RetroZilla/security/nss/lib/freebl/ecl/ecp_fp.c

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2018-05-04 16:08:28 +02:00
/* 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/. */
2015-10-21 05:03:22 +02:00
#include "ecp_fp.h"
#include "ecl-priv.h"
#include <stdlib.h>
/* Performs tidying on a short multi-precision floating point integer (the
* lower group->numDoubles floats). */
void
ecfp_tidyShort(double *t, const EC_group_fp * group)
{
group->ecfp_tidy(t, group->alpha, group);
}
/* Performs tidying on only the upper float digits of a multi-precision
* floating point integer, i.e. the digits beyond the regular length which
* are removed in the reduction step. */
void
ecfp_tidyUpper(double *t, const EC_group_fp * group)
{
group->ecfp_tidy(t + group->numDoubles,
group->alpha + group->numDoubles, group);
}
/* Performs a "tidy" operation, which performs carrying, moving excess
* bits from one double to the next double, so that the precision of the
* doubles is reduced to the regular precision group->doubleBitSize. This
* might result in some float digits being negative. Alternative C version
* for portability. */
void
ecfp_tidy(double *t, const double *alpha, const EC_group_fp * group)
{
double q;
int i;
/* Do carrying */
for (i = 0; i < group->numDoubles - 1; i++) {
q = t[i] + alpha[i + 1];
q -= alpha[i + 1];
t[i] -= q;
t[i + 1] += q;
/* If we don't assume that truncation rounding is used, then q
* might be 2^n bigger than expected (if it rounds up), then t[0]
* could be negative and t[1] 2^n larger than expected. */
}
}
/* Performs a more mathematically precise "tidying" so that each term is
* positive. This is slower than the regular tidying, and is used for
* conversion from floating point to integer. */
void
ecfp_positiveTidy(double *t, const EC_group_fp * group)
{
double q;
int i;
/* Do carrying */
for (i = 0; i < group->numDoubles - 1; i++) {
/* Subtract beta to force rounding down */
q = t[i] - ecfp_beta[i + 1];
q += group->alpha[i + 1];
q -= group->alpha[i + 1];
t[i] -= q;
t[i + 1] += q;
/* Due to subtracting ecfp_beta, we should have each term a
* non-negative int */
ECFP_ASSERT(t[i] / ecfp_exp[i] ==
(unsigned long long) (t[i] / ecfp_exp[i]));
ECFP_ASSERT(t[i] >= 0);
}
}
/* Converts from a floating point representation into an mp_int. Expects
* that d is already reduced. */
void
ecfp_fp2i(mp_int *mpout, double *d, const ECGroup *ecgroup)
{
EC_group_fp *group = (EC_group_fp *) ecgroup->extra1;
unsigned short i16[(group->primeBitSize + 15) / 16];
double q = 1;
#ifdef ECL_THIRTY_TWO_BIT
/* TEST uint32_t z = 0; */
unsigned int z = 0;
#else
uint64_t z = 0;
#endif
int zBits = 0;
int copiedBits = 0;
int i = 0;
int j = 0;
mp_digit *out;
/* Result should always be >= 0, so set sign accordingly */
MP_SIGN(mpout) = MP_ZPOS;
/* Tidy up so we're just dealing with positive numbers */
ecfp_positiveTidy(d, group);
/* We might need to do this reduction step more than once if the
* reduction adds smaller terms which carry-over to cause another
* reduction. However, this should happen very rarely, if ever,
* depending on the elliptic curve. */
do {
/* Init loop data */
z = 0;
zBits = 0;
q = 1;
i = 0;
j = 0;
copiedBits = 0;
/* Might have to do a bit more reduction */
group->ecfp_singleReduce(d, group);
