Exemplo n.º 1
0
/**
 * Doubles a point represented in affine coordinates on an ordinary prime
 * elliptic curve.
 *
 * @param[out] r			- the result.
 * @param[out] s			- the resulting slope.
 * @param[in] p				- the point to double.
 */
static void ep2_dbl_basic_imp(ep2_t r, fp2_t s, ep2_t p) {
	fp2_t t0, t1, t2;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);

		/* t0 = 1/(2 * y1). */
		fp2_dbl(t0, p->y);
		fp2_inv(t0, t0);

		/* t1 = 3 * x1^2 + a. */
		fp2_sqr(t1, p->x);
		fp2_copy(t2, t1);
		fp2_dbl(t1, t1);
		fp2_add(t1, t1, t2);

		ep2_curve_get_a(t2);
		fp2_add(t1, t1, t2);

		/* t1 = (3 * x1^2 + a)/(2 * y1). */
		fp2_mul(t1, t1, t0);

		if (s != NULL) {
			fp2_copy(s, t1);
		}

		/* t2 = t1^2. */
		fp2_sqr(t2, t1);

		/* x3 = t1^2 - 2 * x1. */
		fp2_dbl(t0, p->x);
		fp2_sub(t0, t2, t0);

		/* y3 = t1 * (x1 - x3) - y1. */
		fp2_sub(t2, p->x, t0);
		fp2_mul(t1, t1, t2);

		fp2_sub(r->y, t1, p->y);

		fp2_copy(r->x, t0);
		fp2_copy(r->z, p->z);

		r->norm = 1;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
	}
}
Exemplo n.º 2
0
void fp6_inv(fp6_t c, fp6_t a) {
	fp2_t v0;
	fp2_t v1;
	fp2_t v2;
	fp2_t t0;

	fp2_null(v0);
	fp2_null(v1);
	fp2_null(v2);
	fp2_null(t0);

	TRY {
		fp2_new(v0);
		fp2_new(v1);
		fp2_new(v2);
		fp2_new(t0);

		/* v0 = a_0^2 - E * a_1 * a_2. */
		fp2_sqr(t0, a[0]);
		fp2_mul(v0, a[1], a[2]);
		fp2_mul_nor(v2, v0);
		fp2_sub(v0, t0, v2);

		/* v1 = E * a_2^2 - a_0 * a_1. */
		fp2_sqr(t0, a[2]);
		fp2_mul_nor(v2, t0);
		fp2_mul(v1, a[0], a[1]);
		fp2_sub(v1, v2, v1);

		/* v2 = a_1^2 - a_0 * a_2. */
		fp2_sqr(t0, a[1]);
		fp2_mul(v2, a[0], a[2]);
		fp2_sub(v2, t0, v2);

		fp2_mul(t0, a[1], v2);
		fp2_mul_nor(c[1], t0);

		fp2_mul(c[0], a[0], v0);

		fp2_mul(t0, a[2], v1);
		fp2_mul_nor(c[2], t0);

		fp2_add(t0, c[0], c[1]);
		fp2_add(t0, t0, c[2]);
		fp2_inv(t0, t0);

		fp2_mul(c[0], v0, t0);
		fp2_mul(c[1], v1, t0);
		fp2_mul(c[2], v2, t0);
	} CATCH_ANY {
		THROW(ERR_CAUGHT);
	} FINALLY {
		fp2_free(v0);
		fp2_free(v1);
		fp2_free(v2);
		fp2_free(t0);
	}
}
Exemplo n.º 3
0
void ep2_rhs(fp2_t rhs, ep2_t p) {
	fp2_t t0;
	fp2_t t1;

	fp2_null(t0);
	fp2_null(t1);

	TRY {
		fp2_new(t0);
		fp2_new(t1);

		/* t0 = x1^2. */
		fp2_sqr(t0, p->x);
		/* t1 = x1^3. */
		fp2_mul(t1, t0, p->x);

		ep2_curve_get_a(t0);
		fp2_mul(t0, p->x, t0);
		fp2_add(t1, t1, t0);

		ep2_curve_get_b(t0);
		fp2_add(t1, t1, t0);

		fp2_copy(rhs, t1);

