table>
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<tr>
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<td>
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<table border=4>
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<tr>
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<td colspan=2>
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<strong> PUBLIC KEY </strong>
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</td>
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</tr>
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<tr>
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<td>
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MODULUS (n)
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</td>
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<td>
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<? echo $n ?>
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</td>
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</tr>
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<tr>
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<td>
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Public Key (e)
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</td>
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<td>
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<? echo $e ?>
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</td>
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</tr>
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</table>
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</td>
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<td>
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<table border=4>
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<tr>
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<td colspan=2>
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<strong> PRIVATE KEY </strong>
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</td>
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</tr>
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<tr>
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<td>
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MODULUS (n)
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</td>
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<td>
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<? echo $n ?>
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</td>
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</tr>
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<tr>
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<td>
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Private Key (d)
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</td>
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<td>
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<? echo $d ?>
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</td>
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</tr>
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</table>
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</td>
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</tr>
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</table>
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<h3>
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Now we have an RSA key set, we can use these
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to send encrypted data both ways. A user seeing the
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public key can encrypt using it, and the receiving party
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de-crypts with the private key. Note that no other user
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can de-crypt the message without knowing (or finding by brute force)
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the private key.
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</h3>
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<table>
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<tr>
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<td>
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<form enctype="multipart/form-data" method="post"
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action="encode_pub.php">
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<input type="hidden" name=phi value=<? echo $phi ?>>
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<input type="hidden" name=d value=<? echo $d ?>>
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<input type="hidden" name=e value=<? echo $e ?>>
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<input type="hidden" name=p value=<? echo $p ?>>
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<input type="hidden" name=q value=<? echo $q ?>>
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<input type="hidden" name=n value=<? echo $n ?>>
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<tr><td><input type="submit" name="submit" value="Encode Using Public Key"> </td></tr>
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</table>
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</form>
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</td>
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<td>
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<center> <a href="index.php" border=0> <img src="home.png" border=0> </a> </center>
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<center>
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<a href="javascript:history.back();">
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<img src=back.png align=center border=0> </a>
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</center>
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</body>
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</html>
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