/* Grow the size of the mpint if it's too small */
s_mp_grow(mpout, group->numInts);
MP_USED(mpout) = group->numInts;
out = MP_DIGITS(mpout);
/* Convert double to 16 bit integers */
while (copiedBits < group->primeBitSize) {
if (zBits < 16) {
z += d[i] * q;
i++;
ECFP_ASSERT(i < (group->primeBitSize + 15) / 16);
zBits += group->doubleBitSize;
}
i16[j] = z;
j++;
z >>= 16;
zBits -= 16;
q *= ecfp_twom16;
copiedBits += 16;
}
} while (z != 0);
/* Convert 16 bit integers to mp_digit */
#ifdef ECL_THIRTY_TWO_BIT
for (i = 0; i < (group->primeBitSize + 15) / 16; i += 2) {
*out = 0;
if (i + 1 < (group->primeBitSize + 15) / 16) {
*out = i16[i + 1];
*out <<= 16;
}
*out++ += i16[i];
}
#else /* 64 bit */
for (i = 0; i < (group->primeBitSize + 15) / 16; i += 4) {
*out = 0;
if (i + 3 < (group->primeBitSize + 15) / 16) {
*out = i16[i + 3];
*out <<= 16;
}
if (i + 2 < (group->primeBitSize + 15) / 16) {
*out += i16[i + 2];
*out <<= 16;
}
if (i + 1 < (group->primeBitSize + 15) / 16) {
*out += i16[i + 1];
*out <<= 16;
}
*out++ += i16[i];
}
#endif
/* Perform final reduction. mpout should already be the same number
* of bits as p, but might not be less than p. Make it so. Since
* mpout has the same number of bits as p, and 2p has a larger bit
* size, then mpout < 2p, so a single subtraction of p will suffice. */
if (mp_cmp(mpout, &ecgroup->meth->irr) >= 0) {
mp_sub(mpout, &ecgroup->meth->irr, mpout);
}
/* Shrink the size of the mp_int to the actual used size (required for
* mp_cmp_z == 0) */
out = MP_DIGITS(mpout);
for (i = group->numInts - 1; i > 0; i--) {
if (out[i] != 0)
break;
}
MP_USED(mpout) = i + 1;
/* Should be between 0 and p-1 */
ECFP_ASSERT(mp_cmp(mpout, &ecgroup->meth->irr) < 0);
ECFP_ASSERT(mp_cmp_z(mpout) >= 0);
}
/* Converts from an mpint into a floating point representation. */
void
ecfp_i2fp(double *out, const mp_int *x, const ECGroup *ecgroup)
{
int i;
int j = 0;
int size;
double shift = 1;
mp_digit *in;
EC_group_fp *group = (EC_group_fp *) ecgroup->extra1;
#ifdef ECL_DEBUG
/* if debug mode, convert result back using ecfp_fp2i into cmp, then
* compare to x. */
mp_int cmp;
MP_DIGITS(&cmp) = NULL;
mp_init(&cmp);
#endif
ECFP_ASSERT(group != NULL);
/* init output to 0 (since we skip over some terms) */
for (i = 0; i < group->numDoubles; i++)
out[i] = 0;
i = 0;
size = MP_USED(x);
in = MP_DIGITS(x);
/* Copy from int into doubles */
#ifdef ECL_THIRTY_TWO_BIT
while (j < size) {
while (group->doubleBitSize * (i + 1) <= 32 * j) {
i++;
}
ECFP_ASSERT(group->doubleBitSize * i <= 32 * j);
out[i] = in[j];
out[i] *= shift;
shift *= ecfp_two32;
j++;
}
#else
while (j < size) {
while (group->doubleBitSize * (i + 1) <= 64 * j) {
i++;
}
ECFP_ASSERT(group->doubleBitSize * i <= 64 * j);
out[i] = (in[j] & 0x00000000FFFFFFFF) * shift;
while (group->doubleBitSize * (i + 1) <= 64 * j + 32) {
i++;
}
ECFP_ASSERT(24 * i <= 64 * j + 32);
out[i] = (in[j] & 0xFFFFFFFF00000000) * shift;
shift *= ecfp_two64;
j++;
}
#endif
/* Realign bits to match double boundaries */
ecfp_tidyShort(out, group);
#ifdef ECL_DEBUG
/* Convert result back to mp_int, compare to original */
ecfp_fp2i(&cmp, out, ecgroup);
ECFP_ASSERT(mp_cmp(&cmp, x) == 0);
mp_clear(&cmp);
#endif
}
/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
* a, b and p are the elliptic curve coefficients and the prime that