	} CATCH_ANY {
		THROW(ERR_CAUGHT);
	} FINALLY {
		fp2_free(t0);
		fp2_free(t1);
	}
}
Exemplo n.º 4
0
/**
 * Doubles a point represented in affine coordinates on an ordinary prime
 * elliptic curve.
 *
 * @param[out] r				- the result.
 * @param[in] p					- the point to double.
 */
static void ep2_dbl_projc_imp(ep2_t r, ep2_t p) {
	fp2_t t0, t1, t2, t3;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);
	fp2_null(t3);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);
		fp2_new(t3);

		fp2_sqr(t0, p->x);
		fp2_add(t2, t0, t0);
		fp2_add(t0, t2, t0);

		fp2_sqr(t3, p->y);
		fp2_mul(t1, t3, p->x);
		fp2_add(t1, t1, t1);
		fp2_add(t1, t1, t1);
		fp2_sqr(r->x, t0);
		fp2_add(t2, t1, t1);
		fp2_sub(r->x, r->x, t2);
		fp2_mul(r->z, p->z, p->y);
		fp2_add(r->z, r->z, r->z);
		fp2_add(t3, t3, t3);

		fp2_sqr(t3, t3);
		fp2_add(t3, t3, t3);
		fp2_sub(t1, t1, r->x);
		fp2_mul(r->y, t0, t1);
		fp2_sub(r->y, r->y, t3);

		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
		fp2_free(t3);
	}
}
Exemplo n.º 5
0
/**
 * Compute the Miller loop for pairings of type G_1 x G_2 over the bits of a
 * given parameter.
 *
 * @param[out] r			- the result.
 * @param[out] t			- the resulting point.
 * @param[in] p				- the first pairing argument in affine coordinates.
 * @param[in] q				- the second pairing argument in affine coordinates.
 * @param[in] a				- the loop parameter.
 */
static void pp_mil_lit_k2(fp2_t r, ep_t *t, ep_t *p, ep_t *q, int m, bn_t a) {
	fp2_t l, _l;
	ep_t _q[m];
	int i, j;

	fp2_null(_l);
	ep_null(_q);

	TRY {
		fp2_new(_l);
		for (j = 0; j < m; j++) {
			ep_null(_q[j]);
			ep_new(_q[j]);
			ep_copy(t[j], p[j]);
			ep_neg(_q[j], q[j]);
		}

		for (i = bn_bits(a) - 2; i >= 0; i--) {
			fp2_sqr(r, r);
			for (j = 0; j < m; j++) {
				pp_dbl_k2(l, t[j], t[j], _q[j]);
				fp_copy(_l[0], l[1]);
				fp_copy(_l[1], l[0]);
				fp2_mul(r, r, _l);
				if (bn_get_bit(a, i)) {
					pp_add_k2(l, t[j], p[j], q[j]);
					fp_copy(_l[0], l[1]);
					fp_copy(_l[1], l[0]);
					fp2_mul(r, r, _l);
				}
			}
		}
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(_l);
		fp2_free(m);
		ep_free(_q);
	}
}
Exemplo n.º 6
0
int ep2_is_valid(ep2_t p) {
	ep2_t t;
	int r = 0;

	ep2_null(t);

	TRY {
		ep2_new(t);

		ep2_norm(t, p);

		ep2_rhs(t->x, t);
		fp2_sqr(t->y, t->y);

		r = (fp2_cmp(t->x, t->y) == CMP_EQ) || ep2_is_infty(p);
	} CATCH_ANY {
		THROW(ERR_CAUGHT);
	} FINALLY {
		ep2_free(t);
	}
	return r;
}
Exemplo n.º 7
0
/**
 * Doubles a point represented in affine coordinates on an ordinary prime
 * elliptic curve.
 *
 * @param[out] r			- the result.
 * @param[out] s			- the resulting slope.
 * @param[in] p				- the point to double.
 */
static void ep2_dbl_basic_imp(ep2_t r, fp2_t s, ep2_t p) {
	fp2_t t0, t1, t2;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);

		/* t0 = 1/(2 * y1). */
		fp2_dbl(t0, p->y);
		fp2_inv(t0, t0);

		/* t1 = 3 * x1^2 + a. */
		fp2_sqr(t1, p->x);
		fp2_copy(t2, t1);
		fp2_dbl(t1, t1);
		fp2_add(t1, t1, t2);

		if (ep2_curve_is_twist()) {
			switch (ep_curve_opt_a()) {
				case OPT_ZERO:
					break;
				case OPT_ONE:
					fp_set_dig(t2[0], 1);
					fp2_mul_art(t2, t2);
					fp2_mul_art(t2, t2);
					fp2_add(t1, t1, t2);
					break;
				case OPT_DIGIT:
					fp_set_dig(t2[0], ep_curve_get_a()[0]);
					fp2_mul_art(t2, t2);
					fp2_mul_art(t2, t2);
					fp2_add(t1, t1, t2);
					break;
				default:
					fp_copy(t2[0], ep_curve_get_a());
					fp_zero(t2[1]);
					fp2_mul_art(t2, t2);
					fp2_mul_art(t2, t2);
					fp2_add(t1, t1, t2);
					break;
			}
		}

