/* Reverse the operation above for one mp_int.
* Reconstruct one mp_int from its column in the weaved array.
* Every read accesses every element of the weaved array, in order to
* avoid timing attacks based on patterns of memory accesses.
*/
mp_err weave_to_mpi(mp_int *a, /* out, result */
const mp_digit *weaved, /* in, byte matrix */
mp_size index, /* which column to read */
mp_size nDigits, /* number of mp_digits in each bignum */
mp_size nBignums) /* width of the matrix */
{
/* these are indices, but need to be the same size as mp_digit
* because of the CONST_TIME operations */
mp_digit i, j;
mp_digit d;
mp_digit *pDest = MP_DIGITS(a);
MP_SIGN(a) = MP_ZPOS;
MP_USED(a) = nDigits;
assert(weaved != NULL);
/* Fetch the proper column in constant time, indexing over the whole array */
for (i = 0; i < nDigits; ++i) {
d = 0;
for (j = 0; j < nBignums; ++j) {
d |= weaved[i * nBignums + j] & CONST_TIME_EQ(j, index);
}
pDest[i] = d;
}
s_mp_clamp(a);
return MP_OKAY;
}
/*
* mpi_to_weave takes an array of bignums, a matrix in which each bignum
* occupies all the columns of a row, and transposes it into a matrix in
* which each bignum occupies a column of every row. The first row of the
* input matrix becomes the first column of the output matrix. The n'th
* row of input becomes the n'th column of output. The input data is said
* to be "interleaved" or "woven" into the output matrix.
*
* The array of bignums is left in this woven form. Each time a single
* bignum value is needed, it is recreated by fetching the n'th column,
* forming a single row which is the new bignum.
*
* The purpose of this interleaving is make it impossible to determine which
* of the bignums is being used in any one operation by examining the pattern
* of cache misses.
*
* The weaving function does not transpose the entire input matrix in one call.
* It transposes 4 rows of mp_ints into their respective columns of output.
*
* There are two different implementations of the weaving and unweaving code
* in this file. One uses byte loads and stores. The second uses loads and
* stores of mp_weave_word size values. The weaved forms of these two
* implementations differ. Consequently, each one has its own explanation.
*
* Here is the explanation for the byte-at-a-time implementation.
*
* This implementation treats each mp_int bignum as an array of bytes,
* rather than as an array of mp_digits. It stores those bytes as a
* column of bytes in the output matrix. It doesn't care if the machine
* uses big-endian or little-endian byte ordering within mp_digits.
* The first byte of the mp_digit array becomes the first byte in the output
* column, regardless of whether that byte is the MSB or LSB of the mp_digit.
*
* "bignums" is an array of mp_ints.
* It points to four rows, four mp_ints, a subset of a larger array of mp_ints.
*
* "weaved" is the weaved output matrix.
* The first byte of bignums[0] is stored in weaved[0].
*
* "nBignums" is the total number of bignums in the array of which "bignums"
* is a part.
*
* "nDigits" is the size in mp_digits of each mp_int in the "bignums" array.
* mp_ints that use less than nDigits digits are logically padded with zeros
* while being stored in the weaved array.
*/
mp_err mpi_to_weave(const mp_int *bignums,
unsigned char *weaved,
mp_size nDigits, /* in each mp_int of input */
mp_size nBignums) /* in the entire source array */
{
mp_size i;
unsigned char * endDest = weaved + (nDigits * nBignums * sizeof(mp_digit));
for (i=0; i < WEAVE_WORD_SIZE; i++) {
mp_size used = MP_USED(&bignums[i]);
unsigned char *pSrc = (unsigned char *)MP_DIGITS(&bignums[i]);
unsigned char *endSrc = pSrc + (used * sizeof(mp_digit));
unsigned char *pDest = weaved + i;
ARGCHK(MP_SIGN(&bignums[i]) == MP_ZPOS, MP_BADARG);
ARGCHK(used <= nDigits, MP_BADARG);
for (; pSrc < endSrc; pSrc++) {
*pDest = *pSrc;
pDest += nBignums;
}
while (pDest < endDest) {
*pDest = 0;
pDest += nBignums;
}
}
return MP_OKAY;
}
/* reverse the operation above for one entry.
