83 lines
1.2 KiB
C
83 lines
1.2 KiB
C
|
#include "os.h"
|
||
|
|
#include <mp.h>
|
||
|
|
|
||
|
|
// extended euclid
|
||
|
|
//
|
||
|
|
// For a and b it solves, d = gcd(a,b) and finds x and y s.t.
|
||
|
|
// ax + by = d
|
||
|
|
//
|
||
|
|
// Handbook of Applied Cryptography, Menezes et al, 1997, pg 67
|
||
|
|
|
||
|
|
void
|
||
|
|
mpeuclid(mpint *a, mpint *b, mpint *d, mpint *x, mpint *y)
|
||
|
|
{
|
||
|
|
mpint *tmp, *x0, *x1, *x2, *y0, *y1, *y2, *q, *r;
|
||
|
|
|
||
|
|
if(mpcmp(a, b) < 0){
|
||
|
|
tmp = a;
|
||
|
|
a = b;
|
||
|
|
b = tmp;
|
||
|
|
tmp = x;
|
||
|
|
x = y;
|
||
|
|
y = tmp;
|
||
|
|
}
|
||
|
|
|
||
|
|
if(b->top == 0){
|
||
|
|
mpassign(a, d);
|
||
|
|
mpassign(mpone, x);
|
||
|
|
mpassign(mpzero, y);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
a = mpcopy(a);
|
||
|
|
b = mpcopy(b);
|
||
|
|
x0 = mpnew(0);
|
||
|
|
x1 = mpcopy(mpzero);
|
||
|
|
x2 = mpcopy(mpone);
|
||
|
|
y0 = mpnew(0);
|
||
|
|
y1 = mpcopy(mpone);
|
||
|
|
y2 = mpcopy(mpzero);
|
||
|
|
q = mpnew(0);
|
||
|
|
r = mpnew(0);
|
||
|
|
|
||
|
|
while(b->top != 0 && b->sign > 0){
|
||
|
|
// q = a/b
|
||
|
|
// r = a mod b
|
||
|
|
mpdiv(a, b, q, r);
|
||
|
|
// x0 = x2 - qx1
|
||
|
|
mpmul(q, x1, x0);
|
||
|
|
mpsub(x2, x0, x0);
|
||
|
|
// y0 = y2 - qy1
|
||
|
|
mpmul(q, y1, y0);
|
||
|
|
mpsub(y2, y0, y0);
|
||
|
|
// rotate values
|
||
|
|
tmp = a;
|
||
|
|
a = b;
|
||
|
|
b = r;
|
||
|
|
r = tmp;
|
||
|
|
tmp = x2;
|
||
|
|
x2 = x1;
|
||
|
|
x1 = x0;
|
||
|
|
x0 = tmp;
|
||
|
|
tmp = y2;
|
||
|
|
y2 = y1;
|
||
|
|
y1 = y0;
|
||
|
|
y0 = tmp;
|
||
|
|
}
|
||
|
|
|
||
|
|
mpassign(a, d);
|
||
|
|
mpassign(x2, x);
|
||
|
|
mpassign(y2, y);
|
||
|
|
|
||
|
|
mpfree(x0);
|
||
|
|
mpfree(x1);
|
||
|
|
mpfree(x2);
|
||
|
|
mpfree(y0);
|
||
|
|
mpfree(y1);
|
||
|
|
mpfree(y2);
|
||
|
|
mpfree(q);
|
||
|
|
mpfree(r);
|
||
|
|
mpfree(a);
|
||
|
|
mpfree(b);
|
||
|
|
}
|