		/* t1 = (3 * x1^2 + a)/(2 * y1). */
		fp2_mul(t1, t1, t0);

		if (s != NULL) {
			fp2_copy(s, t1);
		}

		/* t2 = t1^2. */
		fp2_sqr(t2, t1);

		/* x3 = t1^2 - 2 * x1. */
		fp2_dbl(t0, p->x);
		fp2_sub(t0, t2, t0);

		/* y3 = t1 * (x1 - x3) - y1. */
		fp2_sub(t2, p->x, t0);
		fp2_mul(t1, t1, t2);

		fp2_sub(r->y, t1, p->y);

		fp2_copy(r->x, t0);
		fp2_copy(r->z, p->z);

		r->norm = 1;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
	}
}
Exemplo n.º 8
0
/**
 * Doubles a point represented in affine coordinates on an ordinary prime
 * elliptic curve.
 *
 * @param[out] r				- the result.
 * @param[in] p					- the point to double.
 */
static void ep2_dbl_projc_imp(ep2_t r, ep2_t p) {
	fp2_t t0, t1, t2, t3, t4, t5;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);
	fp2_null(t3);
	fp2_null(t4);
	fp2_null(t5);

	TRY {
		if (ep_curve_opt_a() == OPT_ZERO) {
			fp2_new(t0);
			fp2_new(t1);
			fp2_new(t2);
			fp2_new(t3);
			fp2_new(t4);
			fp2_new(t5);

			fp2_sqr(t0, p->x);
			fp2_add(t2, t0, t0);
			fp2_add(t0, t2, t0);

			fp2_sqr(t3, p->y);
			fp2_mul(t1, t3, p->x);
			fp2_add(t1, t1, t1);
			fp2_add(t1, t1, t1);
			fp2_sqr(r->x, t0);
			fp2_add(t2, t1, t1);
			fp2_sub(r->x, r->x, t2);
			fp2_mul(r->z, p->z, p->y);
			fp2_add(r->z, r->z, r->z);
			fp2_add(t3, t3, t3);

			fp2_sqr(t3, t3);
			fp2_add(t3, t3, t3);
			fp2_sub(t1, t1, r->x);
			fp2_mul(r->y, t0, t1);
			fp2_sub(r->y, r->y, t3);
		} else {
			/* dbl-2007-bl formulas: 1M + 8S + 1*a + 10add + 1*8 + 2*2 + 1*3 */
			/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl */

			/* t0 = x1^2, t1 = y1^2, t2 = y1^4. */
			fp2_sqr(t0, p->x);
			fp2_sqr(t1, p->y);
			fp2_sqr(t2, t1);

			if (!p->norm) {
				/* t3 = z1^2. */
				fp2_sqr(t3, p->z);

				if (ep_curve_get_a() == OPT_ZERO) {
					/* z3 = 2 * y1 * z1. */
					fp2_mul(r->z, p->y, p->z);
					fp2_dbl(r->z, r->z);
				} else {
					/* z3 = (y1 + z1)^2 - y1^2 - z1^2. */
					fp2_add(r->z, p->y, p->z);
					fp2_sqr(r->z, r->z);
					fp2_sub(r->z, r->z, t1);
					fp2_sub(r->z, r->z, t3);
				}
			} else {
				/* z3 = 2 * y1. */
				fp2_dbl(r->z, p->y);
			}

			/* t4 = S = 2*((x1 + y1^2)^2 - x1^2 - y1^4). */
			fp2_add(t4, p->x, t1);
			fp2_sqr(t4, t4);
			fp2_sub(t4, t4, t0);
			fp2_sub(t4, t4, t2);
			fp2_dbl(t4, t4);

			/* t5 = M = 3 * x1^2 + a * z1^4. */
			fp2_dbl(t5, t0);
			fp2_add(t5, t5, t0);
			ep2_curve_get_a(t0);
			if (!p->norm) {
				fp2_sqr(t3, t3);
				fp2_mul(t1, t0, t3);
				fp2_add(t5, t5, t1);
			} else {
				fp2_add(t5, t5, t0);
			}

			/* x3 = T = M^2 - 2 * S. */
			fp2_sqr(r->x, t5);
			fp2_dbl(t1, t4);
			fp2_sub(r->x, r->x, t1);

