diff options
Diffstat (limited to 'nss/lib/freebl/ecl/ecp_jm.c')
| -rw-r--r-- | nss/lib/freebl/ecl/ecp_jm.c | 444 |
1 files changed, 219 insertions, 225 deletions
diff --git a/nss/lib/freebl/ecl/ecp_jm.c b/nss/lib/freebl/ecl/ecp_jm.c index 2d56412..a1106ce 100644 --- a/nss/lib/freebl/ecl/ecp_jm.c +++ b/nss/lib/freebl/ecl/ecp_jm.c @@ -9,76 +9,74 @@ #define MAX_SCRATCH 6 -/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses +/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses * Modified Jacobian coordinates. * - * Assumes input is already field-encoded using field_enc, and returns + * Assumes input is already field-encoded using field_enc, and returns * output that is still field-encoded. * */ static mp_err ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz, - const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz, - mp_int *raz4, mp_int scratch[], const ECGroup *group) + const mp_int *paz4, 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 *t0, *t1, *M, *S; + mp_err res = MP_OKAY; + mp_int *t0, *t1, *M, *S; - t0 = &scratch[0]; - t1 = &scratch[1]; - M = &scratch[2]; - S = &scratch[3]; + t0 = &scratch[0]; + t1 = &scratch[1]; + M = &scratch[2]; + S = &scratch[3]; #if MAX_SCRATCH < 4 #error "Scratch array defined too small " #endif - /* Check for point at infinity */ - if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { - /* Set r = pt at infinity by setting rz = 0 */ + /* Check for point at infinity */ + if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { + /* Set r = pt at infinity by setting rz = 0 */ - MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); - goto CLEANUP; - } + MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); + goto CLEANUP; + } - /* M = 3 (px^2) + a*(pz^4) */ - MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth)); - MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth)); - MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth)); - MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth)); + /* M = 3 (px^2) + a*(pz^4) */ + MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth)); + MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth)); + MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth)); + MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth)); - /* rz = 2 * py * pz */ - MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth)); - MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth)); + /* rz = 2 * py * pz */ + MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth)); + MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth)); - /* t0 = 2y^2 , t1 = 8y^4 */ - MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth)); - MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth)); - MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth)); - MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth)); + /* t0 = 2y^2 , t1 = 8y^4 */ + MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth)); + MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth)); + MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth)); + MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth)); - /* S = 4 * px * py^2 = 2 * px * t0 */ - MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth)); - MP_CHECKOK(group->meth->field_add(S, S, S, group->meth)); + /* S = 4 * px * py^2 = 2 * px * t0 */ + MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth)); + MP_CHECKOK(group->meth->field_add(S, S, S, group->meth)); + /* rx = M^2 - 2S */ + MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth)); + MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth)); + MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth)); - /* rx = M^2 - 2S */ - MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth)); - MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth)); - MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth)); + /* ry = M * (S - rx) - t1 */ + MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth)); + MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth)); + MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth)); - /* ry = M * (S - rx) - t1 */ - MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth)); - MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth)); - MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth)); + /* ra*z^4 = 2*t1*(apz4) */ + MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth)); + MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth)); - /* ra*z^4 = 2*t1*(apz4) */ - MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth)); - MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth)); - - - CLEANUP: - return res; +CLEANUP: + return res; } /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is @@ -88,84 +86,82 @@ ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz, * field-encoded. */ static 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) + 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; + 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]; + 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)); + /* 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; + return res; } /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic @@ -174,116 +170,114 @@ CLEANUP: * additions. Assumes input is already field-encoded using field_enc, and * returns output that is still field-encoded. Uses 5-bit window NAF * method (algorithm 11) for scalar-point multiplication from Brown, - * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic + * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic * Curves Over Prime Fields. */ mp_err ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py, - mp_int *rx, mp_int *ry, const ECGroup *group) + mp_int *rx, mp_int *ry, const ECGroup *group) { - mp_err res = MP_OKAY; - mp_int precomp[16][2], rz, tpx, tpy; - mp_int raz4; - mp_int scratch[MAX_SCRATCH]; - signed char *naf = NULL; - int i, orderBitSize; - - MP_DIGITS(&rz) = 0; - MP_DIGITS(&raz4) = 0; - MP_DIGITS(&tpx) = 0; - MP_DIGITS(&tpy) = 0; - for (i = 0; i < 16; i++) { - MP_DIGITS(&precomp[i][0]) = 0; - MP_DIGITS(&precomp[i][1]) = 0; - } - for (i = 0; i < MAX_SCRATCH; i++) { - MP_DIGITS(&scratch[i]) = 0; - } - - ARGCHK(group != NULL, MP_BADARG); - ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG); - - /* initialize precomputation table */ - MP_CHECKOK(mp_init(&tpx)); - MP_CHECKOK(mp_init(&tpy));; - MP_CHECKOK(mp_init(&rz)); - MP_CHECKOK(mp_init(&raz4)); - - for (i = 0; i < 16; i++) { - MP_CHECKOK(mp_init(&precomp[i][0])); - MP_CHECKOK(mp_init(&precomp[i][1])); - } - for (i = 0; i < MAX_SCRATCH; i++) { - MP_CHECKOK(mp_init(&scratch[i])); - } - - /* Set out[8] = P */ - MP_CHECKOK(mp_copy(px, &precomp[8][0])); - MP_CHECKOK(mp_copy(py, &precomp[8][1])); - - /* Set (tpx, tpy) = 2P */ - MP_CHECKOK(group-> - point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy, - group)); - - /* Set 3P, 5P, ..., 15P */ - for (i = 8; i < 15; i++) { - MP_CHECKOK(group-> - point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy, - &precomp[i + 1][0], &precomp[i + 1][1], - group)); - } - - /* Set -15P, -13P, ..., -P */ - for (i = 0; i < 8; i++) { - MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0])); - MP_CHECKOK(group->meth-> - field_neg(&precomp[15 - i][1], &precomp[i][1], - group->meth)); - } - - /* R = inf */ - MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); - - orderBitSize = mpl_significant_bits(&group->order); - - /* Allocate memory for NAF */ - naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1)); - if (naf == NULL) { - res = MP_MEM; - goto CLEANUP; - } - - /* Compute 5NAF */ - ec_compute_wNAF(naf, orderBitSize, n, 5); - - /* wNAF method */ - for (i = orderBitSize; i >= 0; i--) { - /* R = 2R */ - ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz, - &raz4, scratch, group); - if (naf[i] != 0) { - ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4, - &precomp[(naf[i] + 15) / 2][0], - &precomp[(naf[i] + 15) / 2][1], rx, ry, - &rz, &raz4, scratch, group); - } - } - - /* convert result S to affine coordinates */ - MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); - - CLEANUP: - for (i = 0; i < MAX_SCRATCH; i++) { - mp_clear(&scratch[i]); - } - for (i = 0; i < 16; i++) { - mp_clear(&precomp[i][0]); - mp_clear(&precomp[i][1]); - } - mp_clear(&tpx); - mp_clear(&tpy); - mp_clear(&rz); - mp_clear(&raz4); - free(naf); - return res; + mp_err res = MP_OKAY; + mp_int precomp[16][2], rz, tpx, tpy; + mp_int raz4; + mp_int scratch[MAX_SCRATCH]; + signed char *naf = NULL; + int i, orderBitSize; + + MP_DIGITS(&rz) = 0; + MP_DIGITS(&raz4) = 0; + MP_DIGITS(&tpx) = 0; + MP_DIGITS(&tpy) = 0; + for (i = 0; i < 16; i++) { + MP_DIGITS(&precomp[i][0]) = 0; + MP_DIGITS(&precomp[i][1]) = 0; + } + for (i = 0; i < MAX_SCRATCH; i++) { + MP_DIGITS(&scratch[i]) = 0; + } + + ARGCHK(group != NULL, MP_BADARG); + ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG); + + /* initialize precomputation table */ + MP_CHECKOK(mp_init(&tpx)); + MP_CHECKOK(mp_init(&tpy)); + ; + MP_CHECKOK(mp_init(&rz)); + MP_CHECKOK(mp_init(&raz4)); + + for (i = 0; i < 16; i++) { + MP_CHECKOK(mp_init(&precomp[i][0])); + MP_CHECKOK(mp_init(&precomp[i][1])); + } + for (i = 0; i < MAX_SCRATCH; i++) { + MP_CHECKOK(mp_init(&scratch[i])); + } + + /* Set out[8] = P */ + MP_CHECKOK(mp_copy(px, &precomp[8][0])); + MP_CHECKOK(mp_copy(py, &precomp[8][1])); + + /* Set (tpx, tpy) = 2P */ + MP_CHECKOK(group->point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy, + group)); + + /* Set 3P, 5P, ..., 15P */ + for (i = 8; i < 15; i++) { + MP_CHECKOK(group->point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy, + &precomp[i + 1][0], &precomp[i + 1][1], + group)); + } + + /* Set -15P, -13P, ..., -P */ + for (i = 0; i < 8; i++) { + MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0])); + MP_CHECKOK(group->meth->field_neg(&precomp[15 - i][1], &precomp[i][1], + group->meth)); + } + + /* R = inf */ + MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); + + orderBitSize = mpl_significant_bits(&group->order); + + /* Allocate memory for NAF */ + naf = (signed char *)malloc(sizeof(signed char) * (orderBitSize + 1)); + if (naf == NULL) { + res = MP_MEM; + goto CLEANUP; + } + + /* Compute 5NAF */ + ec_compute_wNAF(naf, orderBitSize, n, 5); + + /* wNAF method */ + for (i = orderBitSize; i >= 0; i--) { + /* R = 2R */ + ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz, + &raz4, scratch, group); + if (naf[i] != 0) { + ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4, + &precomp[(naf[i] + 15) / 2][0], + &precomp[(naf[i] + 15) / 2][1], rx, ry, + &rz, &raz4, scratch, group); + } + } + + /* convert result S to affine coordinates */ + MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); + +CLEANUP: + for (i = 0; i < MAX_SCRATCH; i++) { + mp_clear(&scratch[i]); + } + for (i = 0; i < 16; i++) { + mp_clear(&precomp[i][0]); + mp_clear(&precomp[i][1]); + } + mp_clear(&tpx); + mp_clear(&tpy); + mp_clear(&rz); + mp_clear(&raz4); + free(naf); + return res; } |