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pairing.c
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pairing.c
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/*
* Copyright 2016 naehrwert
* Licensed under the terms of the GNU GPL, version 2
* http://www.gnu.org/licenses/old-licenses/gpl-2.0.txt
*/
#include <assert.h>
#include <stdlib.h>
#include "pairing.h"
poly_t *_pairing_line(poly_t *d, ec_pqr_point_t *P, ec_pqr_point_t *R, ec_pqr_point_t *Q, ec_pqr_group_t *ecg)
{
if (ec_pqr_point_is_zero(P) || ec_pqr_point_is_zero(R))
{
if (ec_pqr_point_cmp(P, R) == POINT_CMP_E)
return poly_one(d);
if (ec_pqr_point_is_zero(P))
return pqr_sub(d, Q->x, R->x, ecg->p);
if (ec_pqr_point_is_zero(R))
return pqr_sub(d, Q->x, P->x, ecg->p);
}
else if (ec_pqr_point_cmp(P, R) != POINT_CMP_E)
{
if (poly_cmp(P->x, R->x) == POLY_CMP_E)
return pqr_sub(d, Q->x, P->x, ecg->p);
poly_t *l = poly_alloc(d->degree, d->N, 1);
pqr_sub(l, R->x, P->x, ecg->p); //l = R.x - P.x
pqr_inv(d, l, ecg->p); //d = 1 / (R.x - P.x)
pqr_sub(l, R->y, P->y, ecg->p); //l = R.y - P.y
pqr_mul(l, l, d, ecg->p); //l = (R.y - P.y) / (R.x - P.x)
pqr_sub(d, Q->x, P->x, ecg->p); //d = Q.x - P.x
pqr_mul(l, l, d, ecg->p); //l = l * (Q.x - P.x)
pqr_sub(d, Q->y, P->y, ecg->p); //d = Q.y - P.y
pqr_sub(d, d, l, ecg->p); //d = Q.y - P.y - l * (Q.x - P.x)
poly_free(l, 1);
return d;
}
poly_t *t = poly_alloc(d->degree, d->N, 1);
poly_t *s = poly_alloc(d->degree, d->N, 1);
pqr_mul(t, P->x, P->x, ecg->p); //t = P.x*P.x
pqr_add(s, t, t, ecg->p); //s = 2*P.x*P.x
pqr_add(s, s, t, ecg->p); //s = 3*P.x*P.x
pqr_add(s, s, ecg->a, ecg->p); //s = 3*px*px + a
pqr_add(t, P->y, P->y, ecg->p); //t = 2*py
if (poly_is_zero(t))
pqr_sub(d, Q->x, P->x, ecg->p);
else
{
pqr_inv(t, t, ecg->p); //t = 1 / (2*py)
pqr_mul(s, s, t, ecg->p); //s = (3*px*px + a) / (2*py)
pqr_sub(t, Q->x, P->x, ecg->p); //t = Q.x - P.x
pqr_mul(s, s, t, ecg->p); //s = s * (Q.x - P.x)
pqr_sub(d, Q->y, P->y, ecg->p); //d = Q.y - P.y
pqr_sub(d, d, s, ecg->p); //d = Q.y - P.y - s * (Q.x - P.x)
}
poly_free(s, 1);
poly_free(t, 1);
return d;
}
poly_t *_pairing_miller(poly_t *d, ec_pqr_point_t *P, ec_pqr_point_t *Q, bn_t *n, ec_pqr_group_t *ecg)
{
assert(!ec_pqr_point_is_zero(Q));
assert(!bn_is_zero(n));
int i;
ec_pqr_point_t *R = ec_pqr_point_copy(ec_pqr_point_alloc(ecg), P);
ec_pqr_point_t *S = ec_pqr_point_alloc(ecg);
poly_t *l = poly_alloc(d->degree, d->N, 1);
poly_t *v = poly_alloc(d->degree, d->N, 1);
poly_one(d);
for (i = bn_maxbit(n) - 1; i >= 0; i--)
{
ec_pqr_point_double(S, R, ecg); //S = [2]R
_pairing_line(l, R, R, Q, ecg); //l_{R,R}
ec_pqr_point_neg(R, S, ecg);
_pairing_line(v, S, R, Q, ecg);
pqr_inv(v, v, ecg->p); //1 / v_{[2]R}
pqr_mul(d, d, d, ecg->p);
pqr_mul(d, d, l, ecg->p);
pqr_mul(d, d, v, ecg->p); //d = d^2 * l_{R,R} / v_{[2]R}
ec_pqr_point_copy(R, S);
if (!bn_getbit(n, i))
continue;
ec_pqr_point_add(S, R, P, ecg); //S = R + P
_pairing_line(l, R, P, Q, ecg); //l_{R,P}
ec_pqr_point_neg(R, S, ecg);
_pairing_line(v, S, R, Q, ecg);
pqr_inv(v, v, ecg->p); //1 / v_{R+P}
pqr_mul(d, d, l, ecg->p);
pqr_mul(d, d, v, ecg->p); //d = d * l_{R,P} / v_{R+P}
ec_pqr_point_copy(R, S);
}
poly_free(v, 1);
poly_free(l, 1);
ec_pqr_point_free(S);
ec_pqr_point_free(R);
return d;
}
poly_t *pairing_weil(poly_t *d, ec_pqr_point_t *P, ec_pqr_point_t *Q, bn_t *n, ec_pqr_group_t *ecg)
{
poly_t *t = poly_alloc(d->degree, d->N, 1);
//d = f_{n,P}(D_Q) / f_{n,Q}(D_P)
_pairing_miller(d, P, Q, n, ecg);
_pairing_miller(t, Q, P, n, ecg);
pqr_inv(t, t, ecg->p);
pqr_mul(d, d, t, ecg->p);
if (bn_getbit(n, 0))
{
//d = -d
poly_zero(t);
pqr_sub(d, t, d, ecg->p);
}
poly_free(t, 1);
return d;
}
/*poly_t *pairing_tate(poly_t *d, ec_pqr_point_t *P, ec_pqr_point_t *Q, bn_t *n, bn_t *k, ec_pqr_group_t *ecg)
{
bn_t *e = bn_alloc(ecg->p->N->n);
_pairing_miller(d, P, Q, n, ecg);
//(q^k - 1) / n
bn_exp(e, ecg->p->N, k);
bn_sub(e, e, one);
bn_div(e, e, n);
pqr_exp(d, d, e, ecg->p);
bn_free(e);
return d;
}*/