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57 lines
1000 B
Plaintext
57 lines
1000 B
Plaintext
/*
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* Copyright (c) 1995 David I. Bell
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* Permission is granted to use, distribute, or modify this source,
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* provided that this copyright notice remains intact.
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*
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* Calculate square roots modulo a prime.
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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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global lib_debug;
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if (lib_debug >= 0) {
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print "psqrt(u, p) defined";
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}
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