diff options
Diffstat (limited to 'nss/lib/freebl/ecl/ecp_fpinc.c')
-rw-r--r-- | nss/lib/freebl/ecl/ecp_fpinc.c | 821 |
1 files changed, 0 insertions, 821 deletions
diff --git a/nss/lib/freebl/ecl/ecp_fpinc.c b/nss/lib/freebl/ecl/ecp_fpinc.c deleted file mode 100644 index be0f966..0000000 --- a/nss/lib/freebl/ecl/ecp_fpinc.c +++ /dev/null @@ -1,821 +0,0 @@ -/* 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/. */ - -/* This source file is meant to be included by other source files - * (ecp_fp###.c, where ### is one of 160, 192, 224) and should not - * constitute an independent compilation unit. It requires the following - * preprocessor definitions be made: ECFP_BSIZE - the number of bits in - * the field's prime - * ECFP_NUMDOUBLES - the number of doubles to store one - * multi-precision integer in floating point - -/* Adds a prefix to a given token to give a unique token name. Prefixes - * with "ecfp" + ECFP_BSIZE + "_". e.g. if ECFP_BSIZE = 160, then - * PREFIX(hello) = ecfp160_hello This optimization allows static function - * linking and compiler loop unrolling without code duplication. */ -#ifndef PREFIX -#define PREFIX(b) PREFIX1(ECFP_BSIZE, b) -#define PREFIX1(bsize, b) PREFIX2(bsize, b) -#define PREFIX2(bsize, b) ecfp ## bsize ## _ ## b -#endif - -/* Returns true iff every double in d is 0. (If d == 0 and it is tidied, - * this will be true.) */ -mp_err PREFIX(isZero) (const double *d) { - int i; - - for (i = 0; i < ECFP_NUMDOUBLES; i++) { - if (d[i] != 0) - return MP_NO; - } - return MP_YES; -} - -/* Sets the multi-precision floating point number at t = 0 */ -void PREFIX(zero) (double *t) { - int i; - - for (i = 0; i < ECFP_NUMDOUBLES; i++) { - t[i] = 0; - } -} - -/* Sets the multi-precision floating point number at t = 1 */ -void PREFIX(one) (double *t) { - int i; - - t[0] = 1; - for (i = 1; i < ECFP_NUMDOUBLES; i++) { - t[i] = 0; - } -} - -/* Checks if point P(x, y, z) is at infinity. Uses Jacobian coordinates. */ -mp_err PREFIX(pt_is_inf_jac) (const ecfp_jac_pt * p) { - return PREFIX(isZero) (p->z); -} - -/* Sets the Jacobian point P to be at infinity. */ -void PREFIX(set_pt_inf_jac) (ecfp_jac_pt * p) { - PREFIX(zero) (p->z); -} - -/* Checks if point P(x, y) is at infinity. Uses Affine coordinates. */ -mp_err PREFIX(pt_is_inf_aff) (const ecfp_aff_pt * p) { - if (PREFIX(isZero) (p->x) == MP_YES && PREFIX(isZero) (p->y) == MP_YES) - return MP_YES; - return MP_NO; -} - -/* Sets the affine point P to be at infinity. */ -void PREFIX(set_pt_inf_aff) (ecfp_aff_pt * p) { - PREFIX(zero) (p->x); - PREFIX(zero) (p->y); -} - -/* Checks if point P(x, y, z, a*z^4) is at infinity. Uses Modified - * Jacobian coordinates. */ -mp_err PREFIX(pt_is_inf_jm) (const ecfp_jm_pt * p) { - return PREFIX(isZero) (p->z); -} - -/* Sets the Modified Jacobian point P to be at infinity. */ -void PREFIX(set_pt_inf_jm) (ecfp_jm_pt * p) { - PREFIX(zero) (p->z); -} - -/* Checks if point P(x, y, z, z^2, z^3) is at infinity. Uses Chudnovsky - * Jacobian coordinates */ -mp_err PREFIX(pt_is_inf_chud) (const ecfp_chud_pt * p) { - return PREFIX(isZero) (p->z); -} - -/* Sets the Chudnovsky Jacobian point P to