			/* y3 = M * (S - T) - 8 * y1^4. */
			fp2_dbl(t2, t2);
			fp2_dbl(t2, t2);
			fp2_dbl(t2, t2);
			fp2_sub(t4, t4, r->x);
			fp2_mul(t5, t5, t4);
			fp2_sub(r->y, t5, t2);
		}

		r->norm = 0;


		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
		fp2_free(t3);
		fp2_free(t4);
		fp2_free(t5);
	}
}
Exemplo n.º 9
0
/**
 * Adds two points represented in affine coordinates on an ordinary prime
 * elliptic curve.
 *
 * @param r					- the result.
 * @param s					- the resulting slope.
 * @param p					- the first point to add.
 * @param q					- the second point to add.
 */
static void ep2_add_basic_imp(ep2_t r, fp2_t s, ep2_t p, ep2_t q) {
	fp2_t t0, t1, t2;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);

		/* t0 = x2 - x1. */
		fp2_sub(t0, q->x, p->x);
		/* t1 = y2 - y1. */
		fp2_sub(t1, q->y, p->y);

		/* If t0 is zero. */
		if (fp2_is_zero(t0)) {
			if (fp2_is_zero(t1)) {
				/* If t1 is zero, q = p, should have doubled. */
				ep2_dbl_basic(r, p);
			} else {
				/* If t1 is not zero and t0 is zero, q = -p and r = infty. */
				ep2_set_infty(r);
			}
		} else {
			/* t2 = 1/(x2 - x1). */
			fp2_inv(t2, t0);
			/* t2 = lambda = (y2 - y1)/(x2 - x1). */
			fp2_mul(t2, t1, t2);

			/* x3 = lambda^2 - x2 - x1. */
			fp2_sqr(t1, t2);
			fp2_sub(t0, t1, p->x);
			fp2_sub(t0, t0, q->x);

			/* y3 = lambda * (x1 - x3) - y1. */
			fp2_sub(t1, p->x, t0);
			fp2_mul(t1, t2, t1);
			fp2_sub(r->y, t1, p->y);

			fp2_copy(r->x, t0);
			fp2_copy(r->z, p->z);

			if (s != NULL) {
				fp2_copy(s, t2);
			}

			r->norm = 1;
		}
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
	}
}
Exemplo n.º 10
0
/**
 * Adds two points represented in projective coordinates on an ordinary prime
 * elliptic curve.
 *
 * @param r					- the result.
 * @param p					- the first point to add.
 * @param q					- the second point to add.
 */
static void ep2_add_projc_imp(ep2_t r, ep2_t p, ep2_t q) {
#if defined(EP_MIXED) && defined(STRIP)
	ep2_add_projc_mix(r, p, q);
#else /* General addition. */
	fp2_t t0, t1, t2, t3, t4, t5, t6;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);
	fp2_null(t3);
	fp2_null(t4);
	fp2_null(t5);
	fp2_null(t6);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);
		fp2_new(t3);
		fp2_new(t4);
		fp2_new(t5);
		fp2_new(t6);

		if (q->norm) {
			ep2_add_projc_mix(r, p, q);
		} else {
			/* t0 = z1^2. */
			fp2_sqr(t0, p->z);

			/* t1 = z2^2. */
			fp2_sqr(t1, q->z);

			/* t2 = U1 = x1 * z2^2. */
			fp2_mul(t2, p->x, t1);

			/* t3 = U2 = x2 * z1^2. */
			fp2_mul(t3, q->x, t0);

			/* t6 = z1^2 + z2^2. */
			fp2_add(t6, t0, t1);

			/* t0 = S2 = y2 * z1^3. */
			fp2_mul(t0, t0, p->z);
			fp2_mul(t0, t0, q->y);

			/* t1 = S1 = y1 * z2^3. */
			fp2_mul(t1, t1, q->z);
			fp2_mul(t1, t1, p->y);

			/* t3 = H = U2 - U1. */
			fp2_sub(t3, t3, t2);

			/* t0 = R = 2 * (S2 - S1). */
			fp2_sub(t0, t0, t1);

			fp2_dbl(t0, t0);

			/* If E is zero. */
			if (fp2_is_zero(t3)) {
				if (fp2_is_zero(t0)) {
					/* If I is zero, p = q, should have doubled. */
					ep2_dbl_projc(r, p);
				} else {
					/* If I is not zero, q = -p, r = infinity. */
					ep2_set_infty(r);
				}
			} else {
				/* t4 = I = (2*H)^2. */
				fp2_dbl(t4, t3);
				fp2_sqr(t4, t4);

