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remove disabled code

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This commit is contained in:
Bodo Möller 2002-04-14 13:28:41 +00:00
parent 1dcb6c994f
commit 617f461c9d
1 changed files with 1 additions and 310 deletions
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311
crypto/ec/ec_mult.c
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@ -61,14 +61,13 @@
/* TODO: optional precomputation of multiples of the generator */
#if 1
/*
* wNAF-based interleaving multi-exponentation method
* (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>)
*/
/* Determine the width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
* This is an array r[] of values that are either zero or odd with an
* absolute value less than 2^w satisfying
@ -417,314 +416,6 @@ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
return ret;
}
#else
/*
* Basic interleaving multi-exponentation method
*/
#define EC_window_bits_for_scalar_size(b) \
((b) >= 2000 ? 6 : \
(b) >= 800 ? 5 : \
(b) >= 300 ? 4 : \
(b) >= 70 ? 3 : \
(b) >= 20 ? 2 : \
1)
/* For window size 'w' (w >= 2), we compute the odd multiples
* 1*P .. (2^w-1)*P.
* This accounts for 2^(w-1) point additions (neglecting constants),
* each of which requires 16 field multiplications (4 squarings
* and 12 general multiplications) in the case of curves defined
* over GF(p), which are the only curves we have so far.
*
* Converting these precomputed points into affine form takes
* three field multiplications for inverting Z and one squaring
* and three multiplications for adjusting X and Y, i.e.
* 7 multiplications in total (1 squaring and 6 general multiplications),
* again except for constants.
*
* The average number of windows for a 'b' bit scalar is roughly
* b/(w+1).
* Each of these windows (except possibly for the first one, but
* we are ignoring constants anyway) requires one point addition.
* As the precomputed table stores points in affine form, these
* additions take only 11 field multiplications each (3 squarings
* and 8 general multiplications).
*
* So the total workload, except for constants, is
*
* 2^(w-1)*[5 squarings + 18 multiplications]
* + (b/(w+1))*[3 squarings + 8 multiplications]
*
* If we assume that 10 squarings are as costly as 9 multiplications,
* our task is to find the 'w' that, given 'b', minimizes
*
* 2^(w-1)*(5*9 + 18*10) + (b/(w+1))*(3*9 + 8*10)
* = 2^(w-1)*225 + (b/(w+1))*107.
*
* Thus optimal window sizes should be roughly as follows:
*
* w >= 6 if b >= 1414
* w = 5 if 1413 >= b >= 505
* w = 4 if 504 >= b >= 169
* w = 3 if 168 >= b >= 51
* w = 2 if 50 >= b >= 13
* w = 1 if 12 >= b
*
* If we assume instead that squarings are exactly as costly as
* multiplications, we have to minimize
* 2^(w-1)*23 + (b/(w+1))*11.
*
* This gives us the following (nearly unchanged) table of optimal
* windows sizes:
*
* w >= 6 if b >= 1406
* w = 5 if 1405 >= b >= 502
* w = 4 if 501 >= b >= 168
* w = 3 if 167 >= b >= 51
* w = 2 if 50 >= b >= 13
* w = 1 if 12 >= b
*
* Note that neither table tries to take into account memory usage
* (allocation overhead, code locality etc.). Actual timings with
* NIST curves P-192, P-224, and P-256 with scalars of 192, 224,
* and 256 bits, respectively, show that w = 3 (instead of 4) is
* preferrable; timings with NIST curve P-384 and 384-bit scalars
* confirm that w = 4 is optimal for this case; and timings with
* NIST curve P-521 and 521-bit scalars show that w = 4 (instead
* of 5) is preferrable. So we generously round up all the
* boundaries and use the following table:
*
* w >= 6 if b >= 2000
* w = 5 if 1999 >= b >= 800
* w = 4 if 799 >= b >= 300
* w = 3 if 299 >= b >= 70
* w = 2 if 69 >= b >= 20
* w = 1 if 19 >= b
*/
int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
{
BN_CTX *new_ctx = NULL;
EC_POINT *generator = NULL;
EC_POINT *tmp = NULL;
size_t totalnum;
size_t i, j;
int k, t;
int r_is_at_infinity = 1;
size_t max_bits = 0;
size_t *wsize = NULL; /* individual window sizes */
