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/*
* psqrt - calculate square roots modulo a prime
*
* Copyright (C) 1999 David I. Bell
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 1990/02/15 01:50:35
* File existed as early as: before 1990
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* 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);
}