				/* t5 = J = H * I. */
				fp2_mul(t5, t3, t4);

				/* t4 = V = U1 * I. */
				fp2_mul(t4, t2, t4);

				/* x3 = R^2 - J - 2 * V. */
				fp2_sqr(r->x, t0);
				fp2_sub(r->x, r->x, t5);
				fp2_dbl(t2, t4);
				fp2_sub(r->x, r->x, t2);

				/* y3 = R * (V - x3) - 2 * S1 * J. */
				fp2_sub(t4, t4, r->x);
				fp2_mul(t4, t4, t0);
				fp2_mul(t1, t1, t5);
				fp2_dbl(t1, t1);
				fp2_sub(r->y, t4, t1);

				/* z3 = ((z1 + z2)^2 - z1^2 - z2^2) * H. */
				fp2_add(r->z, p->z, q->z);
				fp2_sqr(r->z, r->z);
				fp2_sub(r->z, r->z, t6);
				fp2_mul(r->z, r->z, t3);
			}
		}
		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
		fp2_free(t3);
		fp2_free(t4);
		fp2_free(t5);
		fp2_free(t6);
	}
#endif
}
Exemplo n.º 11
0
/**
 * Adds a point represented in affine coordinates to a point represented in
 * projective coordinates.
 *
 * @param r					- the result.
 * @param s					- the slope.
 * @param p					- the affine point.
 * @param q					- the projective point.
 */
static void ep2_add_projc_mix(ep2_t r, ep2_t p, ep2_t q) {
	fp2_t t0, t1, t2, t3, t4, t5, t6;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);
	fp2_null(t3);
	fp2_null(t4);
	fp2_null(t5);
	fp2_null(t6);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);
		fp2_new(t3);
		fp2_new(t4);
		fp2_new(t5);
		fp2_new(t6);

		if (!p->norm) {
			/* t0 = z1^2. */
			fp2_sqr(t0, p->z);

			/* t3 = U2 = x2 * z1^2. */
			fp2_mul(t3, q->x, t0);

			/* t1 = S2 = y2 * z1^3. */
			fp2_mul(t1, t0, p->z);
			fp2_mul(t1, t1, q->y);

			/* t3 = H = U2 - x1. */
			fp2_sub(t3, t3, p->x);

			/* t1 = R = 2 * (S2 - y1). */
			fp2_sub(t1, t1, p->y);
		} else {
			/* H = x2 - x1. */
			fp2_sub(t3, q->x, p->x);

			/* t1 = R = 2 * (y2 - y1). */
			fp2_sub(t1, q->y, p->y);
		}

		/* t2 = HH = H^2. */
		fp2_sqr(t2, t3);

		/* If E is zero. */
		if (fp2_is_zero(t3)) {
			if (fp2_is_zero(t1)) {
				/* If I is zero, p = q, should have doubled. */
				ep2_dbl_projc(r, p);
			} else {
				/* If I is not zero, q = -p, r = infinity. */
				ep2_set_infty(r);
			}
		} else {
			/* t5 = J = H * HH. */
			fp2_mul(t5, t3, t2);

			/* t4 = V = x1 * HH. */
			fp2_mul(t4, p->x, t2);

			/* x3 = R^2 - J - 2 * V. */
			fp2_sqr(r->x, t1);
			fp2_sub(r->x, r->x, t5);
			fp2_dbl(t6, t4);
			fp2_sub(r->x, r->x, t6);

			/* y3 = R * (V - x3) - Y1 * J. */
			fp2_sub(t4, t4, r->x);
			fp2_mul(t4, t4, t1);
			fp2_mul(t1, p->y, t5);
			fp2_sub(r->y, t4, t1);

			if (!p->norm) {
				/* z3 = z1 * H. */
				fp2_mul(r->z, p->z, t3);
			} else {
				/* z3 = H. */
				fp2_copy(r->z, t3);
			}
		}
		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
		fp2_free(t3);
		fp2_free(t4);
		fp2_free(t5);
		fp2_free(t6);
	}
}
Exemplo n.º 12
0
/**
 * Computes the constantes required for evaluating Frobenius maps.
 */
static void fp2_calc() {
	bn_t e;
	fp2_t t0;
	fp2_t t1;
	ctx_t *ctx = core_get();

	bn_null(e);
	fp2_null(t0);
	fp2_null(t1);

