/* Performs basic tests of elliptic curve cryptography over prime fields.
* If tests fail, then it prints an error message, aborts, and returns an
* error code. Otherwise, returns 0. */
int
ectest_curve_GFp(ECGroup *group, int ectestPrint, int ectestTime,
int generic)
{
mp_int one, order_1, gx, gy, rx, ry, n;
int size;
mp_err res;
char s[1000];
/* initialize values */
MP_CHECKOK(mp_init(&one));
MP_CHECKOK(mp_init(&order_1));
MP_CHECKOK(mp_init(&gx));
MP_CHECKOK(mp_init(&gy));
MP_CHECKOK(mp_init(&rx));
MP_CHECKOK(mp_init(&ry));
MP_CHECKOK(mp_init(&n));
MP_CHECKOK(mp_set_int(&one, 1));
MP_CHECKOK(mp_sub(&group->order, &one, &order_1));
/* encode base point */
if (group->meth->field_dec) {
MP_CHECKOK(group->meth->field_dec(&group->genx, &gx, group->meth));
MP_CHECKOK(group->meth->field_dec(&group->geny, &gy, group->meth));
} else {
MP_CHECKOK(mp_copy(&group->genx, &gx));
MP_CHECKOK(mp_copy(&group->geny, &gy));
}
if (ectestPrint) {
/* output base point */
printf(" base point P:\n");
MP_CHECKOK(mp_toradix(&gx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&gy, s, 16));
printf(" %s\n", s);
if (group->meth->field_enc) {
printf(" base point P (encoded):\n");
MP_CHECKOK(mp_toradix(&group->genx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&group->geny, s, 16));
printf(" %s\n", s);
}
}
#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
/* multiply base point by order - 1 and check for negative of base
* point */
MP_CHECKOK(ec_GFp_pt_mul_aff(&order_1, &group->genx, &group->geny, &rx, &ry, group));
if (ectestPrint) {
printf(" (order-1)*P (affine):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
MP_CHECKOK(group->meth->field_neg(&ry, &ry, group->meth));
if ((mp_cmp(&rx, &group->genx) != 0) || (mp_cmp(&ry, &group->geny) != 0)) {
printf(" Error: invalid result (expected (- base point)).\n");
res = MP_NO;
goto CLEANUP;
}
#endif
#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
/* multiply base point by order - 1 and check for negative of base
* point */
MP_CHECKOK(ec_GFp_pt_mul_jac(&order_1, &group->genx, &group->geny, &rx, &ry, group));
if (ectestPrint) {
printf(" (order-1)*P (jacobian):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
MP_CHECKOK(group->meth->field_neg(&ry, &ry, group->meth));
if ((mp_cmp(&rx, &group->genx) != 0) || (mp_cmp(&ry, &group->geny) != 0)) {
printf(" Error: invalid result (expected (- base point)).\n");
res = MP_NO;
goto CLEANUP;
}
#endif
/* multiply base point by order - 1 and check for negative of base
* point */
MP_CHECKOK(ECPoint_mul(group, &order_1, NULL, NULL, &rx, &ry));
if (ectestPrint) {
printf(" (order-1)*P (ECPoint_mul):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
MP_CHECKOK(mp_submod(&group->meth->irr, &ry, &group->meth->irr, &ry));
if ((mp_cmp(&rx, &gx) != 0) || (mp_cmp(&ry, &gy) != 0)) {
printf(" Error: invalid result (expected (- base point)).\n");
