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psqrt.cal
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1995-07-17
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/*
* Copyright (c) 1993 David I. Bell
* Permission is granted to use, distribute, or modify this source,
* provided that this copyright notice remains intact.
*
* Calculate square roots modulo a prime.
*
* Returns null if number is not prime or if there is no square root.
* The smaller square root is always returned.
*/
define psqrt(u, p)
{
local p1, q, n, y, r, v, w, t, k;
p1 = p - 1;
r = lowbit(p1);
q = p >> r;
t = 1 << (r - 1);
for (n = 2; ; n++) {
if (ptest(n, 1) == 0)
continue;
y = pmod(n, q, p);
k = pmod(y, t, p);
if (k == 1)
continue;
if (k != p1)
return;
break;
}
t = pmod(u, (q - 1) / 2, p);
v = (t * u) % p;
w = (t^2 * u) % p;
while (w != 1) {
k = 0;
t = w;
do {
k++;
t = t^2 % p;
} while (t != 1);
if (k == r)
return;
t = pmod(y, 1 << (r - k - 1), p);
y = t^2 % p;
v = (v * t) % p;
w = (w * y) % p;
r = k;
}
return min(v, p - v);
}
global lib_debug;
if (lib_debug >= 0) {
print "psqrt(u, p) defined";
}