* b points to the offset into the weave array of the power we are
* calculating */
mp_err weave_to_mpi(mp_int *a, const unsigned char *b,
mp_size b_size, mp_size count)
{
mp_digit *pb = MP_DIGITS(a);
mp_digit *end = &pb[b_size];
MP_SIGN(a) = MP_ZPOS;
MP_USED(a) = b_size;
for (; pb < end; pb++) {
register mp_digit digit;
digit = *b << 8; b += count;
#define MPI_UNWEAVE_ONE_STEP digit |= *b; b += count; digit = digit << 8;
switch (sizeof(mp_digit)) {
case 32:
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
case 16:
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
case 8:
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
case 4:
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
case 2:
break;
}
digit |= *b; b += count;
*pb = digit;
}
s_mp_clamp(a);
return MP_OKAY;
}
/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
* y). If x, y = NULL, then P is assumed to be the generator (base point)
* of the group of points on the elliptic curve. Input and output values
* are assumed to be NOT field-encoded. */
mp_err
ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
const mp_int *py, mp_int *rx, mp_int *ry)
{
mp_err res = MP_OKAY;
mp_int kt;
ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
MP_DIGITS(&kt) = 0;
/* want scalar to be less than or equal to group order */
if (mp_cmp(k, &group->order) > 0) {
MP_CHECKOK(mp_init(&kt, FLAG(k)));
MP_CHECKOK(mp_mod(k, &group->order, &kt));
} else {
MP_SIGN(&kt) = MP_ZPOS;
MP_USED(&kt) = MP_USED(k);
MP_ALLOC(&kt) = MP_ALLOC(k);
MP_DIGITS(&kt) = MP_DIGITS(k);
}
if ((px == NULL) || (py == NULL)) {
if (group->base_point_mul) {
MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
} else {
MP_CHECKOK(group->
point_mul(&kt, &group->genx, &group->geny, rx, ry,
group));
}
} else {
if (group->meth->field_enc) {
MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
} else {
MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
}
}
if (group->meth->field_dec) {
MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
}
CLEANUP:
if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
mp_clear(&kt);
}
return res;
}
/* Reverse the operation above for one mp_int.
* Reconstruct one mp_int from its column in the weaved array.
* "pSrc" points to the offset into the weave array of the bignum we
* are going to reconstruct.
*/
mp_err weave_to_mpi(mp_int *a, /* output, result */
const unsigned char *pSrc, /* input, byte matrix */
mp_size nDigits, /* per mp_int output */
mp_size nBignums) /* bignums in weaved matrix */
{
unsigned char *pDest = (unsigned char *)MP_DIGITS(a);
unsigned char *endDest = pDest + (nDigits * sizeof(mp_digit));
MP_SIGN(a) = MP_ZPOS;
MP_USED(a) = nDigits;
for (; pDest < endDest; pSrc += nBignums, pDest++) {
*pDest = *pSrc;
}
s_mp_clamp(a);
return MP_OKAY;
}
/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
* Jacobian coordinates.
*
* Assumes input is already field-encoded using field_enc, and returns
* output that is still field-encoded.
*
* This routine implements Point Doubling in the Jacobian Projective
* space as described in the paper "Efficient elliptic curve exponentiation
* using mixed coordinates", by H. Cohen, A Miyaji, T. Ono.