res = MP_NO;
goto CLEANUP;
}
/* multiply base point by order - 1 and check for negative of base
* point */
MP_CHECKOK(ECPoint_mul(group, &order_1, &gx, &gy, &rx, &ry));
if (ectestPrint) {
printf(" (order-1)*P (ECPoint_mul):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
MP_CHECKOK(mp_submod(&group->meth->irr, &ry, &group->meth->irr, &ry));
if ((mp_cmp(&rx, &gx) != 0) || (mp_cmp(&ry, &gy) != 0)) {
printf(" Error: invalid result (expected (- base point)).\n");
res = MP_NO;
goto CLEANUP;
}
#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
/* multiply base point by order and check for point at infinity */
MP_CHECKOK(ec_GFp_pt_mul_aff(&group->order, &group->genx, &group->geny, &rx, &ry,
group));
if (ectestPrint) {
printf(" (order)*P (affine):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
if (ec_GFp_pt_is_inf_aff(&rx, &ry) != MP_YES) {
printf(" Error: invalid result (expected point at infinity).\n");
res = MP_NO;
goto CLEANUP;
}
#endif
#ifdef ECL_ENABLE_GFP_PT_MUL_JAC
/* multiply base point by order and check for point at infinity */
MP_CHECKOK(ec_GFp_pt_mul_jac(&group->order, &group->genx, &group->geny, &rx, &ry,
group));
if (ectestPrint) {
printf(" (order)*P (jacobian):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
if (ec_GFp_pt_is_inf_aff(&rx, &ry) != MP_YES) {
printf(" Error: invalid result (expected point at infinity).\n");
res = MP_NO;
goto CLEANUP;
}
#endif
/* multiply base point by order and check for point at infinity */
MP_CHECKOK(ECPoint_mul(group, &group->order, NULL, NULL, &rx, &ry));
if (ectestPrint) {
printf(" (order)*P (ECPoint_mul):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
if (ec_GFp_pt_is_inf_aff(&rx, &ry) != MP_YES) {
printf(" Error: invalid result (expected point at infinity).\n");
res = MP_NO;
goto CLEANUP;
}
/* multiply base point by order and check for point at infinity */
MP_CHECKOK(ECPoint_mul(group, &group->order, &gx, &gy, &rx, &ry));
if (ectestPrint) {
printf(" (order)*P (ECPoint_mul):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
if (ec_GFp_pt_is_inf_aff(&rx, &ry) != MP_YES) {
printf(" Error: invalid result (expected point at infinity).\n");
res = MP_NO;
goto CLEANUP;
}
/* check that (order-1)P + (order-1)P + P == (order-1)P */
MP_CHECKOK(ECPoints_mul(group, &order_1, &order_1, &gx, &gy, &rx, &ry));
MP_CHECKOK(ECPoints_mul(group, &one, &one, &rx, &ry, &rx, &ry));
if (ectestPrint) {
printf(" (order-1)*P + (order-1)*P + P == (order-1)*P (ECPoints_mul):\n");
MP_CHECKOK(mp_toradix(&rx, s, 16));
printf(" %s\n", s);
MP_CHECKOK(mp_toradix(&ry, s, 16));
printf(" %s\n", s);
}
MP_CHECKOK(mp_submod(&group->meth->irr, &ry, &group->meth->irr, &ry));
if ((mp_cmp(&rx, &gx) != 0) || (mp_cmp(&ry, &gy) != 0)) {
printf(" Error: invalid result (expected (- base point)).\n");
res = MP_NO;
goto CLEANUP;
}
/* test validate_point function */
if (ECPoint_validate(group, &gx, &gy) != MP_YES) {