* determines the field GFp. Elliptic curve points P and R can be
* identical. Uses Jacobian coordinates. Uses 4-bit window method. */
mp_err
ec_GFp_point_mul_jac_4w_fp(const mp_int *n, const mp_int *px,
const mp_int *py, mp_int *rx, mp_int *ry,
const ECGroup *ecgroup)
{
mp_err res = MP_OKAY;
ecfp_jac_pt precomp[16], r;
ecfp_aff_pt p;
EC_group_fp *group;
mp_int rz;
int i, ni, d;
ARGCHK(ecgroup != NULL, MP_BADARG);
ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
group = (EC_group_fp *) ecgroup->extra1;
MP_DIGITS(&rz) = 0;
MP_CHECKOK(mp_init(&rz));
/* init p, da */
ecfp_i2fp(p.x, px, ecgroup);
ecfp_i2fp(p.y, py, ecgroup);
ecfp_i2fp(group->curvea, &ecgroup->curvea, ecgroup);
/* Do precomputation */
group->precompute_jac(precomp, &p, group);
/* Do main body of calculations */
d = (mpl_significant_bits(n) + 3) / 4;
/* R = inf */
for (i = 0; i < group->numDoubles; i++) {
r.z[i] = 0;
}
for (i = d - 1; i >= 0; i--) {
/* compute window ni */
ni = MP_GET_BIT(n, 4 * i + 3);
ni <<= 1;
ni |= MP_GET_BIT(n, 4 * i + 2);
ni <<= 1;
ni |= MP_GET_BIT(n, 4 * i + 1);
ni <<= 1;
ni |= MP_GET_BIT(n, 4 * i);
/* R = 2^4 * R */
group->pt_dbl_jac(&r, &r, group);
group->pt_dbl_jac(&r, &r, group);
group->pt_dbl_jac(&r, &r, group);
group->pt_dbl_jac(&r, &r, group);
/* R = R + (ni * P) */
group->pt_add_jac(&r, &precomp[ni], &r, group);
}
/* Convert back to integer */
ecfp_fp2i(rx, r.x, ecgroup);
ecfp_fp2i(ry, r.y, ecgroup);
ecfp_fp2i(&rz, r.z, ecgroup);
/* convert result S to affine coordinates */
MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, ecgroup));
CLEANUP:
mp_clear(&rz);
return res;
}
/* Uses mixed Jacobian-affine coordinates to perform a point
* multiplication: R = n * P, n scalar. Uses mixed Jacobian-affine
* coordinates (Jacobian coordinates for doubles and affine coordinates
* for additions; based on recommendation from Brown et al.). Not very
* time efficient but quite space efficient, no precomputation needed.
* group contains the elliptic curve coefficients and the prime that
* determines the field GFp. Elliptic curve points P and R can be
* identical. Performs calculations in floating point number format, since
* this is faster than the integer operations on the ULTRASPARC III.
* Uses left-to-right binary method (double & add) (algorithm 9) for
* scalar-point multiplication from Brown, Hankerson, Lopez, Menezes.
* Software Implementation of the NIST Elliptic Curves Over Prime Fields. */
mp_err
ec_GFp_pt_mul_jac_fp(const mp_int *n, const mp_int *px, const mp_int *py,
mp_int *rx, mp_int *ry, const ECGroup *ecgroup)
{
mp_err res;
mp_int sx, sy, sz;
ecfp_aff_pt p;
ecfp_jac_pt r;
EC_group_fp *group = (EC_group_fp *) ecgroup->extra1;
int i, l;
MP_DIGITS(&sx) = 0;
MP_DIGITS(&sy) = 0;
MP_DIGITS(&sz) = 0;
MP_CHECKOK(mp_init(&sx));
MP_CHECKOK(mp_init(&sy));
MP_CHECKOK(mp_init(&sz));
/* if n = 0 then r = inf */
if (mp_cmp_z(n) == 0) {
mp_zero(rx);
mp_zero(ry);
res = MP_OKAY;
goto CLEANUP;
/* if n < 0 then out of range error */
} else if (mp_cmp_z(n) < 0) {
res = MP_RANGE;
goto CLEANUP;
}
/* Convert from integer to floating point */
ecfp_i2fp(p.x, px, ecgroup);
ecfp_i2fp(p.y, py, ecgroup);
ecfp_i2fp(group->curvea, &(ecgroup->curvea), ecgroup);
/* Init r to point at infinity */