	TRY {
		bn_new(e);
		fp2_new(t0);
		fp2_new(t1);

		fp2_zero(t0);
		fp_set_dig(t0[0], 1);
		fp2_mul_nor(t0, t0);
		e->used = FP_DIGS;
		dv_copy(e->dp, fp_prime_get(), FP_DIGS);
		bn_sub_dig(e, e, 1);
		bn_div_dig(e, e, 6);
		fp2_exp(t0, t0, e);
#if ALLOC == AUTO
		fp2_copy(ctx->fp2_p[0], t0);
		fp2_sqr(ctx->fp2_p[1], ctx->fp2_p[0]);
		fp2_mul(ctx->fp2_p[2], ctx->fp2_p[1], ctx->fp2_p[0]);
		fp2_sqr(ctx->fp2_p[3], ctx->fp2_p[1]);
		fp2_mul(ctx->fp2_p[4], ctx->fp2_p[3], ctx->fp2_p[0]);
#else
		fp_copy(ctx->fp2_p[0][0], t0[0]);
		fp_copy(ctx->fp2_p[0][1], t0[1]);
		fp2_sqr(t1, t0);
		fp_copy(ctx->fp2_p[1][0], t1[0]);
		fp_copy(ctx->fp2_p[1][1], t1[1]);
		fp2_mul(t1, t1, t0);
		fp_copy(ctx->fp2_p[2][0], t1[0]);
		fp_copy(ctx->fp2_p[2][1], t1[1]);
		fp2_sqr(t1, t0);
		fp2_sqr(t1, t1);
		fp_copy(ctx->fp2_p[3][0], t1[0]);
		fp_copy(ctx->fp2_p[3][1], t1[1]);
		fp2_mul(t1, t1, t0);
		fp_copy(ctx->fp2_p[4][0], t1[0]);
		fp_copy(ctx->fp2_p[4][1], t1[1]);
#endif
		fp2_frb(t1, t0, 1);
		fp2_mul(t0, t1, t0);
		fp_copy(ctx->fp2_p2[0], t0[0]);
		fp_sqr(ctx->fp2_p2[1], ctx->fp2_p2[0]);
		fp_mul(ctx->fp2_p2[2], ctx->fp2_p2[1], ctx->fp2_p2[0]);
		fp_sqr(ctx->fp2_p2[3], ctx->fp2_p2[1]);

		for (int i = 0; i < 5; i++) {
			fp_mul(ctx->fp2_p3[i][0], ctx->fp2_p2[i % 3], ctx->fp2_p[i][0]);
			fp_mul(ctx->fp2_p3[i][1], ctx->fp2_p2[i % 3], ctx->fp2_p[i][1]);
		}
	} CATCH_ANY {
		THROW(ERR_CAUGHT);
	} FINALLY {
		bn_free(e);
		fp2_free(t0);
		fp2_free(t1);
	}
}
Exemplo n.º 13
0
void pp_dbl_k12_projc_lazyr(fp12_t l, ep2_t r, ep2_t q, ep_t p) {
	fp2_t t0, t1, t2, t3, t4, t5, t6;
	dv2_t u0, u1;
	int one = 1, zero = 0;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);
	fp2_null(t3);
	fp2_null(t4);
	fp2_null(t5);
	fp2_null(t6);
	dv2_null(u0);
	dv2_null(u1);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);
		fp2_new(t3);
		fp2_new(t4);
		fp2_new(t5);
		fp2_new(t6);
		dv2_new(u0);
		dv2_new(u1);

		if (ep2_curve_is_twist() == EP_MTYPE) {
			one ^= 1;
			zero ^= 1;
		}

		if (ep_curve_opt_b() == RLC_TWO) {
			/* C = z1^2. */
			fp2_sqr(t0, q->z);
			/* B = y1^2. */
			fp2_sqr(t1, q->y);
			/* t5 = B + C. */
			fp2_add(t5, t0, t1);
			/* t3 = E = 3b'C = 3C * (1 - i). */
			fp2_dbl(t3, t0);
			fp2_add(t0, t0, t3);
			fp_add(t2[0], t0[0], t0[1]);
			fp_sub(t2[1], t0[1], t0[0]);

			/* t0 = x1^2. */
			fp2_sqr(t0, q->x);
			/* t4 = A = (x1 * y1)/2. */
			fp2_mul(t4, q->x, q->y);
			fp_hlv(t4[0], t4[0]);
			fp_hlv(t4[1], t4[1]);
			/* t3 = F = 3E. */
			fp2_dbl(t3, t2);
			fp2_add(t3, t3, t2);
			/* x3 = A * (B - F). */
			fp2_sub(r->x, t1, t3);
			fp2_mul(r->x, r->x, t4);