printf(" Error: validate point on base point failed.\n");
res = MP_NO;
goto CLEANUP;
}
MP_CHECKOK(mp_add_d(&gy, 1, &ry));
if (ECPoint_validate(group, &gx, &ry) != MP_NO) {
printf(" Error: validate point on invalid point passed.\n");
res = MP_NO;
goto CLEANUP;
}
if (ectestTime) {
/* compute random scalar */
size = mpl_significant_bits(&group->meth->irr);
if (size < MP_OKAY) {
goto CLEANUP;
}
MP_CHECKOK(mpp_random_size(&n, (size + ECL_BITS - 1) / ECL_BITS));
MP_CHECKOK(group->meth->field_mod(&n, &n, group->meth));
/* timed test */
if (generic) {
#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
M_TimeOperation(MP_CHECKOK(ec_GFp_pt_mul_aff(&n, &group->genx, &group->geny, &rx, &ry,
group)),
100);
#endif
M_TimeOperation(MP_CHECKOK(ECPoint_mul(group, &n, NULL, NULL, &rx, &ry)),
100);
M_TimeOperation(MP_CHECKOK(ECPoints_mul(group, &n, &n, &gx, &gy, &rx, &ry)), 100);
} else {
M_TimeOperation(MP_CHECKOK(ECPoint_mul(group, &n, NULL, NULL, &rx, &ry)),
100);
M_TimeOperation(MP_CHECKOK(ECPoint_mul(group, &n, &gx, &gy, &rx, &ry)),
100);
M_TimeOperation(MP_CHECKOK(ECPoints_mul(group, &n, &n, &gx, &gy, &rx, &ry)), 100);
}
}
CLEANUP:
mp_clear(&one);
mp_clear(&order_1);
mp_clear(&gx);
mp_clear(&gy);
mp_clear(&rx);
mp_clear(&ry);
mp_clear(&n);
if (res != MP_OKAY) {
printf(" Error: exiting with error value %i\n", res);
}
return res;
}
/*
* Computes scalar point multiplication pointQ = k1 * G + k2 * pointP for
* the curve whose parameters are encoded in params with base point G.
*/
SECStatus
ec_points_mul(const ECParams *params, const mp_int *k1, const mp_int *k2,
const SECItem *pointP, SECItem *pointQ)
{
mp_int Px, Py, Qx, Qy;
mp_int Gx, Gy, order, irreducible, a, b;
#if 0 /* currently don't support non-named curves */
unsigned int irr_arr[5];
#endif
ECGroup *group = NULL;
SECStatus rv = SECFailure;
mp_err err = MP_OKAY;
int len;
#if EC_DEBUG
int i;
char mpstr[256];
printf("ec_points_mul: params [len=%d]:", params->DEREncoding.len);
for (i = 0; i < params->DEREncoding.len; i++)
printf("%02x:", params->DEREncoding.data[i]);
printf("\n");
if (k1 != NULL) {
mp_tohex(k1, mpstr);
printf("ec_points_mul: scalar k1: %s\n", mpstr);
mp_todecimal(k1, mpstr);
printf("ec_points_mul: scalar k1: %s (dec)\n", mpstr);
}
if (k2 != NULL) {
mp_tohex(k2, mpstr);
printf("ec_points_mul: scalar k2: %s\n", mpstr);
mp_todecimal(k2, mpstr);
printf("ec_points_mul: scalar k2: %s (dec)\n", mpstr);
}
if (pointP != NULL) {
printf("ec_points_mul: pointP [len=%d]:", pointP->len);
for (i = 0; i < pointP->len; i++)
printf("%02x:", pointP->data[i]);
printf("\n");
}
#endif
/* NOTE: We only support uncompressed points for now */
len = (params->fieldID.size + 7) >> 3;
if (pointP != NULL) {
if ((pointP->data[0] != EC_POINT_FORM_UNCOMPRESSED) ||
(pointP->len != (2 * len + 1))) {
PORT_SetError(SEC_ERROR_UNSUPPORTED_EC_POINT_FORM);
return SECFailure;
};
}
