C++ (Cpp) ec_GFp_pt_aff2jac示例

示例#1

文件： ecp_jac.c 项目： biddyweb/switch-oss

/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
 * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
 * Uses mixed Jacobian-affine coordinates. Assumes input is already
 * field-encoded using field_enc, and returns output that is still
 * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and
 * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime
 * Fields. */
mp_err
ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
					  const mp_int *qx, const mp_int *qy, mp_int *rx,
					  mp_int *ry, mp_int *rz, const ECGroup *group)
{
	mp_err res = MP_OKAY;
	mp_int A, B, C, D, C2, C3;

	MP_DIGITS(&A) = 0;
	MP_DIGITS(&B) = 0;
	MP_DIGITS(&C) = 0;
	MP_DIGITS(&D) = 0;
	MP_DIGITS(&C2) = 0;
	MP_DIGITS(&C3) = 0;
	MP_CHECKOK(mp_init(&A));
	MP_CHECKOK(mp_init(&B));
	MP_CHECKOK(mp_init(&C));
	MP_CHECKOK(mp_init(&D));
	MP_CHECKOK(mp_init(&C2));
	MP_CHECKOK(mp_init(&C3));

	/* If either P or Q is the point at infinity, then return the other
	 * point */
	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
		MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
		goto CLEANUP;
	}
	if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
		MP_CHECKOK(mp_copy(px, rx));
		MP_CHECKOK(mp_copy(py, ry));
		MP_CHECKOK(mp_copy(pz, rz));
		goto CLEANUP;
	}

	/* A = qx * pz^2, B = qy * pz^3 */
	MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
	MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
	MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
	MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));

	/* C = A - px, D = B - py */
	MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
	MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));

	if (mp_cmp_z(&C) == 0) {
		/* P == Q or P == -Q */
		if (mp_cmp_z(&D) == 0) {
			/* P == Q */
			/* It is cheaper to double (qx, qy, 1) than (px, py, pz). */
			MP_DIGIT(&D, 0) = 1; /* Set D to 1. */
			MP_CHECKOK(ec_GFp_pt_dbl_jac(qx, qy, &D, rx, ry, rz, group));
		} else {
			/* P == -Q */
			MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
		}
		goto CLEANUP;
	}

	/* C2 = C^2, C3 = C^3 */
	MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
	MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));

	/* rz = pz * C */
	MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));

	/* C = px * C^2 */
	MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
	/* A = D^2 */
	MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));

	/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
	MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
	MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
	MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));

	/* C3 = py * C^3 */
	MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));

	/* ry = D * (px * C^2 - rx) - py * C^3 */
	MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
	MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
	MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));

  CLEANUP:
	mp_clear(&A);
	mp_clear(&B);
	mp_clear(&C);
	mp_clear(&D);
	mp_clear(&C2);
	mp_clear(&C3);
	return res;
}

示例#2

文件： ecp_jm.c 项目： AntinZhu/jdk-source

/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
 * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
 * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
 * already field-encoded using field_enc, and returns output that is still
 * field-encoded. */
mp_err
ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
                                         const mp_int *paz4, const mp_int *qx,
                                         const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
                                         mp_int *raz4, mp_int scratch[], const ECGroup *group)
{
        mp_err res = MP_OKAY;
        mp_int *A, *B, *C, *D, *C2, *C3;

        A = &scratch[0];
        B = &scratch[1];
        C = &scratch[2];
        D = &scratch[3];
        C2 = &scratch[4];
        C3 = &scratch[5];

#if MAX_SCRATCH < 6
#error "Scratch array defined too small "
#endif

        /* If either P or Q is the point at infinity, then return the other
         * point */
        if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
                MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
                MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
                MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
                MP_CHECKOK(group->meth->
                                   field_mul(raz4, &group->curvea, raz4, group->meth));
                goto CLEANUP;
        }
        if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
                MP_CHECKOK(mp_copy(px, rx));
                MP_CHECKOK(mp_copy(py, ry));
                MP_CHECKOK(mp_copy(pz, rz));
                MP_CHECKOK(mp_copy(paz4, raz4));
                goto CLEANUP;
        }

        /* A = qx * pz^2, B = qy * pz^3 */
        MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
        MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
        MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
        MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));

        /* C = A - px, D = B - py */
        MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
        MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));

        /* C2 = C^2, C3 = C^3 */
        MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
        MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));

        /* rz = pz * C */
        MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));

        /* C = px * C^2 */
        MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
        /* A = D^2 */
        MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));

        /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
        MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
        MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
        MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));

        /* C3 = py * C^3 */
        MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));

        /* ry = D * (px * C^2 - rx) - py * C^3 */
        MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
        MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
        MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));

        /* raz4 = a * rz^4 */
        MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
        MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
        MP_CHECKOK(group->meth->
                           field_mul(raz4, &group->curvea, raz4, group->meth));
CLEANUP:
        return res;
}

示例#3

文件： ecp_jm.c 项目： tcdog001/apv5sdk-v15

/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
 * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
 * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
 * already field-encoded using field_enc, and returns output that is still
 * field-encoded. */
mp_err
ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
					 const mp_int *paz4, const mp_int *qx,
					 const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
					 mp_int *raz4, const ECGroup *group)
{
	mp_err res = MP_OKAY;
	mp_int A, B, C, D, C2, C3;

	MP_DIGITS(&A) = 0;
	MP_DIGITS(&B) = 0;
	MP_DIGITS(&C) = 0;
	MP_DIGITS(&D) = 0;
	MP_DIGITS(&C2) = 0;
	MP_DIGITS(&C3) = 0;
	MP_CHECKOK(mp_init(&A));
	MP_CHECKOK(mp_init(&B));
	MP_CHECKOK(mp_init(&C));
	MP_CHECKOK(mp_init(&D));
	MP_CHECKOK(mp_init(&C2));
	MP_CHECKOK(mp_init(&C3));

	/* If either P or Q is the point at infinity, then return the other
	 * point */
	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
		MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
		MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
		MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
		MP_CHECKOK(group->meth->
				   field_mul(raz4, &group->curvea, raz4, group->meth));
		goto CLEANUP;
	}
	if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
		MP_CHECKOK(mp_copy(px, rx));
		MP_CHECKOK(mp_copy(py, ry));
		MP_CHECKOK(mp_copy(pz, rz));
		MP_CHECKOK(mp_copy(paz4, raz4));
		goto CLEANUP;
	}

	/* A = qx * pz^2, B = qy * pz^3 */
	MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
	MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
	MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
	MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));

	/* C = A - px, D = B - py */
	MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
	MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));

	/* C2 = C^2, C3 = C^3 */
	MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
	MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));

	/* rz = pz * C */
	MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));

	/* C = px * C^2 */
	MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
	/* A = D^2 */
	MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));

	/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
	MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
	MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
	MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));

	/* C3 = py * C^3 */
	MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));

	/* ry = D * (px * C^2 - rx) - py * C^3 */
	MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
	MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
	MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));

	/* raz4 = a * rz^4 */
	MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
	MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
	MP_CHECKOK(group->meth->
			   field_mul(raz4, &group->curvea, raz4, group->meth));

  CLEANUP:
	mp_clear(&A);
	mp_clear(&B);
	mp_clear(&C);
	mp_clear(&D);
	mp_clear(&C2);
	mp_clear(&C3);
	return res;
}