*/
mp_err
ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz,
mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int t0, t1, M, S;
MP_DIGITS(&t0) = 0;
MP_DIGITS(&t1) = 0;
MP_DIGITS(&M) = 0;
MP_DIGITS(&S) = 0;
MP_CHECKOK(mp_init(&t0));
MP_CHECKOK(mp_init(&t1));
MP_CHECKOK(mp_init(&M));
MP_CHECKOK(mp_init(&S));
/* P == inf or P == -P */
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES || mp_cmp_z(py) == 0) {
MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
goto CLEANUP;
}
if (mp_cmp_d(pz, 1) == 0) {
/* M = 3 * px^2 + a */
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, &group->curvea, &M, group->meth));
} else if (MP_SIGN(&group->curvea) == MP_NEG &&
MP_USED(&group->curvea) == 1 &&
MP_DIGIT(&group->curvea, 0) == 3) {
/* M = 3 * (px + pz^2) * (px - pz^2) */
MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth));
MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth));
MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth));
MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth));
} else {
/* 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_sqr(pz, &M, group->meth));
MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth));
MP_CHECKOK(group->meth->
field_mul(&M, &group->curvea, &M, group->meth));
MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth));
}
/* rz = 2 * py * pz */
/* t0 = 4 * py^2 */
if (mp_cmp_d(pz, 1) == 0) {
MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth));
MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth));
} else {
MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth));
MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth));
MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth));
}
/* S = 4 * px * py^2 = px * (2 * py)^2 */
MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth));
/* rx = M^2 - 2 * S */
MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth));
MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth));
/* ry = M * (S - rx) - 8 * py^4 */
MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth));
if (mp_isodd(&t1)) {
MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1));
}
MP_CHECKOK(mp_div_2(&t1, &t1));
MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth));
MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth));
MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth));
CLEANUP:
mp_clear(&t0);
mp_clear(&t1);
mp_clear(&M);
mp_clear(&S);
return res;
}
/* 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;
}
/* 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);
}
/*
* on some platforms character stores into memory is very expensive since they
* generate a read/modify/write operation on the bus. On those platforms
* we need to do integer writes to the bus. Because of some unrolled code,
* in this current code the size of mp_weave_word must be four. The code that
* makes this assumption explicity is called out. (on some platforms a write
* of 4 bytes still requires a single read-modify-write operation.
*
* This function is takes the identical parameters as the function above,
* however it lays out the final array differently. Where the previous function
* treats the mpi_int as an byte array, this function treats it as an array of
* mp_digits where each digit is stored in big endian order.
*
* since we need to interleave on a byte by byte basis, we need to collect
* several mpi structures together into a single uint32 before we write. We
* also need to make sure the uint32 is arranged so that the first value of
* the first array winds up in b[0]. This means construction of that uint32
* is endian specific (even though the layout of the mp_digits in the array
* is always big endian).
*
* The final data is stored as follows :
*
* Our same logical array p array, m is sizeof(mp_digit),
* N is still count and n is now b_size. If we define p[i].digit[j]0 as the
* most significant byte of the word p[i].digit[j], p[i].digit[j]1 as
* the next most significant byte of p[i].digit[j], ... and p[i].digit[j]m-1
* is the least significant byte.
* Our array would look like:
* p[0].digit[0]0 p[1].digit[0]0 ... p[N-2].digit[0]0 p[N-1].digit[0]0
* p[0].digit[0]1 p[1].digit[0]1 ... p[N-2].digit[0]1 p[N-1].digit[0]1
* . .
* p[0].digit[0]m-1 p[1].digit[0]m-1 ... p[N-2].digit[0]m-1 p[N-1].digit[0]m-1
* p[0].digit[1]0 p[1].digit[1]0 ... p[N-2].digit[1]0 p[N-1].digit[1]0
* . .
* . .
