ecp_smpl.c

OpenSSL 0.9.8k 最新版OpenSSL

	if (!field_mul(group, n1, n2, n5, ctx)) goto end;
	if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
	if (BN_is_odd(n0))
		if (!BN_add(n0, n0, p)) goto end;
	/* now  0 <= n0 < 2*p,  and n0 is even */
	if (!BN_rshift1(&r->Y, n0)) goto end;
	/* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */

	ret = 1;

 end:
	if (ctx) /* otherwise we already called BN_CTX_end */
		BN_CTX_end(ctx);
	if (new_ctx != NULL)
		BN_CTX_free(new_ctx);
	return ret;
	}


int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
	{
	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
	const BIGNUM *p;
	BN_CTX *new_ctx = NULL;
	BIGNUM *n0, *n1, *n2, *n3;
	int ret = 0;
	
	if (EC_POINT_is_at_infinity(group, a))
		{
		BN_zero(&r->Z);
		r->Z_is_one = 0;
		return 1;
		}

	field_mul = group->meth->field_mul;
	field_sqr = group->meth->field_sqr;
	p = &group->field;

	if (ctx == NULL)
		{
		ctx = new_ctx = BN_CTX_new();
		if (ctx == NULL)
			return 0;
		}

	BN_CTX_start(ctx);
	n0 = BN_CTX_get(ctx);
	n1 = BN_CTX_get(ctx);
	n2 = BN_CTX_get(ctx);
	n3 = BN_CTX_get(ctx);
	if (n3 == NULL) goto err;

	/* Note that in this function we must not read components of 'a'
	 * once we have written the corresponding components of 'r'.
	 * ('r' might the same as 'a'.)
	 */

	/* n1 */
	if (a->Z_is_one)
		{
		if (!field_sqr(group, n0, &a->X, ctx)) goto err;
		if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
		if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
		if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
		/* n1 = 3 * X_a^2 + a_curve */
		}
	else if (group->a_is_minus3)
		{
		if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
		if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
		if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
		if (!field_mul(group, n1, n0, n2, ctx)) goto err;
		if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
		if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
		/* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
		 *    = 3 * X_a^2 - 3 * Z_a^4 */
		}
	else
		{
		if (!field_sqr(group, n0, &a->X, ctx)) goto err;
		if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
		if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
		if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
		if (!field_sqr(group, n1, n1, ctx)) goto err;
		if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
		if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
		/* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
		}

	/* Z_r */
	if (a->Z_is_one)
		{
		if (!BN_copy(n0, &a->Y)) goto err;
		}
	else
		{
		if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
		}
	if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
	r->Z_is_one = 0;
	/* Z_r = 2 * Y_a * Z_a */

	/* n2 */
	if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
	if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
	if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
	/* n2 = 4 * X_a * Y_a^2 */

	/* X_r */
	if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
	if (!field_sqr(group, &r->X, n1, ctx)) goto err;
	if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
	/* X_r = n1^2 - 2 * n2 */
	
	/* n3 */
	if (!field_sqr(group, n0, n3, ctx)) goto err;
	if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
	/* n3 = 8 * Y_a^4 */
	
	/* Y_r */
	if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
	if (!field_mul(group, n0, n1, n0, ctx)) goto err;
	if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
	/* Y_r = n1 * (n2 - X_r) - n3 */

	ret = 1;

 err:
	BN_CTX_end(ctx);
	if (new_ctx != NULL)
		BN_CTX_free(new_ctx);
	return ret;
	}


int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
	{
	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
		/* point is its own inverse */
		return 1;
	
	return BN_usub(&point->Y, &group->field, &point->Y);
	}


int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
	{
	return BN_is_zero(&point->Z);
	}


int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
	{
	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
	const BIGNUM *p;
	BN_CTX *new_ctx = NULL;
	BIGNUM *rh, *tmp, *Z4, *Z6;
	int ret = -1;

	if (EC_POINT_is_at_infinity(group, point))
		return 1;
	
	field_mul = group->meth->field_mul;
	field_sqr = group->meth->field_sqr;
	p = &group->field;

	if (ctx == NULL)
		{
		ctx = new_ctx = BN_CTX_new();
		if (ctx == NULL)
			return -1;
		}

	BN_CTX_start(ctx);
	rh = BN_CTX_get(ctx);
	tmp = BN_CTX_get(ctx);
	Z4 = BN_CTX_get(ctx);
	Z6 = BN_CTX_get(ctx);
	if (Z6 == NULL) goto err;

