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/*
Author: Pate Williams (c) 1997
2.149 Algorithm Jacobi symbol (and Legendre
symbol) computation
See "Hanbook of Applied Cryptography" by
Alfred J. Menezes et al page 73.
*/
#include
int JACOBI(long a, long n)
{
int s;
long a1, b = a, e = 0, m, n1;
if (a == 0) return 0;
if (a == 1) return 1;
while ((b & 1) == 0)
b >>= 1, e++;
a1 = b;
m = n % 8;
if (!(e & 1)) s = 1;
else if (m == 1 || m == 7) s = + 1;
else if (m == 3 || m == 5) s = - 1;
if (n % 4 == 3 && a1 % 4 == 3) s = - s;
if (a1 != 1) n1 = n % a1; else n1 = 1;
return s * JACOBI(n1, a1);
}
int main(void)
{
int j, k;
long a = 158, n = 235;
printf("a = %ld n = %ld (a / n) = %ld\n",
a, n, JACOBI(a, n));
for (a = 1; a < 21; a++) {
j = JACOBI(a, 3);
k = JACOBI(a, 7);
if (j != 0 && k != 0)
printf("%2ld %2ld %2d %2d %2d\n", a, a * a % 21,
j, k, JACOBI(a, 21));
}
return 0;
}