MP_DIGITS(&Px) = 0;
MP_DIGITS(&Py) = 0;
MP_DIGITS(&Qx) = 0;
MP_DIGITS(&Qy) = 0;
MP_DIGITS(&Gx) = 0;
MP_DIGITS(&Gy) = 0;
MP_DIGITS(&order) = 0;
MP_DIGITS(&irreducible) = 0;
MP_DIGITS(&a) = 0;
MP_DIGITS(&b) = 0;
CHECK_MPI_OK( mp_init(&Px) );
CHECK_MPI_OK( mp_init(&Py) );
CHECK_MPI_OK( mp_init(&Qx) );
CHECK_MPI_OK( mp_init(&Qy) );
CHECK_MPI_OK( mp_init(&Gx) );
CHECK_MPI_OK( mp_init(&Gy) );
CHECK_MPI_OK( mp_init(&order) );
CHECK_MPI_OK( mp_init(&irreducible) );
CHECK_MPI_OK( mp_init(&a) );
CHECK_MPI_OK( mp_init(&b) );
if ((k2 != NULL) && (pointP != NULL)) {
/* Initialize Px and Py */
CHECK_MPI_OK( mp_read_unsigned_octets(&Px, pointP->data + 1, (mp_size) len) );
CHECK_MPI_OK( mp_read_unsigned_octets(&Py, pointP->data + 1 + len, (mp_size) len) );
}
/* construct from named params, if possible */
if (params->name != ECCurve_noName) {
group = ECGroup_fromName(params->name);
}
#if 0 /* currently don't support non-named curves */
if (group == NULL) {
/* Set up mp_ints containing the curve coefficients */
CHECK_MPI_OK( mp_read_unsigned_octets(&Gx, params->base.data + 1,
(mp_size) len) );
CHECK_MPI_OK( mp_read_unsigned_octets(&Gy, params->base.data + 1 + len,
(mp_size) len) );
SECITEM_TO_MPINT( params->order, &order );
SECITEM_TO_MPINT( params->curve.a, &a );
SECITEM_TO_MPINT( params->curve.b, &b );
if (params->fieldID.type == ec_field_GFp) {
SECITEM_TO_MPINT( params->fieldID.u.prime, &irreducible );
group = ECGroup_consGFp(&irreducible, &a, &b, &Gx, &Gy, &order, params->cofactor);
} else {
SECITEM_TO_MPINT( params->fieldID.u.poly, &irreducible );
irr_arr[0] = params->fieldID.size;
irr_arr[1] = params->fieldID.k1;
irr_arr[2] = params->fieldID.k2;
irr_arr[3] = params->fieldID.k3;
irr_arr[4] = 0;
group = ECGroup_consGF2m(&irreducible, irr_arr, &a, &b, &Gx, &Gy, &order, params->cofactor);
}
}
#endif
if (group == NULL)
goto cleanup;
if ((k2 != NULL) && (pointP != NULL)) {
CHECK_MPI_OK( ECPoints_mul(group, k1, k2, &Px, &Py, &Qx, &Qy) );
} else {
CHECK_MPI_OK( ECPoints_mul(group, k1, NULL, NULL, NULL, &Qx, &Qy) );
}
/* Construct the SECItem representation of point Q */
pointQ->data[0] = EC_POINT_FORM_UNCOMPRESSED;
CHECK_MPI_OK( mp_to_fixlen_octets(&Qx, pointQ->data + 1,
(mp_size) len) );
CHECK_MPI_OK( mp_to_fixlen_octets(&Qy, pointQ->data + 1 + len,
(mp_size) len) );
rv = SECSuccess;
#if EC_DEBUG
printf("ec_points_mul: pointQ [len=%d]:", pointQ->len);
for (i = 0; i < pointQ->len; i++)
printf("%02x:", pointQ->data[i]);
printf("\n");
#endif
cleanup:
ECGroup_free(group);
mp_clear(&Px);
mp_clear(&Py);
mp_clear(&Qx);
mp_clear(&Qy);
mp_clear(&Gx);
mp_clear(&Gy);
mp_clear(&order);
mp_clear(&irreducible);
mp_clear(&a);
mp_clear(&b);
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
return rv;
}
/*
* Computes scalar point multiplication pointQ = k1 * G + k2 * pointP for
* the curve whose parameters are encoded in params with base point G.