			/* G = (B + F)/2. */
			fp2_add(t3, t1, t3);
			fp_hlv(t3[0], t3[0]);
			fp_hlv(t3[1], t3[1]);

			/* y3 = G^2 - 3E^2. */
			fp2_sqrn_low(u0, t2);
			fp2_addd_low(u1, u0, u0);
			fp2_addd_low(u1, u1, u0);
			fp2_sqrn_low(u0, t3);
			fp2_subc_low(u0, u0, u1);

			/* H = (Y + Z)^2 - B - C. */
			fp2_add(t3, q->y, q->z);
			fp2_sqr(t3, t3);
			fp2_sub(t3, t3, t5);

			fp2_rdcn_low(r->y, u0);

			/* z3 = B * H. */
			fp2_mul(r->z, t1, t3);

			/* l11 = E - B. */
			fp2_sub(l[1][1], t2, t1);

			/* l10 = (3 * xp) * t0. */
			fp_mul(l[one][zero][0], p->x, t0[0]);
			fp_mul(l[one][zero][1], p->x, t0[1]);

			/* l01 = F * (-yp). */
			fp_mul(l[zero][zero][0], t3[0], p->y);
			fp_mul(l[zero][zero][1], t3[1], p->y);
		} else {
			/* A = x1^2. */
			fp2_sqr(t0, q->x);
			/* B = y1^2. */
			fp2_sqr(t1, q->y);
			/* C = z1^2. */
			fp2_sqr(t2, q->z);
			/* D = 3bC, for general b. */
			fp2_dbl(t3, t2);
			fp2_add(t3, t3, t2);
			ep2_curve_get_b(t4);
			fp2_mul(t3, t3, t4);
			/* E = (x1 + y1)^2 - A - B. */
			fp2_add(t4, q->x, q->y);
			fp2_sqr(t4, t4);
			fp2_sub(t4, t4, t0);
			fp2_sub(t4, t4, t1);

			/* F = (y1 + z1)^2 - B - C. */
			fp2_add(t5, q->y, q->z);
			fp2_sqr(t5, t5);
			fp2_sub(t5, t5, t1);
			fp2_sub(t5, t5, t2);

			/* G = 3D. */
			fp2_dbl(t6, t3);
			fp2_add(t6, t6, t3);

			/* x3 = E * (B - G). */
			fp2_sub(r->x, t1, t6);
			fp2_mul(r->x, r->x, t4);

			/* y3 = (B + G)^2 -12D^2. */
			fp2_add(t6, t6, t1);
			fp2_sqr(t6, t6);
			fp2_sqr(t2, t3);
			fp2_dbl(r->y, t2);
			fp2_dbl(t2, r->y);
			fp2_dbl(r->y, t2);
			fp2_add(r->y, r->y, t2);
			fp2_sub(r->y, t6, r->y);

			/* z3 = 4B * F. */
			fp2_dbl(r->z, t1);
			fp2_dbl(r->z, r->z);
			fp2_mul(r->z, r->z, t5);

			/* l00 = D - B. */
			fp2_sub(l[one][one], t3, t1);

			/* l10 = (3 * xp) * A. */
			fp_mul(l[one][zero][0], p->x, t0[0]);
			fp_mul(l[one][zero][1], p->x, t0[1]);

			/* l01 = F * (-yp). */
			fp_mul(l[zero][zero][0], t5[0], p->y);
			fp_mul(l[zero][zero][1], t5[1], p->y);
		}
		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
		fp2_free(t3);
		fp2_free(t4);
		fp2_free(t5);
		fp2_free(t6);
		dv2_free(u0);
		dv2_free(u1);
	}
}
Exemplo n.º 14
0
void fp12_sqr_pck_basic(fp12_t c, fp12_t a) {
	fp2_t t0, t1, t2, t3, t4, t5, t6;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);
	fp2_null(t3);
	fp2_null(t4);
	fp2_null(t5);
	fp2_null(t6);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);
		fp2_new(t3);
		fp2_new(t4);
		fp2_new(t5);
		fp2_new(t6);

		fp2_sqr(t0, a[0][1]);
		fp2_sqr(t1, a[1][2]);
		fp2_add(t5, a[0][1], a[1][2]);
		fp2_sqr(t2, t5);

		fp2_add(t3, t0, t1);
		fp2_sub(t5, t2, t3);