* p[0].digit[n-1]m-2 p[1].digit[n-1]m-2 ... p[N-2].digit[n-1]m-2 p[N-1].digit[n-1]m-2
* p[0].digit[n-1]m-1 p[1].digit[n-1]m-1 ... p[N-2].digit[n-1]m-1 p[N-1].digit[n-1]m-1
*
*/
mp_err mpi_to_weave(const mp_int *a, unsigned char *b,
mp_size b_size, mp_size count)
{
mp_size i;
mp_digit *digitsa0;
mp_digit *digitsa1;
mp_digit *digitsa2;
mp_digit *digitsa3;
mp_size useda0;
mp_size useda1;
mp_size useda2;
mp_size useda3;
mp_weave_word *weaved = (mp_weave_word *)b;
count = count/sizeof(mp_weave_word);
/* this code pretty much depends on this ! */
#if MP_ARGCHK == 2
assert(WEAVE_WORD_SIZE == 4);
assert(sizeof(mp_weave_word) == 4);
#endif
digitsa0 = MP_DIGITS(&a[0]);
digitsa1 = MP_DIGITS(&a[1]);
digitsa2 = MP_DIGITS(&a[2]);
digitsa3 = MP_DIGITS(&a[3]);
useda0 = MP_USED(&a[0]);
useda1 = MP_USED(&a[1]);
useda2 = MP_USED(&a[2]);
useda3 = MP_USED(&a[3]);
ARGCHK(MP_SIGN(&a[0]) == MP_ZPOS, MP_BADARG);
ARGCHK(MP_SIGN(&a[1]) == MP_ZPOS, MP_BADARG);
ARGCHK(MP_SIGN(&a[2]) == MP_ZPOS, MP_BADARG);
ARGCHK(MP_SIGN(&a[3]) == MP_ZPOS, MP_BADARG);
ARGCHK(useda0 <= b_size, MP_BADARG);
ARGCHK(useda1 <= b_size, MP_BADARG);
ARGCHK(useda2 <= b_size, MP_BADARG);
ARGCHK(useda3 <= b_size, MP_BADARG);
#define SAFE_FETCH(digit, used, word) ((word) < (used) ? (digit[word]) : 0)
for (i=0; i < b_size; i++) {
mp_digit d0 = SAFE_FETCH(digitsa0,useda0,i);
mp_digit d1 = SAFE_FETCH(digitsa1,useda1,i);
mp_digit d2 = SAFE_FETCH(digitsa2,useda2,i);
mp_digit d3 = SAFE_FETCH(digitsa3,useda3,i);
register mp_weave_word acc;
/*
* ONE_STEP takes the MSB of each of our current digits and places that
* byte in the appropriate position for writing to the weaved array.
* On little endian:
* b3 b2 b1 b0
* On big endian:
* b0 b1 b2 b3
* When the data is written it would always wind up:
* b[0] = b0
* b[1] = b1
* b[2] = b2
* b[3] = b3
*
* Once we've written the MSB, we shift the whole digit up left one
* byte, putting the Next Most Significant Byte in the MSB position,
* so we we repeat the next one step that byte will be written.
* NOTE: This code assumes sizeof(mp_weave_word) and MP_WEAVE_WORD_SIZE
* is 4.
*/
#ifdef MP_IS_LITTLE_ENDIAN
#define MPI_WEAVE_ONE_STEP \
acc = (d0 >> (MP_DIGIT_BIT-8)) & 0x000000ff; d0 <<= 8; /*b0*/ \
acc |= (d1 >> (MP_DIGIT_BIT-16)) & 0x0000ff00; d1 <<= 8; /*b1*/ \
acc |= (d2 >> (MP_DIGIT_BIT-24)) & 0x00ff0000; d2 <<= 8; /*b2*/ \
acc |= (d3 >> (MP_DIGIT_BIT-32)) & 0xff000000; d3 <<= 8; /*b3*/ \
*weaved = acc; weaved += count;
#else
#define MPI_WEAVE_ONE_STEP \
acc = (d0 >> (MP_DIGIT_BIT-32)) & 0xff000000; d0 <<= 8; /*b0*/ \
acc |= (d1 >> (MP_DIGIT_BIT-24)) & 0x00ff0000; d1 <<= 8; /*b1*/ \
