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/*
Author: Pate Williams (c) 1997
Addition chain exponentiation. See "Handbook of
Applied Cryptography" by Alfred J. Menezes et al
14.6.2 Section pages 620 - 623.
*/
#include
#include
#include
#include "lip.h"
#define DEBUG
void long_to_binary(long a, long *e, long *t)
{
long i;
*t = z2logs(a);
for (i = 0; i < *t; i++) {
e[i] = a & 1;
a >>= 1;
}
}
void addition_chain(long exp, verylong zg, verylong *zge)
{
int found;
long I[65][2], d[32], e[32], i, j, k, s, t, u[65];
verylong *zg1;
long_to_binary(exp, e, &t);
for (i = 0, j = t - 1; j >= 0; i++, j--) d[i] = e[j];
u[0] = 1, u[1] = 2 * d[0], u[2] = u[1] + d[1];
for (s = 3, j = 2; j < t; s += 2, j++)
u[s] = 2 * u[s - 1], u[s + 1] = u[s] + d[j];
zg1 = calloc(s, sizeof(verylong));
assert(zg1 != 0);
for (i = 1; i < s; i++) {
found = 0;
for (j = 0; !found && j < i; j++)
for (k = 0; !found && k < i; k++)
if (u[i] == u[j] + u[k])
found = 1, I[i][0] = j, I[i][1] = k;
}
#ifdef DEBUG
for (i = 0; i < s; i++)
printf("%ld ", u[i]);
printf("\n");
for (i = 1; i < s; i++)
printf("%ld %ld %ld\n", i, I[i][0], I[i][1]);
#endif
zcopy(zg, &zg1[0]);
for (i = 1; i < s; i++)
zmul(zg1[I[i][0]], zg1[I[i][1]], &zg1[i]);
zcopy(zg1[s - 1], zge);
free(zg1);
}
void main(void)
{
long exp = 143l;
verylong za = 0, zg = 0, zge = 0;
zintoz(2l, &zg);
addition_chain(exp, zg, &zge);
zwriteln(zge);
zsexp(zg, exp, &za);
zwriteln(za);
zfree(&za);
zfree(&zg);
zfree(&zge);
}