be at infinity. */ -void PREFIX(set_pt_inf_chud) (ecfp_chud_pt * p) { - PREFIX(zero) (p->z); -} - -/* Copies a multi-precision floating point number, Setting dest = src */ -void PREFIX(copy) (double *dest, const double *src) { - int i; - - for (i = 0; i < ECFP_NUMDOUBLES; i++) { - dest[i] = src[i]; - } -} - -/* Sets dest = -src */ -void PREFIX(negLong) (double *dest, const double *src) { - int i; - - for (i = 0; i < 2 * ECFP_NUMDOUBLES; i++) { - dest[i] = -src[i]; - } -} - -/* Sets r = -p p = (x, y, z, z2, z3) r = (x, -y, z, z2, z3) Uses - * Chudnovsky Jacobian coordinates. */ -/* TODO reverse order */ -void PREFIX(pt_neg_chud) (const ecfp_chud_pt * p, ecfp_chud_pt * r) { - int i; - - PREFIX(copy) (r->x, p->x); - PREFIX(copy) (r->z, p->z); - PREFIX(copy) (r->z2, p->z2); - PREFIX(copy) (r->z3, p->z3); - for (i = 0; i < ECFP_NUMDOUBLES; i++) { - r->y[i] = -p->y[i]; - } -} - -/* Computes r = x + y. Does not tidy or reduce. Any combinations of r, x, - * y can point to the same data. Componentwise adds first ECFP_NUMDOUBLES - * doubles of x and y and stores the result in r. */ -void PREFIX(addShort) (double *r, const double *x, const double *y) { - int i; - - for (i = 0; i < ECFP_NUMDOUBLES; i++) { - *r++ = *x++ + *y++; - } -} - -/* Computes r = x + y. Does not tidy or reduce. Any combinations of r, x, - * y can point to the same data. Componentwise adds first - * 2*ECFP_NUMDOUBLES doubles of x and y and stores the result in r. */ -void PREFIX(addLong) (double *r, const double *x, const double *y) { - int i; - - for (i = 0; i < 2 * ECFP_NUMDOUBLES; i++) { - *r++ = *x++ + *y++; - } -} - -/* Computes r = x - y. Does not tidy or reduce. Any combinations of r, x, - * y can point to the same data. Componentwise subtracts first - * ECFP_NUMDOUBLES doubles of x and y and stores the result in r. */ -void PREFIX(subtractShort) (double *r, const double *x, const double *y) { - int i; - - for (i = 0; i < ECFP_NUMDOUBLES; i++) { - *r++ = *x++ - *y++; - } -} - -/* Computes r = x - y. Does not tidy or reduce. Any combinations of r, x, - * y can point to the same data. Componentwise subtracts first - * 2*ECFP_NUMDOUBLES doubles of x and y and stores the result in r. */ -void PREFIX(subtractLong) (double *r, const double *x, const double *y) { - int i; - - for (i = 0; i < 2 * ECFP_NUMDOUBLES; i++) { - *r++ = *x++ - *y++; - } -} - -/* Computes r = x*y. Both x and y should be tidied and reduced, - * r must be different (point to different memory) than x and y. - * Does not tidy or reduce. */ -void PREFIX(multiply)(double *r, const double *x, const double *y) { - int i, j; - - for(j=0;j<ECFP_NUMDOUBLES-1;j++) { - r[j] = x[0] * y[j]; - r[j+(ECFP_NUMDOUBLES-1)] = x[ECFP_NUMDOUBLES-1] * y[j]; - } - r[ECFP_NUMDOUBLES-1] = x[0] * y[ECFP_NUMDOUBLES-1]; - r[ECFP_NUMDOUBLES-1] += x[ECFP_NUMDOUBLES-1] * y[0]; - r[2*ECFP_NUMDOUBLES-2] = x[ECFP_NUMDOUBLES-1] * y[ECFP_NUMDOUBLES-1]; - r[2*ECFP_NUMDOUBLES-1] = 0; - - for(i=1;i<ECFP_NUMDOUBLES-1;i++) { - for(j=0;j<ECFP_NUMDOUBLES;j++) { - r[i+j] += (x[i] * y[j]); - } - } -} - -/* Computes the square of x and stores the result in r. x should be - * tidied & reduced, r will