	/* We have a curve defined by a Weierstrass equation
	 *      y^2 = x^3 + a*x + b.
	 * The point to consider is given in Jacobian projective coordinates
	 * where  (X, Y, Z)  represents  (x, y) = (X/Z^2, Y/Z^3).
	 * Substituting this and multiplying by  Z^6  transforms the above equation into
	 *      Y^2 = X^3 + a*X*Z^4 + b*Z^6.
	 * To test this, we add up the right-hand side in 'rh'.
	 */

	/* rh := X^2 */
	if (!field_sqr(group, rh, &point->X, ctx)) goto err;

	if (!point->Z_is_one)
		{
		if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;
		if (!field_sqr(group, Z4, tmp, ctx)) goto err;
		if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;

		/* rh := (rh + a*Z^4)*X */
		if (group->a_is_minus3)
			{
			if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
			if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
			if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
			if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
			}
		else
			{
			if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;
			if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
			if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
			}

		/* rh := rh + b*Z^6 */
		if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;
		if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
		}
	else
		{
		/* point->Z_is_one */

		/* rh := (rh + a)*X */
		if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;
		if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
		/* rh := rh + b */
		if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
		}

	/* 'lh' := Y^2 */
	if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;

	ret = (0 == BN_ucmp(tmp, rh));

 err:
	BN_CTX_end(ctx);
	if (new_ctx != NULL)
		BN_CTX_free(new_ctx);
	return ret;
	}


int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
	{
	/* return values:
	 *  -1   error
	 *   0   equal (in affine coordinates)
	 *   1   not equal
	 */

	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
	BN_CTX *new_ctx = NULL;
	BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
	const BIGNUM *tmp1_, *tmp2_;
	int ret = -1;
	
	if (EC_POINT_is_at_infinity(group, a))
		{
		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
		}
	
	if (a->Z_is_one && b->Z_is_one)
		{
		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
		}

	field_mul = group->meth->field_mul;
	field_sqr = group->meth->field_sqr;

	if (ctx == NULL)
		{
		ctx = new_ctx = BN_CTX_new();
		if (ctx == NULL)
			return -1;
		}

	BN_CTX_start(ctx);
	tmp1 = BN_CTX_get(ctx);
	tmp2 = BN_CTX_get(ctx);
	Za23 = BN_CTX_get(ctx);
	Zb23 = BN_CTX_get(ctx);
	if (Zb23 == NULL) goto end;

	/* We have to decide whether
	 *     (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
	 * or equivalently, whether
	 *     (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
	 */

	if (!b->Z_is_one)
		{
		if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
		if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
		tmp1_ = tmp1;
		}
	else
		tmp1_ = &a->X;
	if (!a->Z_is_one)
		{
		if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
		if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
		tmp2_ = tmp2;
		}
	else
		tmp2_ = &b->X;
	
	/* compare  X_a*Z_b^2  with  X_b*Z_a^2 */
	if (BN_cmp(tmp1_, tmp2_) != 0)
		{
		ret = 1; /* points differ */
		goto end;
		}


	if (!b->Z_is_one)
		{
		if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
		if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
		/* tmp1_ = tmp1 */
		}
	else
		tmp1_ = &a->Y;
	if (!a->Z_is_one)
		{
		if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
		if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
		/* tmp2_ = tmp2 */
		}
	else
		tmp2_ = &b->Y;

	/* compare  Y_a*Z_b^3  with  Y_b*Z_a^3 */
	if (BN_cmp(tmp1_, tmp2_) != 0)
		{
		ret = 1; /* points differ */
		goto end;
		}

	/* points are equal */
	ret = 0;

 end:
	BN_CTX_end(ctx);
	if (new_ctx != NULL)
		BN_CTX_free(new_ctx);
	return ret;
	}


int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
	{
	BN_CTX *new_ctx = NULL;
	BIGNUM *x, *y;
	int ret = 0;

	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
		return 1;

	if (ctx == NULL)
		{
		ctx = new_ctx = BN_CTX_new();
		if (ctx == NULL)
			return 0;
		}

	BN_CTX_start(ctx);
	x = BN_CTX_get(ctx);
	y = BN_CTX_get(ctx);
	if (y == NULL) goto err;

	if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
	if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
	if (!point->Z_is_one)
		{
		ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
		goto err;
		}
	
	ret = 1;

 err:
	BN_CTX_end(ctx);
	if (new_ctx != NULL)
		BN_CTX_free(new_ctx);
	return ret;
	}


int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
	{
	BN_CTX *new_ctx = NULL;
	BIGNUM *tmp0, *tmp1;
	size_t pow2 = 0;
	BIGNUM **heap = NULL;
	size_t i;
	int ret = 0;

	if (num == 0)
		return 1;

	if (ctx == NULL)
		{
		ctx = new_ctx = BN_CTX_new();
		if (ctx == NULL)
			return 0;
		}