for (i = 0; i < group->numDoubles; i++) {
r.z[i] = 0;
}
/* double and add method */
l = mpl_significant_bits(n) - 1;
for (i = l; i >= 0; i--) {
/* R = 2R */
group->pt_dbl_jac(&r, &r, group);
/* if n_i = 1, then R = R + Q */
if (MP_GET_BIT(n, i) != 0) {
group->pt_add_jac_aff(&r, &p, &r, group);
}
}
/* Convert from floating point to integer */
ecfp_fp2i(&sx, r.x, ecgroup);
ecfp_fp2i(&sy, r.y, ecgroup);
ecfp_fp2i(&sz, r.z, ecgroup);
/* convert result R to affine coordinates */
MP_CHECKOK(ec_GFp_pt_jac2aff(&sx, &sy, &sz, rx, ry, ecgroup));
CLEANUP:
mp_clear(&sx);
mp_clear(&sy);
mp_clear(&sz);
return res;
}
/* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
* curve points P and R can be identical. Uses mixed Modified-Jacobian
* co-ordinates for doubling and Chudnovsky Jacobian coordinates for
* additions. Uses 5-bit window NAF method (algorithm 11) for scalar-point
* multiplication from Brown, Hankerson, Lopez, Menezes. Software
* Implementation of the NIST Elliptic Curves Over Prime Fields. */
mp_err
ec_GFp_point_mul_wNAF_fp(const mp_int *n, const mp_int *px,
const mp_int *py, mp_int *rx, mp_int *ry,
const ECGroup *ecgroup)
{
mp_err res = MP_OKAY;
mp_int sx, sy, sz;
EC_group_fp *group = (EC_group_fp *) ecgroup->extra1;
ecfp_chud_pt precomp[16];
ecfp_aff_pt p;
ecfp_jm_pt r;
signed char naf[group->orderBitSize + 1];
int i;
MP_DIGITS(&sx) = 0;
MP_DIGITS(&sy) = 0;
MP_DIGITS(&sz) = 0;
MP_CHECKOK(mp_init(&sx));
MP_CHECKOK(mp_init(&sy));
MP_CHECKOK(mp_init(&sz));
/* if n = 0 then r = inf */
if (mp_cmp_z(n) == 0) {
mp_zero(rx);
mp_zero(ry);
res = MP_OKAY;
goto CLEANUP;
/* if n < 0 then out of range error */
} else if (mp_cmp_z(n) < 0) {
res = MP_RANGE;
goto CLEANUP;
}
/* Convert from integer to floating point */
ecfp_i2fp(p.x, px, ecgroup);
ecfp_i2fp(p.y, py, ecgroup);
ecfp_i2fp(group->curvea, &(ecgroup->curvea), ecgroup);
/* Perform precomputation */
group->precompute_chud(precomp, &p, group);
/* Compute 5NAF */
ec_compute_wNAF(naf, group->orderBitSize, n, 5);
/* Init R = pt at infinity */
for (i = 0; i < group->numDoubles; i++) {
r.z[i] = 0;
}
/* wNAF method */
for (i = group->orderBitSize; i >= 0; i--) {
/* R = 2R */
group->pt_dbl_jm(&r, &r, group);
if (naf[i] != 0) {
group->pt_add_jm_chud(&r, &precomp[(naf[i] + 15) / 2], &r,
group);
}
}
/* Convert from floating point to integer */
ecfp_fp2i(&sx, r.x, ecgroup);
ecfp_fp2i(&sy, r.y, ecgroup);
ecfp_fp2i(&sz, r.z, ecgroup);
/* convert result R to affine coordinates */
MP_CHECKOK(ec_GFp_pt_jac2aff(&sx, &sy, &sz, rx, ry, ecgroup));
CLEANUP:
mp_clear(&sx);
mp_clear(&sy);
mp_clear(&sz);
return res;
}
/* Cleans up extra memory allocated in ECGroup for this implementation. */
void
ec_GFp_extra_free_fp(ECGroup *group)
{
if (group->extra1 != NULL) {
free(group->extra1);
group->extra1 = NULL;
}
}
/* Tests what precision floating point arithmetic is set to. This should
* be either a 53-bit mantissa (IEEE standard) or a 64-bit mantissa
* (extended precision on x86) and sets it into the EC_group_fp. Returns
* either 53 or 64 accordingly. */
int
ec_set_fp_precision(EC_group_fp * group)
{
double a = 9007199254740992.0; /* 2^53 */
double b = a + 1;
if (a == b) {
group->fpPrecision = 53;
group->alpha = ecfp_alpha_53;
return 53;
}
group->fpPrecision = 64;
group->alpha = ecfp_alpha_64;
return 64;
}