be neither tidied nor reduced. - * r should point to different memory than x */ -void PREFIX(square) (double *r, const double *x) { - PREFIX(multiply) (r, x, x); -} - -/* Perform a point doubling in Jacobian coordinates. Input and output - * should be multi-precision floating point integers. */ -void PREFIX(pt_dbl_jac) (const ecfp_jac_pt * dp, ecfp_jac_pt * dr, - const EC_group_fp * group) { - double t0[2 * ECFP_NUMDOUBLES], t1[2 * ECFP_NUMDOUBLES], - M[2 * ECFP_NUMDOUBLES], S[2 * ECFP_NUMDOUBLES]; - - /* Check for point at infinity */ - if (PREFIX(pt_is_inf_jac) (dp) == MP_YES) { - /* Set r = pt at infinity */ - PREFIX(set_pt_inf_jac) (dr); - goto CLEANUP; - } - - /* Perform typical point doubling operations */ - - /* TODO? is it worthwhile to do optimizations for when pz = 1? */ - - if (group->aIsM3) { - /* When a = -3, M = 3(px - pz^2)(px + pz^2) */ - PREFIX(square) (t1, dp->z); - group->ecfp_reduce(t1, t1, group); /* 2^23 since the negative - * rounding buys another bit */ - PREFIX(addShort) (t0, dp->x, t1); /* 2*2^23 */ - PREFIX(subtractShort) (t1, dp->x, t1); /* 2 * 2^23 */ - PREFIX(multiply) (M, t0, t1); /* 40 * 2^46 */ - PREFIX(addLong) (t0, M, M); /* 80 * 2^46 */ - PREFIX(addLong) (M, t0, M); /* 120 * 2^46 < 2^53 */ - group->ecfp_reduce(M, M, group); - } else { - /* Generic case */ - /* M = 3 (px^2) + a*(pz^4) */ - PREFIX(square) (t0, dp->x); - PREFIX(addLong) (M, t0, t0); - PREFIX(addLong) (t0, t0, M); /* t0 = 3(px^2) */ - PREFIX(square) (M, dp->z); - group->ecfp_reduce(M, M, group); - PREFIX(square) (t1, M); - group->ecfp_reduce(t1, t1, group); - PREFIX(multiply) (M, t1, group->curvea); /* M = a(pz^4) */ - PREFIX(addLong) (M, M, t0); - group->ecfp_reduce(M, M, group); - } - - /* rz = 2 * py * pz */ - PREFIX(multiply) (t1, dp->y, dp->z); - PREFIX(addLong) (t1, t1, t1); - group->ecfp_reduce(dr->z, t1, group); - - /* t0 = 2y^2 */ - PREFIX(square) (t0, dp->y); - group->ecfp_reduce(t0, t0, group); - PREFIX(addShort) (t0, t0, t0); - - /* S = 4 * px * py^2 = 2 * px * t0 */ - PREFIX(multiply) (S, dp->x, t0); - PREFIX(addLong) (S, S, S); - group->ecfp_reduce(S, S, group); - - /* rx = M^2 - 2 * S */ - PREFIX(square) (t1, M); - PREFIX(subtractShort) (t1, t1, S); - PREFIX(subtractShort) (t1, t1, S); - group->ecfp_reduce(dr->x, t1, group); - - /* ry = M * (S - rx) - 8 * py^4 */ - PREFIX(square) (t1, t0); /* t1 = 4y^4 */ - PREFIX(subtractShort) (S, S, dr->x); - PREFIX(multiply) (t0, M, S); - PREFIX(subtractLong) (t0, t0, t1); - PREFIX(subtractLong) (t0, t0, t1); - group->ecfp_reduce(dr->y, t0, group); - - CLEANUP: - return; -} - -/* Perform a point addition using coordinate system Jacobian + Affine -> - * Jacobian. Input and output should be multi-precision floating point - * integers. */ -void PREFIX(pt_add_jac_aff) (const ecfp_jac_pt * p, const ecfp_aff_pt * q, - ecfp_jac_pt * r, const EC_group_fp * group) { - /* Temporary storage */ - double A[2 * ECFP_NUMDOUBLES], B[2 * ECFP_NUMDOUBLES], - C[2 * ECFP_NUMDOUBLES], C2[2 * ECFP_NUMDOUBLES], - D[2 * ECFP_NUMDOUBLES], C3[2 * ECFP_NUMDOUBLES]; - - /* Check for point at infinity for p or q */ - if (PREFIX(pt_is_inf_aff) (q) == MP_YES) { - PREFIX(copy) (r->x, p->x); - PREFIX(copy) (r->y, p->y); - PREFIX(copy) (r->z, p->z); - goto CLEANUP; - } else if (PREFIX(pt_is_inf_jac) (p) == MP_YES) { - PREFIX(copy) (r->x, q->x); - PREFIX(copy) (r->y, q->y); - /* Since the affine point is not infinity, we can set r->z = 1 */ - PREFIX(one) (r->z); - goto CLEANUP; - } - - /* Calculates c = qx * pz^2 - px d = (qy * b - py) rx = d^2 - c^3 + 2 - * (px * c^2) ry = d * (c-rx) - py*c^3 rz = c * pz */ - - /* A = pz^2, B = pz^3 */ - PREFIX(square) (A, p->z); - group->ecfp_reduce(A, A, group); - PREFIX(multiply) (B, A, p->z); - group->ecfp_reduce(B, B, group); - - /* C = qx * A - px */ - PREFIX(multiply) (C, q->x, A); - PREFIX(subtractShort) (C, C, p->x); - group->ecfp_reduce(C, C, group); - - /* D = qy * B - py */ - PREFIX(multiply) (D, q->y, B); - PREFIX(subtractShort) (D, D, p->y); - group->ecfp_reduce(D, D, group); - - /* C2 = C^2, C3 = C^3 */ - PREFIX(square) (C2, C); - group->ecfp_reduce(C2, C2, group); - PREFIX(multiply) (C3, C2, C); - group->ecfp_reduce(C3, C3, group); - - /* rz = A = pz * C */ - PREFIX(multiply) (A, p->z, C); - group->ecfp_reduce(r->z, A, group); - - /* C = px * C^2, untidied, unreduced */ - PREFIX(multiply) (C, p->x, C2); - - /* A = D^2, untidied, unreduced */ - PREFIX(square) (A, D); - - /* rx = B = A - C3 - C - C = D^2 - (C^3 + 2 * (px * C^2) */ - PREFIX(subtractShort) (A, A, C3); - PREFIX(subtractLong) (A, A, C); - PREFIX(subtractLong) (A, A, C); - group->ecfp_reduce(r->x, A, group); - - /* B = py * C3, untidied, unreduced */ - PREFIX(multiply) (B, p->y, C3); - - /* C = px * C^2 - rx */ - PREFIX(subtractShort) (C, C, r->x); - group->ecfp_reduce(C, C, group); - - /* ry = A = D * C - py * C^3 */ - PREFIX(multiply) (A, D, C); - PREFIX(subtractLong) (A, A, B); - group->ecfp_reduce(r->y, A, group); - - CLEANUP: - return; -} - -/* Perform a point addition using Jacobian coordinate system. Input and - * output should be multi-precision floating point integers. */ -void PREFIX(pt_add_jac) (const ecfp_jac_pt * p, const ecfp_jac_pt * q, - ecfp_jac_pt * r, const EC_group_fp * group) { - - /* Temporary Storage */ - double t0[2 * ECFP_NUMDOUBLES], t1[2 * ECFP_NUMDOUBLES], - U[2 * ECFP_NUMDOUBLES], R[2 * ECFP_NUMDOUBLES], - S[2 * ECFP_NUMDOUBLES], H[2 * ECFP_NUMDOUBLES], - H3[2 * ECFP_NUMDOUBLES]; - - /* Check for point at infinity for p, if so set r = q */ - if (PREFIX(pt_is_inf_jac) (p) == MP_YES) { - PREFIX(copy) (r->x, q->x); - PREFIX(copy) (r->y, q->y); - PREFIX(copy) (r->z, q->z); - goto CLEANUP; - } - - /* Check for point at infinity for p, if so set r = q */ - if (PREFIX(pt_is_inf_jac) (q) == MP_YES) { - PREFIX(copy) (r->x, p->x); - PREFIX(copy) (r->y, p->y); - PREFIX(copy) (r->z, p->z); - goto CLEANUP; - } - - /* U = px * qz^2 , S = py * qz^3 */ - PREFIX(square) (t0, q->z); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (U, p->x, t0); - group->ecfp_reduce(U, U, group); - PREFIX(multiply) (t1, t0, q->z); - group->ecfp_reduce(t1, t1, group); - PREFIX(multiply) (t0, p->y, t1); - group->ecfp_reduce(S, t0, group); - - /* H = qx*(pz)^2 - U , R = (qy * pz^3 - S) */ - PREFIX(square) (t0, p->z); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (H, q->x, t0); - PREFIX(subtractShort) (H, H, U); - group->ecfp_reduce(H, H, group); - PREFIX(multiply) (t1, t0, p->z); /* t1 = pz^3 */ - group->ecfp_reduce(t1, t1, group); - PREFIX(multiply) (t0, t1, q->y); /* t0 = qy * pz^3 */ - PREFIX(subtractShort) (t0, t0, S); - group->ecfp_reduce(R, t0, group); - - /* U = U*H^2, H3 = H^3 */ - PREFIX(square) (t0, H); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (t1, U, t0); - group->ecfp_reduce(U, t1, group); - PREFIX(multiply) (H3, t0, H); - group->ecfp_reduce(H3, H3, group); - - /* rz = pz * qz * H */ - PREFIX(multiply) (t0, q->z, H); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (t1, t0, p->z); - group->ecfp_reduce(r->z, t1, group); - - /* rx = R^2 - H^3 - 2 * U */ - PREFIX(square) (t0, R); - PREFIX(subtractShort) (t0, t0, H3); - PREFIX(subtractShort) (t0, t0, U); - PREFIX(subtractShort) (t0, t0, U); - group->ecfp_reduce(r->x, t0, group); - - /* ry = R(U - rx) - S*H3 */ - PREFIX(subtractShort) (t1, U, r->x); - PREFIX(multiply) (t0, t1, R); - PREFIX(multiply) (t1, S, H3); - PREFIX(subtractLong) (t1, t0, t1); - group->ecfp_reduce(r->y, t1, group); - - CLEANUP: - return; -} - -/* Perform a point doubling in Modified Jacobian coordinates. Input and - * output should be multi-precision floating point integers. */ -void PREFIX(pt_dbl_jm) (const ecfp_jm_pt * p, ecfp_jm_pt * r, - const EC_group_fp * group) { - - /* Temporary storage */ - double t0[2 * ECFP_NUMDOUBLES], t1[2 * ECFP_NUMDOUBLES], - M[2 * ECFP_NUMDOUBLES], S[2 * ECFP_NUMDOUBLES], - U[2 * ECFP_NUMDOUBLES], T[2 * ECFP_NUMDOUBLES]; - - /* Check for point at infinity */ - if (PREFIX(pt_is_inf_jm) (p) == MP_YES) { - /* Set r = pt at infinity by setting rz = 0 */ - PREFIX(set_pt_inf_jm) (r); - goto CLEANUP; - } - - /* M = 3 (px^2) + a*(pz^4) */ - PREFIX(square) (t0, p->x); - PREFIX(addLong) (M, t0, t0); - PREFIX(addLong) (t0, t0, M); /* t0 = 3(px^2) */ - PREFIX(addShort) (t0, t0, p->az4); - group->ecfp_reduce(M, t0, group); - - /* rz = 2 * py * pz */ - PREFIX(multiply) (t1, p->y, p->z); - PREFIX(addLong) (t1, t1, t1); - group->ecfp_reduce(r->z, t1, group); - - /* t0 = 2y^2, U = 8y^4 */ - PREFIX(square) (t0, p->y); - group->ecfp_reduce(t0, t0, group); - PREFIX(addShort) (t0, t0, t0); - PREFIX(square) (U, t0); - group->ecfp_reduce(U, U, group); - PREFIX(addShort) (U, U, U); - - /* S = 4 * px * py^2 = 2 * px * t0 */ - PREFIX(multiply) (S, p->x, t0); - group->ecfp_reduce(S, S, group); - PREFIX(addShort) (S, S, S); - - /* rx = M^2 - 2S */ - PREFIX(square) (T, M); - PREFIX(subtractShort) (T, T, S); - PREFIX(subtractShort) (T, T, S); - group->ecfp_reduce(r->x, T, group); - - /* ry = M * (S - rx) - U */ - PREFIX(subtractShort) (S, S, r->x); - PREFIX(multiply) (t0, M, S); - PREFIX(subtractShort) (t0, t0, U); - group->ecfp_reduce(r->y, t0, group); - - /* ra*z^4 = 2*U*(apz4) */ - PREFIX(multiply) (t1, U, p->az4); - PREFIX(addLong) (t1, t1, t1); - group->ecfp_reduce(r->az4, t1, group); - - CLEANUP: - return; -} - -/* Perform a point doubling using coordinates Affine -> Chudnovsky - * Jacobian. Input and output should be multi-precision floating point - * integers. */ -void