	BN_CTX_start(ctx);
	tmp0 = BN_CTX_get(ctx);
	tmp1 = BN_CTX_get(ctx);
	if (tmp0  == NULL || tmp1 == NULL) goto err;

	/* Before converting the individual points, compute inverses of all Z values.
	 * Modular inversion is rather slow, but luckily we can do with a single
	 * explicit inversion, plus about 3 multiplications per input value.
	 */

	pow2 = 1;
	while (num > pow2)
		pow2 <<= 1;
	/* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
	 * We need twice that. */
	pow2 <<= 1;

	heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
	if (heap == NULL) goto err;
	
	/* The array is used as a binary tree, exactly as in heapsort:
	 *
	 *                               heap[1]
	 *                 heap[2]                     heap[3]
	 *          heap[4]       heap[5]       heap[6]       heap[7]
	 *   heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
	 *
	 * We put the Z's in the last line;
	 * then we set each other node to the product of its two child-nodes (where
	 * empty or 0 entries are treated as ones);
	 * then we invert heap[1];
	 * then we invert each other node by replacing it by the product of its
	 * parent (after inversion) and its sibling (before inversion).
	 */
	heap[0] = NULL;
	for (i = pow2/2 - 1; i > 0; i--)
		heap[i] = NULL;
	for (i = 0; i < num; i++)
		heap[pow2/2 + i] = &points[i]->Z;
	for (i = pow2/2 + num; i < pow2; i++)
		heap[i] = NULL;
	
	/* set each node to the product of its children */
	for (i = pow2/2 - 1; i > 0; i--)
		{
		heap[i] = BN_new();
		if (heap[i] == NULL) goto err;
		
		if (heap[2*i] != NULL)
			{
			if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
				{
				if (!BN_copy(heap[i], heap[2*i])) goto err;
				}
			else
				{
				if (BN_is_zero(heap[2*i]))
					{
					if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
					}
				else
					{
					if (!group->meth->field_mul(group, heap[i],
						heap[2*i], heap[2*i + 1], ctx)) goto err;
					}
				}
			}
		}

	/* invert heap[1] */
	if (!BN_is_zero(heap[1]))
		{
		if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
			{
			ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
			goto err;
			}
		}
	if (group->meth->field_encode != 0)
		{
		/* in the Montgomery case, we just turned  R*H  (representing H)
		 * into  1/(R*H),  but we need  R*(1/H)  (representing 1/H);
		 * i.e. we have need to multiply by the Montgomery factor twice */
		if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
		if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
		}

	/* set other heap[i]'s to their inverses */
	for (i = 2; i < pow2/2 + num; i += 2)
		{
		/* i is even */
		if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
			{
			if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
			if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
			if (!BN_copy(heap[i], tmp0)) goto err;
			if (!BN_copy(heap[i + 1], tmp1)) goto err;
			}
		else
			{
			if (!BN_copy(heap[i], heap[i/2])) goto err;
			}
		}

	/* we have replaced all non-zero Z's by their inverses, now fix up all the points */
	for (i = 0; i < num; i++)
		{
		EC_POINT *p = points[i];
		
		if (!BN_is_zero(&p->Z))
			{
			/* turn  (X, Y, 1/Z)  into  (X/Z^2, Y/Z^3, 1) */

			if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
			if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;

			if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
			if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
		
			if (group->meth->field_set_to_one != 0)
				{
				if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
				}
			else
				{
				if (!BN_one(&p->Z)) goto err;
				}
			p->Z_is_one = 1;
			}
		}

	ret = 1;
		
 err:
	BN_CTX_end(ctx);
	if (new_ctx != NULL)
		BN_CTX_free(new_ctx);
	if (heap != NULL)
		{
		/* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
		for (i = pow2/2 - 1; i > 0; i--)
			{
			if (heap[i] != NULL)
				BN_clear_free(heap[i]);
			}
		OPENSSL_free(heap);
		}
	return ret;
	}


int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
	{
	return BN_mod_mul(r, a, b, &group->field, ctx);
	}


int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
	{
	return BN_mod_sqr(r, a, &group->field, ctx);
	}