diff options
Diffstat (limited to 'security/nss/lib/freebl/ecl/ecp_aff.c')
| -rw-r--r-- | security/nss/lib/freebl/ecl/ecp_aff.c | 308 |
1 files changed, 308 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/ecl/ecp_aff.c b/security/nss/lib/freebl/ecl/ecp_aff.c new file mode 100644 index 000000000..47fb27326 --- /dev/null +++ b/security/nss/lib/freebl/ecl/ecp_aff.c @@ -0,0 +1,308 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ + +#include "ecp.h" +#include "mplogic.h" +#include <stdlib.h> + +/* Checks if point P(px, py) is at infinity. Uses affine coordinates. */ +mp_err +ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py) +{ + + if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) { + return MP_YES; + } else { + return MP_NO; + } +} + +/* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */ +mp_err +ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py) +{ + mp_zero(px); + mp_zero(py); + return MP_OKAY; +} + +/* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P, + * Q, and R can all be identical. Uses 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_aff(const mp_int *px, const mp_int *py, const mp_int *qx, + const mp_int *qy, mp_int *rx, mp_int *ry, + const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int lambda, temp, tempx, tempy; + + MP_DIGITS(&lambda) = 0; + MP_DIGITS(&temp) = 0; + MP_DIGITS(&tempx) = 0; + MP_DIGITS(&tempy) = 0; + MP_CHECKOK(mp_init(&lambda)); + MP_CHECKOK(mp_init(&temp)); + MP_CHECKOK(mp_init(&tempx)); + MP_CHECKOK(mp_init(&tempy)); + /* if P = inf, then R = Q */ + if (ec_GFp_pt_is_inf_aff(px, py) == 0) { + MP_CHECKOK(mp_copy(qx, rx)); + MP_CHECKOK(mp_copy(qy, ry)); + res = MP_OKAY; + goto CLEANUP; + } + /* if Q = inf, then R = P */ + if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) { + MP_CHECKOK(mp_copy(px, rx)); + MP_CHECKOK(mp_copy(py, ry)); + res = MP_OKAY; + goto CLEANUP; + } + /* if px != qx, then lambda = (py-qy) / (px-qx) */ + if (mp_cmp(px, qx) != 0) { + MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth)); + MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth)); + MP_CHECKOK(group->meth->field_div(&tempy, &tempx, &lambda, group->meth)); + } else { + /* if py != qy or qy = 0, then R = inf */ + if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) { + mp_zero(rx); + mp_zero(ry); + res = MP_OKAY; + goto CLEANUP; + } + /* lambda = (3qx^2+a) / (2qy) */ + MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth)); + MP_CHECKOK(mp_set_int(&temp, 3)); + if (group->meth->field_enc) { + MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth)); + } + MP_CHECKOK(group->meth->field_mul(&tempx, &temp, &tempx, group->meth)); + MP_CHECKOK(group->meth->field_add(&tempx, &group->curvea, &tempx, group->meth)); + MP_CHECKOK(mp_set_int(&temp, 2)); + if (group->meth->field_enc) { + MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth)); + } + MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth)); + MP_CHECKOK(group->meth->field_div(&tempx, &tempy, &lambda, group->meth)); + } + /* rx = lambda^2 - px - qx */ + MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth)); + MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth)); + MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth)); + /* ry = (x1-x2) * lambda - y1 */ + MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth)); + MP_CHECKOK(group->meth->field_mul(&tempy, &lambda, &tempy, group->meth)); + MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth)); + MP_CHECKOK(mp_copy(&tempx, rx)); + MP_CHECKOK(mp_copy(&tempy, ry)); + +CLEANUP: + mp_clear(&lambda); + mp_clear(&temp); + mp_clear(&tempx); + mp_clear(&tempy); + return res; +} + +/* Computes R = P - Q. Elliptic curve points P, Q, and R can all be + * identical. Uses affine coordinates. Assumes input is already + * field-encoded using field_enc, and returns output that is still + * field-encoded. */ +mp_err +ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx, + const mp_int *qy, mp_int *rx, mp_int *ry, + const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int nqy; + + MP_DIGITS(&nqy) = 0; + MP_CHECKOK(mp_init(&nqy)); + /* nqy = -qy */ + MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth)); + res = group->point_add(px, py, qx, &nqy, rx, ry, group); +CLEANUP: + mp_clear(&nqy); + return res; +} + +/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses + * affine coordinates. Assumes input is already field-encoded using + * field_enc, and returns output that is still field-encoded. */ +mp_err +ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx, + mp_int *ry, const ECGroup *group) +{ + return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group); +} + +/* by default, this routine is unused and thus doesn't need to be compiled */ +#ifdef ECL_ENABLE_GFP_PT_MUL_AFF +/* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and + * R can be identical. Uses affine coordinates. Assumes input is already + * field-encoded using field_enc, and returns output that is still + * field-encoded. */ +mp_err +ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py, + mp_int *rx, mp_int *ry, const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int k, k3, qx, qy, sx, sy; + int b1, b3, i, l; + + MP_DIGITS(&k) = 0; + MP_DIGITS(&k3) = 0; + MP_DIGITS(&qx) = 0; + MP_DIGITS(&qy) = 0; + MP_DIGITS(&sx) = 0; + MP_DIGITS(&sy) = 0; + MP_CHECKOK(mp_init(&k)); + MP_CHECKOK(mp_init(&k3)); + MP_CHECKOK(mp_init(&qx)); + MP_CHECKOK(mp_init(&qy)); + MP_CHECKOK(mp_init(&sx)); + MP_CHECKOK(mp_init(&sy)); + + /* if n = 0 then r = inf */ + if (mp_cmp_z(n) == 0) { + mp_zero(rx); + mp_zero(ry); + res = MP_OKAY; + goto CLEANUP; + } + /* Q = P, k = n */ + MP_CHECKOK(mp_copy(px, &qx)); + MP_CHECKOK(mp_copy(py, &qy)); + MP_CHECKOK(mp_copy(n, &k)); + /* if n < 0 then Q = -Q, k = -k */ + if (mp_cmp_z(n) < 0) { + MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth)); + MP_CHECKOK(mp_neg(&k, &k)); + } +#ifdef ECL_DEBUG /* basic double and add method */ + l = mpl_significant_bits(&k) - 1; + MP_CHECKOK(mp_copy(&qx, &sx)); + MP_CHECKOK(mp_copy(&qy, &sy)); + for (i = l - 1; i >= 0; i--) { + /* S = 2S */ + MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); + /* if k_i = 1, then S = S + Q */ + if (mpl_get_bit(&k, i) != 0) { + MP_CHECKOK(group->point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); + } + } +#else /* double and add/subtract method from \ + * standard */ + /* k3 = 3 * k */ + MP_CHECKOK(mp_set_int(&k3, 3)); + MP_CHECKOK(mp_mul(&k, &k3, &k3)); + /* S = Q */ + MP_CHECKOK(mp_copy(&qx, &sx)); + MP_CHECKOK(mp_copy(&qy, &sy)); + /* l = index of high order bit in binary representation of 3*k */ + l = mpl_significant_bits(&k3) - 1; + /* for i = l-1 downto 1 */ + for (i = l - 1; i >= 1; i--) { + /* S = 2S */ + MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); + b3 = MP_GET_BIT(&k3, i); + b1 = MP_GET_BIT(&k, i); + /* if k3_i = 1 and k_i = 0, then S = S + Q */ + if ((b3 == 1) && (b1 == 0)) { + MP_CHECKOK(group->point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); + /* if k3_i = 0 and k_i = 1, then S = S - Q */ + } else if ((b3 == 0) && (b1 == 1)) { + MP_CHECKOK(group->point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group)); + } + } +#endif + /* output S */ + MP_CHECKOK(mp_copy(&sx, rx)); + MP_CHECKOK(mp_copy(&sy, ry)); + +CLEANUP: + mp_clear(&k); + mp_clear(&k3); + mp_clear(&qx); + mp_clear(&qy); + mp_clear(&sx); + mp_clear(&sy); + return res; +} +#endif + +/* Validates a point on a GFp curve. */ +mp_err +ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group) +{ + mp_err res = MP_NO; + mp_int accl, accr, tmp, pxt, pyt; + + MP_DIGITS(&accl) = 0; + MP_DIGITS(&accr) = 0; + MP_DIGITS(&tmp) = 0; + MP_DIGITS(&pxt) = 0; + MP_DIGITS(&pyt) = 0; + MP_CHECKOK(mp_init(&accl)); + MP_CHECKOK(mp_init(&accr)); + MP_CHECKOK(mp_init(&tmp)); + MP_CHECKOK(mp_init(&pxt)); + MP_CHECKOK(mp_init(&pyt)); + + /* 1: Verify that publicValue is not the point at infinity */ + if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) { + res = MP_NO; + goto CLEANUP; + } + /* 2: Verify that the coordinates of publicValue are elements + * of the field. + */ + if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) || + (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) { + res = MP_NO; + goto CLEANUP; + } + /* 3: Verify that publicValue is on the curve. */ + if (group->meth->field_enc) { + group->meth->field_enc(px, &pxt, group->meth); + group->meth->field_enc(py, &pyt, group->meth); + } else { + MP_CHECKOK(mp_copy(px, &pxt)); + MP_CHECKOK(mp_copy(py, &pyt)); + } + /* left-hand side: y^2 */ + MP_CHECKOK(group->meth->field_sqr(&pyt, &accl, group->meth)); + /* right-hand side: x^3 + a*x + b = (x^2 + a)*x + b by Horner's rule */ + MP_CHECKOK(group->meth->field_sqr(&pxt, &tmp, group->meth)); + MP_CHECKOK(group->meth->field_add(&tmp, &group->curvea, &tmp, group->meth)); + MP_CHECKOK(group->meth->field_mul(&tmp, &pxt, &accr, group->meth)); + MP_CHECKOK(group->meth->field_add(&accr, &group->curveb, &accr, group->meth)); + /* check LHS - RHS == 0 */ + MP_CHECKOK(group->meth->field_sub(&accl, &accr, &accr, group->meth)); + if (mp_cmp_z(&accr) != 0) { + res = MP_NO; + goto CLEANUP; + } + /* 4: Verify that the order of the curve times the publicValue + * is the point at infinity. + */ + MP_CHECKOK(ECPoint_mul(group, &group->order, px, py, &pxt, &pyt)); + if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) { + res = MP_NO; + goto CLEANUP; + } + + res = MP_YES; + +CLEANUP: + mp_clear(&accl); + mp_clear(&accr); + mp_clear(&tmp); + mp_clear(&pxt); + mp_clear(&pyt); + return res; +} |