PREFIX(pt_dbl_aff2chud) (const ecfp_aff_pt * p, ecfp_chud_pt * r, - const EC_group_fp * group) { - double t0[2 * ECFP_NUMDOUBLES], t1[2 * ECFP_NUMDOUBLES], - M[2 * ECFP_NUMDOUBLES], twoY2[2 * ECFP_NUMDOUBLES], - S[2 * ECFP_NUMDOUBLES]; - - /* Check for point at infinity for p, if so set r = O */ - if (PREFIX(pt_is_inf_aff) (p) == MP_YES) { - PREFIX(set_pt_inf_chud) (r); - goto CLEANUP; - } - - /* M = 3(px)^2 + a */ - PREFIX(square) (t0, p->x); - PREFIX(addLong) (t1, t0, t0); - PREFIX(addLong) (t1, t1, t0); - PREFIX(addShort) (t1, t1, group->curvea); - group->ecfp_reduce(M, t1, group); - - /* twoY2 = 2*(py)^2, S = 4(px)(py)^2 */ - PREFIX(square) (twoY2, p->y); - PREFIX(addLong) (twoY2, twoY2, twoY2); - group->ecfp_reduce(twoY2, twoY2, group); - PREFIX(multiply) (S, p->x, twoY2); - PREFIX(addLong) (S, S, S); - group->ecfp_reduce(S, S, group); - - /* rx = M^2 - 2S */ - PREFIX(square) (t0, M); - PREFIX(subtractShort) (t0, t0, S); - PREFIX(subtractShort) (t0, t0, S); - group->ecfp_reduce(r->x, t0, group); - - /* ry = M(S-rx) - 8y^4 */ - PREFIX(subtractShort) (t0, S, r->x); - PREFIX(multiply) (t1, t0, M); - PREFIX(square) (t0, twoY2); - PREFIX(subtractLong) (t1, t1, t0); - PREFIX(subtractLong) (t1, t1, t0); - group->ecfp_reduce(r->y, t1, group); - - /* rz = 2py */ - PREFIX(addShort) (r->z, p->y, p->y); - - /* rz2 = rz^2 */ - PREFIX(square) (t0, r->z); - group->ecfp_reduce(r->z2, t0, group); - - /* rz3 = rz^3 */ - PREFIX(multiply) (t0, r->z, r->z2); - group->ecfp_reduce(r->z3, t0, group); - - CLEANUP: - return; -} - -/* Perform a point addition using coordinates: Modified Jacobian + - * Chudnovsky Jacobian -> Modified Jacobian. Input and output should be - * multi-precision floating point integers. */ -void PREFIX(pt_add_jm_chud) (ecfp_jm_pt * p, ecfp_chud_pt * q, - ecfp_jm_pt * r, const EC_group_fp * group) { - - double t0[2 * ECFP_NUMDOUBLES], t1[2 * ECFP_NUMDOUBLES], - U[2 * ECFP_NUMDOUBLES], R[2 * ECFP_NUMDOUBLES], - S[2 * ECFP_NUMDOUBLES], H[2 * ECFP_NUMDOUBLES], - H3[2 * ECFP_NUMDOUBLES], pz2[2 * ECFP_NUMDOUBLES]; - - /* Check for point at infinity for p, if so set r = q need to convert - * from Chudnovsky form to Modified Jacobian form */ - if (PREFIX(pt_is_inf_jm) (p) == MP_YES) { - PREFIX(copy) (r->x, q->x); - PREFIX(copy) (r->y, q->y); - PREFIX(copy) (r->z, q->z); - PREFIX(square) (t0, q->z2); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (t1, t0, group->curvea); - group->ecfp_reduce(r->az4, t1, group); - goto CLEANUP; - } - /* Check for point at infinity for q, if so set r = p */ - if (PREFIX(pt_is_inf_chud) (q) == MP_YES) { - PREFIX(copy) (r->x, p->x); - PREFIX(copy) (r->y, p->y); - PREFIX(copy) (r->z, p->z); - PREFIX(copy) (r->az4, p->az4); - goto CLEANUP; - } - - /* U = px * qz^2 */ - PREFIX(multiply) (U, p->x, q->z2); - group->ecfp_reduce(U, U, group); - - /* H = qx*(pz)^2 - U */ - PREFIX(square) (t0, p->z); - group->ecfp_reduce(pz2, t0, group); - PREFIX(multiply) (H, pz2, q->x); - group->ecfp_reduce(H, H, group); - PREFIX(subtractShort) (H, H, U); - - /* U = U*H^2, H3 = H^3 */ - PREFIX(square) (t0, H); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (t1, U, t0); - group->ecfp_reduce(U, t1, group); - PREFIX(multiply) (H3, t0, H); - group->ecfp_reduce(H3, H3, group); - - /* S = py * qz^3 */ - PREFIX(multiply) (S, p->y, q->z3); - group->ecfp_reduce(S, S, group); - - /* R = (qy * z1^3 - s) */ - PREFIX(multiply) (t0, pz2, p->z); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (R, t0, q->y); - PREFIX(subtractShort) (R, R, S); - group->ecfp_reduce(R, R, group); - - /* rz = pz * qz * H */ - PREFIX(multiply) (t1, q->z, H); - group->ecfp_reduce(t1, t1, group); - PREFIX(multiply) (t0, p->z, t1); - group->ecfp_reduce(r->z, t0, group); - - /* rx = R^2 - H^3 - 2 * U */ - PREFIX(square) (t0, R); - PREFIX(subtractShort) (t0, t0, H3); - PREFIX(subtractShort) (t0, t0, U); - PREFIX(subtractShort) (t0, t0, U); - group->ecfp_reduce(r->x, t0, group); - - /* ry = R(U - rx) - S*H3 */ - PREFIX(subtractShort) (t1, U, r->x); - PREFIX(multiply) (t0, t1, R); - PREFIX(multiply) (t1, S, H3); - PREFIX(subtractLong) (t1, t0, t1); - group->ecfp_reduce(r->y, t1, group); - - if (group->aIsM3) { /* a == -3 */ - /* a(rz^4) = -3 * ((rz^2)^2) */ - PREFIX(square) (t0, r->z); - group->ecfp_reduce(t0, t0, group); - PREFIX(square) (t1, t0); - PREFIX(addLong) (t0, t1, t1); - PREFIX(addLong) (t0, t0, t1); - PREFIX(negLong) (t0, t0); - group->ecfp_reduce(r->az4, t0, group); - } else { /* Generic case */ - /* a(rz^4) = a * ((rz^2)^2) */ - PREFIX(square) (t0, r->z); - group->ecfp_reduce(t0, t0, group); - PREFIX(square) (t1, t0); - group->ecfp_reduce(t1, t1, group); - PREFIX(multiply) (t0, group->curvea, t1); - group->ecfp_reduce(r->az4, t0, group); - } - CLEANUP: - return; -} - -/* Perform a point addition using Chudnovsky Jacobian coordinates. Input - * and output should be multi-precision floating point integers. */ -void PREFIX(pt_add_chud) (const ecfp_chud_pt * p, const ecfp_chud_pt * q, - ecfp_chud_pt * r, const EC_group_fp * group) { - - /* Temporary Storage */ - double t0[2 * ECFP_NUMDOUBLES], t1[2 * ECFP_NUMDOUBLES], - U[2 * ECFP_NUMDOUBLES], R[2 * ECFP_NUMDOUBLES], - S[2 * ECFP_NUMDOUBLES], H[2 * ECFP_NUMDOUBLES], - H3[2 * ECFP_NUMDOUBLES]; - - /* Check for point at infinity for p, if so set r = q */ - if (PREFIX(pt_is_inf_chud) (p) == MP_YES) { - PREFIX(copy) (r->x, q->x); - PREFIX(copy) (r->y, q->y); - PREFIX(copy) (r->z, q->z); - PREFIX(copy) (r->z2, q->z2); - PREFIX(copy) (r->z3, q->z3); - goto CLEANUP; - } - - /* Check for point at infinity for p, if so set r = q */ - if (PREFIX(pt_is_inf_chud) (q) == MP_YES) { - PREFIX(copy) (r->x, p->x); - PREFIX(copy) (r->y, p->y); - PREFIX(copy) (r->z, p->z); - PREFIX(copy) (r->z2, p->z2); - PREFIX(copy) (r->z3, p->z3); - goto CLEANUP; - } - - /* U = px * qz^2 */ - PREFIX(multiply) (U, p->x, q->z2); - group->ecfp_reduce(U, U, group); - - /* H = qx*(pz)^2 - U */ - PREFIX(multiply) (H, q->x, p->z2); - PREFIX(subtractShort) (H, H, U); - group->ecfp_reduce(H, H, group); - - /* U = U*H^2, H3 = H^3 */ - PREFIX(square) (t0, H); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (t1, U, t0); - group->ecfp_reduce(U, t1, group); - PREFIX(multiply) (H3, t0, H); - group->ecfp_reduce(H3, H3, group); - - /* S = py * qz^3 */ - PREFIX(multiply) (S, p->y, q->z3); - group->ecfp_reduce(S, S, group); - - /* rz = pz * qz * H */ - PREFIX(multiply) (t0, q->z, H); - group->ecfp_reduce(t0, t0, group); - PREFIX(multiply) (t1, t0, p->z); - group->ecfp_reduce(r->z, t1, group); - - /* R = (qy * z1^3 - s) */ - PREFIX(multiply) (t0, q->y, p->z3); - PREFIX(subtractShort) (t0, t0, S); - group->ecfp_reduce(R, t0, group); - - /* rx = R^2 - H^3 - 2 * U */ - PREFIX(square) (t0, R); - PREFIX(subtractShort) (t0, t0, H3); - PREFIX(subtractShort) (t0, t0, U); - PREFIX(subtractShort) (t0, t0, U); - group->ecfp_reduce(r->x, t0, group); - - /* ry = R(U - rx) - S*H3 */ - PREFIX(subtractShort) (t1, U, r->x); - PREFIX(multiply) (t0, t1, R); - PREFIX(multiply) (t1, S, H3); - PREFIX(subtractLong) (t1, t0, t1); - group->ecfp_reduce(r->y, t1, group); - - /* rz2 = rz^2 */ - PREFIX(square) (t0, r->z); - group->ecfp_reduce(r->z2, t0, group); - - /* rz3 = rz^3 */ - PREFIX(multiply) (t0, r->z, r->z2); - group->ecfp_reduce(r->z3, t0, group); - - CLEANUP: - return; -} - -/* Expects out to be an array of size 16 of Chudnovsky Jacobian points. - * Fills in Chudnovsky Jacobian form (x, y, z, z^2, z^3), for -15P, -13P, - * -11P, -9P, -7P, -5P, -3P, -P, P, 3P, 5P, 7P, 9P, 11P, 13P, 15P */ -void PREFIX(precompute_chud) (ecfp_chud_pt * out, const ecfp_aff_pt * p, - const EC_group_fp * group) { - - ecfp_chud_pt p2; - - /* Set out[8] = P */ - PREFIX(copy) (out[8].x, p->x); - PREFIX(copy) (out[8].y, p->y); - PREFIX(one) (out[8].z); - PREFIX(one) (out[8].z2); - PREFIX(one) (out[8].z3); - - /* Set p2 = 2P */ - PREFIX(pt_dbl_aff2chud) (p, &p2, group); - - /* Set 3P, 5P, ..., 15P */ - PREFIX(pt_add_chud) (&out[8], &p2, &out[9], group); - PREFIX(pt_add_chud) (&out[9], &p2, &out[10], group); - PREFIX(pt_add_chud) (&out[10], &p2, &out[11], group); - PREFIX(pt_add_chud) (&out[11], &p2, &out[12], group); - PREFIX(pt_add_chud) (&out[12], &p2, &out[13], group); - PREFIX(pt_add_chud) (&out[13], &p2, &out[14], group); - PREFIX(pt_add_chud) (&out[14], &p2, &out[15], group); - - /* Set -15P, -13P, ..., -P */ - PREFIX(pt_neg_chud) (&out[8], &out[7]); - PREFIX(pt_neg_chud) (&out[9], &out[6]); - PREFIX(pt_neg_chud) (&out[10], &out[5]); - PREFIX(pt_neg_chud) (&out[11], &out[4]); - PREFIX(pt_neg_chud) (&out[12], &out[3]); - PREFIX(pt_neg_chud) (&out[13], &out[2]); - PREFIX(pt_neg_chud) (&out[14], &out[1]); - PREFIX(pt_neg_chud) (&out[15], &out[0]); -} - -/* Expects out to be an array of size 16 of Jacobian points. Fills in - * Jacobian form (x, y, z), for O, P, 2P, ... 15P */ -void PREFIX(precompute_jac) (ecfp_jac_pt * precomp, const ecfp_aff_pt * p, - const EC_group_fp * group) { - int i; - - /* fill precomputation table */ - /* set precomp[0] */ - PREFIX(set_pt_inf_jac) (&precomp[0]); - /* set precomp[1] */ - PREFIX(copy) (precomp[1].x, p->x); - PREFIX(copy) (precomp[1].y, p->y); - if (PREFIX(pt_is_inf_aff) (p) == MP_YES) { - PREFIX(zero) (precomp[1].z); - } else { - PREFIX(one) (precomp[1].z); - } - /* set precomp[2] */ - group->pt_dbl_jac(&precomp[1], &precomp[2], group); - - /* set rest of precomp */ - for (i = 3; i < 16; i++) { - group->pt_add_jac_aff(&precomp[i - 1], p, &precomp[i], group); - } -} |