acc |= (d2 >> (MP_DIGIT_BIT-16)) & 0x0000ff00; d2 <<= 8; /*b2*/ \
acc |= (d3 >> (MP_DIGIT_BIT-8)) & 0x000000ff; d3 <<= 8; /*b3*/ \
*weaved = acc; weaved += count;
#endif
switch (sizeof(mp_digit)) {
case 32:
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
case 16:
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
case 8:
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
case 4:
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
case 2:
MPI_WEAVE_ONE_STEP
case 1:
MPI_WEAVE_ONE_STEP
break;
}
}
return MP_OKAY;
}
/* 6 words */
mp_err
ec_GFp_sub_6(const mp_int *a, const mp_int *b, mp_int *r,
const GFMethod *meth)
{
mp_err res = MP_OKAY;
mp_digit b0 = 0, b1 = 0, b2 = 0, b3 = 0, b4 = 0, b5 = 0;
mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0;
mp_digit borrow;
switch (MP_USED(a)) {
case 6:
r5 = MP_DIGIT(a, 5);
case 5:
r4 = MP_DIGIT(a, 4);
case 4:
r3 = MP_DIGIT(a, 3);
case 3:
r2 = MP_DIGIT(a, 2);
case 2:
r1 = MP_DIGIT(a, 1);
case 1:
r0 = MP_DIGIT(a, 0);
}
switch (MP_USED(b)) {
case 6:
b5 = MP_DIGIT(b, 5);
case 5:
b4 = MP_DIGIT(b, 4);
case 4:
b3 = MP_DIGIT(b, 3);
case 3:
b2 = MP_DIGIT(b, 2);
case 2:
b1 = MP_DIGIT(b, 1);
case 1:
b0 = MP_DIGIT(b, 0);
}
borrow = 0;
MP_SUB_BORROW(r0, b0, r0, borrow);
MP_SUB_BORROW(r1, b1, r1, borrow);
MP_SUB_BORROW(r2, b2, r2, borrow);
MP_SUB_BORROW(r3, b3, r3, borrow);
MP_SUB_BORROW(r4, b4, r4, borrow);
MP_SUB_BORROW(r5, b5, r5, borrow);
/* Do quick 'add' if we've gone under 0
* (subtract the 2's complement of the curve field) */
if (borrow) {
b5 = MP_DIGIT(&meth->irr, 5);
b4 = MP_DIGIT(&meth->irr, 4);
b3 = MP_DIGIT(&meth->irr, 3);
b2 = MP_DIGIT(&meth->irr, 2);
b1 = MP_DIGIT(&meth->irr, 1);
b0 = MP_DIGIT(&meth->irr, 0);
borrow = 0;
MP_ADD_CARRY(b0, r0, r0, borrow);
MP_ADD_CARRY(b1, r1, r1, borrow);
MP_ADD_CARRY(b2, r2, r2, borrow);
MP_ADD_CARRY(b3, r3, r3, borrow);
MP_ADD_CARRY(b4, r4, r4, borrow);
MP_ADD_CARRY(b5, r5, r5, borrow);
}
MP_CHECKOK(s_mp_pad(r, 6));
MP_DIGIT(r, 5) = r5;
MP_DIGIT(r, 4) = r4;
MP_DIGIT(r, 3) = r3;
MP_DIGIT(r, 2) = r2;
MP_DIGIT(r, 1) = r1;
MP_DIGIT(r, 0) = r0;
MP_SIGN(r) = MP_ZPOS;
MP_USED(r) = 6;
s_mp_clamp(r);
CLEANUP:
return res;
}
/* 4 words */
mp_err
ec_GFp_sub_4(const mp_int *a, const mp_int *b, mp_int *r,
const GFMethod *meth)
{
mp_err res = MP_OKAY;
mp_digit b0 = 0, b1 = 0, b2 = 0, b3 = 0;
mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0;
mp_digit borrow;
switch (MP_USED(a)) {
case 4:
r3 = MP_DIGIT(a, 3);
case 3:
r2 = MP_DIGIT(a, 2);
case 2:
r1 = MP_DIGIT(a, 1);
case 1:
r0 = MP_DIGIT(a, 0);
}
switch (MP_USED(b)) {
case 4:
