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-<head>
-<title>prime(3) - Plan 9 from User Space</title>
-<meta content="text/html; charset=utf-8" http-equiv=Content-Type>
-</head>
-<body bgcolor=#ffffff>
-<table border=0 cellpadding=0 cellspacing=0 width=100%>
-<tr height=10><td>
-<tr><td width=20><td>
-<tr><td width=20><td><b>PRIME(3)</b><td align=right><b>PRIME(3)</b>
-<tr><td width=20><td colspan=2>
- <br>
-<p><font size=+1><b>NAME </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- genprime, gensafeprime, genstrongprime, DSAprimes, probably_prime,
- smallprimetest &ndash; prime number generation<br>
-
-</table>
-<p><font size=+1><b>SYNOPSIS </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- <tt><font size=+1>#include &lt;u.h&gt;<br>
- #include &lt;libc.h&gt;<br>
- #include &lt;mp.h&gt;<br>
- #include &lt;libsec.h&gt;
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>int &nbsp;&nbsp;&nbsp;smallprimetest(mpint *p)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>int &nbsp;&nbsp;&nbsp;probably_prime(mpint *p, int nrep)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>void genprime(mpint *p, int n, int nrep)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>void gensafeprime(mpint *p, mpint *alpha, int n, int accuracy)
-
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>void genstrongprime(mpint *p, int n, int nrep)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>void DSAprimes(mpint *q, mpint *p, uchar seed[SHA1dlen])<br>
- </font></tt>
-</table>
-<p><font size=+1><b>DESCRIPTION </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
-
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- Public key algorithms abound in prime numbers. The following routines
- generate primes or test numbers for primality.
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
-
- <i>Smallprimetest</i> checks for divisibility by the first 10000 primes.
- It returns 0 if <i>p</i> is not divisible by the primes and &ndash;1 if it is.
-
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
-
- <i>Probably_prime</i> uses the Miller-Rabin test to test <i>p</i>. It returns
- non-zero if <i>P</i> is probably prime. The probability of it not being
- prime is 1/4**<i>nrep</i>.
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
-
- <i>Genprime</i> generates a random <i>n</i> bit prime. Since it uses the Miller-Rabin
- test, <i>nrep</i> is the repetition count passed to <i>probably_prime</i>. <i>Gensafegprime</i>
- generates an <i>n</i>-bit prime <i>p</i> and a generator <i>alpha</i> of the multiplicative
- group of integers mod <i>p</i>; there is a prime <i>q</i> such that <i>p-1=2*q</i>.
- <i>Genstrongprime</i> generates a
- prime, <i>p</i>, with the following properties:<br>
- &ndash;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(<i>p</i>-1)/2 is prime. Therefore <i>p</i>-1 has a large prime factor, <i>p</i>&#8217;.<br>
- &ndash;<i>p</i>&#8217;-1 has a large prime factor<br>
- &ndash;<i>p</i>+1 has a large prime factor
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
-
- <i>DSAprimes</i> generates two primes, <i>q</i> and <i>p,</i> using the NIST recommended
- algorithm for DSA primes. <i>q</i> divides <i>p</i>-1. The random seed used
- is also returned, so that skeptics can later confirm the computation.
- Be patient; this is a slow algorithm.<br>
-
-</table>
-<p><font size=+1><b>SOURCE </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- <tt><font size=+1>/usr/local/plan9/src/libsec<br>
- </font></tt>
-</table>
-<p><font size=+1><b>SEE ALSO </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- <a href="../man3/aes.html"><i>aes</i>(3)</a> <a href="../man3/blowfish.html"><i>blowfish</i>(3)</a>, <a href="../man3/des.html"><i>des</i>(3)</a>, <a href="../man3/elgamal.html"><i>elgamal</i>(3)</a>, <a href="../man3/rsa.html"><i>rsa</i>(3)</a>,<br>
-
-</table>
-
-<td width=20>
-<tr height=20><td>
-</table>
-<!-- TRAILER -->
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