unsigned long *wbits = NULL; /* individual window contents */
int *wpos = NULL; /* position of bottom bit of current individual windows
* (wpos[i] is valid if wbits[i] != 0) */
size_t num_val;
EC_POINT **val = NULL; /* precomputation */
EC_POINT **v;
EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */
int ret = 0;
if (scalar != NULL)
{
generator = EC_GROUP_get0_generator(group);
if (generator == NULL)
{
ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
return 0;
}
}
for (i = 0; i < num; i++)
{
if (group->meth != points[i]->meth)
{
ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
}
totalnum = num + (scalar != NULL);
wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
wbits = OPENSSL_malloc(totalnum * sizeof wbits[0]);
wpos = OPENSSL_malloc(totalnum * sizeof wpos[0]);
if (wsize == NULL || wbits == NULL || wpos == NULL) goto err;
/* num_val := total number of points to precompute */
num_val = 0;
for (i = 0; i < totalnum; i++)
{
size_t bits;
bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
wsize[i] = EC_window_bits_for_scalar_size(bits);
num_val += 1u << (wsize[i] - 1);
if (bits > max_bits)
max_bits = bits;
wbits[i] = 0;
wpos[i] = 0;
}
/* all precomputed points go into a single array 'val',
* 'val_sub[i]' is a pointer to the subarray for the i-th point */
val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
if (val == NULL) goto err;
val[num_val] = NULL; /* pivot element */
val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
if (val_sub == NULL) goto err;
/* allocate points for precomputation */
v = val;
for (i = 0; i < totalnum; i++)
{
val_sub[i] = v;
for (j = 0; j < (1u << (wsize[i] - 1)); j++)
{
*v = EC_POINT_new(group);
if (*v == NULL) goto err;
v++;
}
}
if (!(v == val + num_val))
{
ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
if (ctx == NULL)
{
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
goto err;
}
tmp = EC_POINT_new(group);
if (tmp == NULL) goto err;
/* prepare precomputed values:
* val_sub[i][0] := points[i]
* val_sub[i][1] := 3 * points[i]
* val_sub[i][2] := 5 * points[i]
* ...
*/
for (i = 0; i < totalnum; i++)
{
if (i < num)
{
if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
if (scalars[i]->neg)
{
if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err;
}
}
else
{
if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
if (scalar->neg)
{
if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err;
}
}
if (wsize[i] > 1)
{
if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
for (j = 1; j < (1u << (wsize[i] - 1)); j++)
{
if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
}
}
}
#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err;
#endif
r_is_at_infinity = 1;
for (k = max_bits - 1; k >= 0; k--)
{
if (!r_is_at_infinity)
{
if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
}
for (i = 0; i < totalnum; i++)
{
if (wbits[i] == 0)
{
const BIGNUM *s;
s = i < num ? scalars[i] : scalar;
if (BN_is_bit_set(s, k))
{
/* look at bits k - wsize[i] + 1 .. k for this window */
t = k - wsize[i] + 1;
while (!BN_is_bit_set(s, t)) /* BN_is_bit_set is false for t < 0 */
t++;
wpos[i] = t;
wbits[i] = 1;
for (t = k - 1; t >= wpos[i]; t--)
{
wbits[i] <<= 1;
if (BN_is_bit_set(s, t))
wbits[i]++;
}
/* now wbits[i] is the odd bit pattern at bits wpos[i] .. k */
}
}
if ((wbits[i] != 0) && (wpos[i] == k))
{
if (r_is_at_infinity)
{
if (!EC_POINT_copy(r, val_sub[i][wbits[i] >> 1])) goto err;
r_is_at_infinity = 0;
}
else
{
if (!EC_POINT_add(group, r, r, val_sub[i][wbits[i] >> 1], ctx)) goto err;
}
wbits[i] = 0;
}
}
}
if (r_is_at_infinity)
if (!EC_POINT_set_to_infinity(group, r)) goto err;
ret = 1;
err:
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
if (tmp != NULL)
EC_POINT_free(tmp);
if (wsize != NULL)
OPENSSL_free(wsize);
if (wbits != NULL)
OPENSSL_free(wbits);
if (wpos != NULL)
OPENSSL_free(wpos);
if (val != NULL)
{
for (v = val; *v != NULL; v++)
EC_POINT_clear_free(*v);
OPENSSL_free(val);
}
if (val_sub != NULL)
{
OPENSSL_free(val_sub);
}
return ret;
}
#endif
int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
{