		fp2_add(t6, a[1][0], a[0][2]);
		fp2_sqr(t3, t6);
		fp2_sqr(t2, a[1][0]);

		fp2_mul_nor(t6, t5);
		fp2_add(t5, t6, a[1][0]);
		fp2_dbl(t5, t5);
		fp2_add(c[1][0], t5, t6);

		fp2_mul_nor(t4, t1);
		fp2_add(t5, t0, t4);
		fp2_sub(t6, t5, a[0][2]);

		fp2_sqr(t1, a[0][2]);

		fp2_dbl(t6, t6);
		fp2_add(c[0][2], t6, t5);

		fp2_mul_nor(t4, t1);
		fp2_add(t5, t2, t4);
		fp2_sub(t6, t5, a[0][1]);
		fp2_dbl(t6, t6);
		fp2_add(c[0][1], t6, t5);

		fp2_add(t0, t2, t1);
		fp2_sub(t5, t3, t0);
		fp2_add(t6, t5, a[1][2]);
		fp2_dbl(t6, t6);
		fp2_add(c[1][2], t5, t6);
	} CATCH_ANY {
		THROW(ERR_CAUGHT);
	} FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
		fp2_free(t3);
		fp2_free(t4);
		fp2_free(t5);
		fp2_free(t6);
	}
}
Exemplo n.º 15
0
void fp12_sqr_cyc_basic(fp12_t c, fp12_t a) {
	fp2_t t0, t1, t2, t3, t4, t5, t6;

	fp2_null(t0);
	fp2_null(t1);
	fp2_null(t2);
	fp2_null(t3);
	fp2_null(t4);
	fp2_null(t5);
	fp2_null(t6);

	TRY {
		fp2_new(t0);
		fp2_new(t1);
		fp2_new(t2);
		fp2_new(t3);
		fp2_new(t4);
		fp2_new(t5);
		fp2_new(t6);

		/* Define z = sqrt(E) */

		/* Now a is seen as (t0,t1) + (t2,t3) * w + (t4,t5) * w^2 */

		/* (t0, t1) = (a00 + a11*z)^2. */
		fp2_sqr(t2, a[0][0]);
		fp2_sqr(t3, a[1][1]);
		fp2_add(t1, a[0][0], a[1][1]);

		fp2_mul_nor(t0, t3);
		fp2_add(t0, t0, t2);

		fp2_sqr(t1, t1);
		fp2_sub(t1, t1, t2);
		fp2_sub(t1, t1, t3);

		fp2_sub(c[0][0], t0, a[0][0]);
		fp2_add(c[0][0], c[0][0], c[0][0]);
		fp2_add(c[0][0], t0, c[0][0]);

		fp2_add(c[1][1], t1, a[1][1]);
		fp2_add(c[1][1], c[1][1], c[1][1]);
		fp2_add(c[1][1], t1, c[1][1]);

		fp2_sqr(t0, a[0][1]);
		fp2_sqr(t1, a[1][2]);
		fp2_add(t5, a[0][1], a[1][2]);
		fp2_sqr(t2, t5);

		fp2_add(t3, t0, t1);
		fp2_sub(t5, t2, t3);

		fp2_add(t6, a[1][0], a[0][2]);
		fp2_sqr(t3, t6);
		fp2_sqr(t2, a[1][0]);

		fp2_mul_nor(t6, t5);
		fp2_add(t5, t6, a[1][0]);
		fp2_dbl(t5, t5);
		fp2_add(c[1][0], t5, t6);

		fp2_mul_nor(t4, t1);
		fp2_add(t5, t0, t4);
		fp2_sub(t6, t5, a[0][2]);

		fp2_sqr(t1, a[0][2]);

		fp2_dbl(t6, t6);
		fp2_add(c[0][2], t6, t5);

		fp2_mul_nor(t4, t1);
		fp2_add(t5, t2, t4);
		fp2_sub(t6, t5, a[0][1]);
		fp2_dbl(t6, t6);
		fp2_add(c[0][1], t6, t5);

		fp2_add(t0, t2, t1);
		fp2_sub(t5, t3, t0);
		fp2_add(t6, t5, a[1][2]);
		fp2_dbl(t6, t6);
		fp2_add(c[1][2], t5, t6);
	} CATCH_ANY {
		THROW(ERR_CAUGHT);
	} FINALLY {
		fp2_free(t0);
		fp2_free(t1);
		fp2_free(t2);
		fp2_free(t3);
		fp2_free(t4);
		fp2_free(t5);
		fp2_free(t6);
	}
}