b3 = MP_DIGIT(b, 3);
case 3:
b2 = MP_DIGIT(b, 2);
case 2:
b1 = MP_DIGIT(b, 1);
case 1:
b0 = MP_DIGIT(b, 0);
}
#ifndef MPI_AMD64_ADD
borrow = 0;
MP_SUB_BORROW(r0, b0, r0, borrow);
MP_SUB_BORROW(r1, b1, r1, borrow);
MP_SUB_BORROW(r2, b2, r2, borrow);
MP_SUB_BORROW(r3, b3, r3, borrow);
#else
__asm__(
"xorq %4,%4 \n\t"
"subq %5,%0 \n\t"
"sbbq %6,%1 \n\t"
"sbbq %7,%2 \n\t"
"sbbq %8,%3 \n\t"
"adcq $0,%4 \n\t"
: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(borrow)
: "r"(b0), "r"(b1), "r"(b2), "r"(b3),
"0"(r0), "1"(r1), "2"(r2), "3"(r3)
: "%cc");
#endif
/* Do quick 'add' if we've gone under 0
* (subtract the 2's complement of the curve field) */
if (borrow) {
b3 = MP_DIGIT(&meth->irr, 3);
b2 = MP_DIGIT(&meth->irr, 2);
b1 = MP_DIGIT(&meth->irr, 1);
b0 = MP_DIGIT(&meth->irr, 0);
#ifndef MPI_AMD64_ADD
borrow = 0;
MP_ADD_CARRY(b0, r0, r0, borrow);
MP_ADD_CARRY(b1, r1, r1, borrow);
MP_ADD_CARRY(b2, r2, r2, borrow);
MP_ADD_CARRY(b3, r3, r3, borrow);
#else
__asm__(
"addq %4,%0 \n\t"
"adcq %5,%1 \n\t"
"adcq %6,%2 \n\t"
"adcq %7,%3 \n\t"
: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3)
: "r"(b0), "r"(b1), "r"(b2), "r"(b3),
"0"(r0), "1"(r1), "2"(r2), "3"(r3)
: "%cc");
#endif
}
#ifdef MPI_AMD64_ADD
/* compiler fakeout? */
if ((r3 == b0) && (r1 == b0) && (r0 == b0)) {
MP_CHECKOK(s_mp_pad(r, 4));
}
#endif
MP_CHECKOK(s_mp_pad(r, 4));
MP_DIGIT(r, 3) = r3;
MP_DIGIT(r, 2) = r2;
MP_DIGIT(r, 1) = r1;
MP_DIGIT(r, 0) = r0;
MP_SIGN(r) = MP_ZPOS;
MP_USED(r) = 4;
s_mp_clamp(r);
CLEANUP:
return res;
}
/* 6 words */
mp_err
ec_GFp_add_6(const mp_int *a, const mp_int *b, mp_int *r,
const GFMethod *meth)
{
mp_err res = MP_OKAY;
mp_digit a0 = 0, a1 = 0, a2 = 0, a3 = 0, a4 = 0, a5 = 0;
mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0;
mp_digit carry;
switch (MP_USED(a)) {
case 6:
a5 = MP_DIGIT(a, 5);
case 5:
a4 = MP_DIGIT(a, 4);
case 4:
a3 = MP_DIGIT(a, 3);
case 3:
a2 = MP_DIGIT(a, 2);
case 2:
a1 = MP_DIGIT(a, 1);
case 1:
a0 = MP_DIGIT(a, 0);
}
switch (MP_USED(b)) {
case 6:
r5 = MP_DIGIT(b, 5);
case 5:
r4 = MP_DIGIT(b, 4);
case 4:
r3 = MP_DIGIT(b, 3);
case 3:
r2 = MP_DIGIT(b, 2);
case 2:
r1 = MP_DIGIT(b, 1);
case 1:
r0 = MP_DIGIT(b, 0);
}
carry = 0;
MP_ADD_CARRY(a0, r0, r0, carry);
MP_ADD_CARRY(a1, r1, r1, carry);
MP_ADD_CARRY(a2, r2, r2, carry);
MP_ADD_CARRY(a3, r3, r3, carry);
MP_ADD_CARRY(a4, r4, r4, carry);
MP_ADD_CARRY(a5, r5, r5, carry);
MP_CHECKOK(s_mp_pad(r, 6));
MP_DIGIT(r, 5) = r5;
MP_DIGIT(r, 4) = r4;
MP_DIGIT(r, 3) = r3;
MP_DIGIT(r, 2) = r2;
MP_DIGIT(r, 1) = r1;
MP_DIGIT(r, 0) = r0;
MP_SIGN(r) = MP_ZPOS;
MP_USED(r) = 6;
/* Do quick 'subract' if we've gone over