*/
SECStatus
ec_points_mul(const ECParams *params, const mp_int *k1, const mp_int *k2,
const SECItem *pointP, SECItem *pointQ, int kmflag)
{
mp_int Px, Py, Qx, Qy;
mp_int Gx, Gy, order, irreducible, a, b;
ECGroup *group = NULL;
SECStatus rv = SECFailure;
mp_err err = MP_OKAY;
int len;
#if EC_DEBUG
int i;
char mpstr[256];
if (k1 != NULL) {
mp_tohex(k1, mpstr);
printf("ec_points_mul: scalar k1: %s\n", mpstr);
mp_todecimal(k1, mpstr);
printf("ec_points_mul: scalar k1: %s (dec)\n", mpstr);
}
if (k2 != NULL) {
mp_tohex(k2, mpstr);
printf("ec_points_mul: scalar k2: %s\n", mpstr);
mp_todecimal(k2, mpstr);
printf("ec_points_mul: scalar k2: %s (dec)\n", mpstr);
}
if (pointP != NULL) {
printf("ec_points_mul: pointP [len=%d]:", pointP->len);
for (i = 0; i < pointP->len; i++)
printf("%02x:", pointP->data[i]);
printf("\n");
}
#endif
/* NOTE: We only support uncompressed points for now */
len = (params->fieldID.size + 7) >> 3;
if (pointP != NULL) {
if ((pointP->data[0] != EC_POINT_FORM_UNCOMPRESSED) ||
(pointP->len != (unsigned int)(2 * len + 1))) {
return SECFailure;
};
}
MP_DIGITS(&Px) = 0;
MP_DIGITS(&Py) = 0;
MP_DIGITS(&Qx) = 0;
MP_DIGITS(&Qy) = 0;
MP_DIGITS(&Gx) = 0;
MP_DIGITS(&Gy) = 0;
MP_DIGITS(&order) = 0;
MP_DIGITS(&irreducible) = 0;
MP_DIGITS(&a) = 0;
MP_DIGITS(&b) = 0;
CHECK_MPI_OK( mp_init(&Px) );
CHECK_MPI_OK( mp_init(&Py) );
CHECK_MPI_OK( mp_init(&Qx) );
CHECK_MPI_OK( mp_init(&Qy) );
CHECK_MPI_OK( mp_init(&Gx) );
CHECK_MPI_OK( mp_init(&Gy) );
CHECK_MPI_OK( mp_init(&order) );
CHECK_MPI_OK( mp_init(&irreducible) );
CHECK_MPI_OK( mp_init(&a) );
CHECK_MPI_OK( mp_init(&b) );
if ((k2 != NULL) && (pointP != NULL)) {
/* Initialize Px and Py */
CHECK_MPI_OK( mp_read_unsigned_octets(&Px, pointP->data + 1, (mp_size) len) );
CHECK_MPI_OK( mp_read_unsigned_octets(&Py, pointP->data + 1 + len, (mp_size) len) );
}
/* construct from named params, if possible */
if (params->name != ECCurve_noName) {
group = ECGroup_fromName(params->name);
}
if (group == NULL)
goto cleanup;
if ((k2 != NULL) && (pointP != NULL)) {
CHECK_MPI_OK( ECPoints_mul(group, k1, k2, &Px, &Py, &Qx, &Qy) );
} else {
CHECK_MPI_OK( ECPoints_mul(group, k1, NULL, NULL, NULL, &Qx, &Qy) );
}
/* Construct the SECItem representation of point Q */
pointQ->data[0] = EC_POINT_FORM_UNCOMPRESSED;
CHECK_MPI_OK( mp_to_fixlen_octets(&Qx, pointQ->data + 1,
(mp_size) len) );
CHECK_MPI_OK( mp_to_fixlen_octets(&Qy, pointQ->data + 1 + len,
(mp_size) len) );
rv = SECSuccess;
#if EC_DEBUG
printf("ec_points_mul: pointQ [len=%d]:", pointQ->len);
for (i = 0; i < pointQ->len; i++)
printf("%02x:", pointQ->data[i]);
printf("\n");
#endif
cleanup:
ECGroup_free(group);
mp_clear(&Px);
mp_clear(&Py);
mp_clear(&Qx);
mp_clear(&Qy);
mp_clear(&Gx);
mp_clear(&Gy);
mp_clear(&order);
mp_clear(&irreducible);
mp_clear(&a);
mp_clear(&b);
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
return rv;
}
