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75 lines
1.8 KiB
Plaintext
75 lines
1.8 KiB
Plaintext
/*
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* psqrt - calculate square roots modulo a prime
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*
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* Copyright (C) 1999 David I. Bell
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
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*
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* @(#) $Revision: 29.1 $
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* @(#) $Id: psqrt.cal,v 29.1 1999/12/14 09:15:32 chongo Exp $
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* @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/psqrt.cal,v $
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*
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* Under source code control: 1990/02/15 01:50:35
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* File existed as early as: before 1990
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*
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* Share and enjoy! :-) http://reality.sgi.com/chongo/tech/comp/calc/
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*/
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/*
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* Returns null if number is not prime or if there is no square root.
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* The smaller square root is always returned.
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*/
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define psqrt(u, p)
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{
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local p1, q, n, y, r, v, w, t, k;
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p1 = p - 1;
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r = lowbit(p1);
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q = p >> r;
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t = 1 << (r - 1);
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for (n = 2; ; n++) {
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if (ptest(n, 1) == 0)
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continue;
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y = pmod(n, q, p);
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k = pmod(y, t, p);
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if (k == 1)
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continue;
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if (k != p1)
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return;
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break;
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}
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t = pmod(u, (q - 1) / 2, p);
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v = (t * u) % p;
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w = (t^2 * u) % p;
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while (w != 1) {
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k = 0;
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t = w;
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do {
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k++;
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t = t^2 % p;
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} while (t != 1);
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if (k == r)
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return;
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t = pmod(y, 1 << (r - k - 1), p);
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y = t^2 % p;
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v = (v * t) % p;
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w = (w * y) % p;
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r = k;
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}
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return min(v, p - v);
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}
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