* (add the 2's complement of the curve field) */
a5 = MP_DIGIT(&meth->irr, 5);
if (carry || r5 > a5 ||
((r5 == a5) && mp_cmp(r, &meth->irr) != MP_LT)) {
a4 = MP_DIGIT(&meth->irr, 4);
a3 = MP_DIGIT(&meth->irr, 3);
a2 = MP_DIGIT(&meth->irr, 2);
a1 = MP_DIGIT(&meth->irr, 1);
a0 = MP_DIGIT(&meth->irr, 0);
carry = 0;
MP_SUB_BORROW(r0, a0, r0, carry);
MP_SUB_BORROW(r1, a1, r1, carry);
MP_SUB_BORROW(r2, a2, r2, carry);
MP_SUB_BORROW(r3, a3, r3, carry);
MP_SUB_BORROW(r4, a4, r4, carry);
MP_SUB_BORROW(r5, a5, r5, carry);
MP_DIGIT(r, 5) = r5;
MP_DIGIT(r, 4) = r4;
MP_DIGIT(r, 3) = r3;
MP_DIGIT(r, 2) = r2;
MP_DIGIT(r, 1) = r1;
MP_DIGIT(r, 0) = r0;
}
s_mp_clamp(r);
CLEANUP:
return res;
}
/* 4 words */
mp_err
ec_GFp_add_4(const mp_int *a, const mp_int *b, mp_int *r,
const GFMethod *meth)
{
mp_err res = MP_OKAY;
mp_digit a0 = 0, a1 = 0, a2 = 0, a3 = 0;
mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0;
mp_digit carry;
switch (MP_USED(a)) {
case 4:
a3 = MP_DIGIT(a, 3);
case 3:
a2 = MP_DIGIT(a, 2);
case 2:
a1 = MP_DIGIT(a, 1);
case 1:
a0 = MP_DIGIT(a, 0);
}
switch (MP_USED(b)) {
case 4:
r3 = MP_DIGIT(b, 3);
case 3:
r2 = MP_DIGIT(b, 2);
case 2:
r1 = MP_DIGIT(b, 1);
case 1:
r0 = MP_DIGIT(b, 0);
}
#ifndef MPI_AMD64_ADD
carry = 0;
MP_ADD_CARRY(a0, r0, r0, carry);
MP_ADD_CARRY(a1, r1, r1, carry);
MP_ADD_CARRY(a2, r2, r2, carry);
MP_ADD_CARRY(a3, r3, r3, carry);
#else
__asm__(
"xorq %4,%4 \n\t"
"addq %5,%0 \n\t"
"adcq %6,%1 \n\t"
"adcq %7,%2 \n\t"
"adcq %8,%3 \n\t"
"adcq $0,%4 \n\t"
: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(carry)
: "r"(a0), "r"(a1), "r"(a2), "r"(a3),
"0"(r0), "1"(r1), "2"(r2), "3"(r3)
: "%cc");
#endif
MP_CHECKOK(s_mp_pad(r, 4));
MP_DIGIT(r, 3) = r3;
MP_DIGIT(r, 2) = r2;
MP_DIGIT(r, 1) = r1;
MP_DIGIT(r, 0) = r0;
MP_SIGN(r) = MP_ZPOS;
MP_USED(r) = 4;
/* Do quick 'subract' if we've gone over
* (add the 2's complement of the curve field) */
a3 = MP_DIGIT(&meth->irr, 3);
if (carry || r3 > a3 ||
((r3 == a3) && mp_cmp(r, &meth->irr) != MP_LT)) {
a2 = MP_DIGIT(&meth->irr, 2);
a1 = MP_DIGIT(&meth->irr, 1);
a0 = MP_DIGIT(&meth->irr, 0);
#ifndef MPI_AMD64_ADD
carry = 0;
MP_SUB_BORROW(r0, a0, r0, carry);
MP_SUB_BORROW(r1, a1, r1, carry);
MP_SUB_BORROW(r2, a2, r2, carry);
MP_SUB_BORROW(r3, a3, r3, carry);
#else
__asm__(
"subq %4,%0 \n\t"
"sbbq %5,%1 \n\t"
"sbbq %6,%2 \n\t"
"sbbq %7,%3 \n\t"
: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3)
: "r"(a0), "r"(a1), "r"(a2), "r"(a3),
"0"(r0), "1"(r1), "2"(r2), "3"(r3)
: "%cc");
#endif
MP_DIGIT(r, 3) = r3;
MP_DIGIT(r, 2) = r2;
MP_DIGIT(r, 1) = r1;
MP_DIGIT(r, 0) = r0;
}