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Merge bitcoin#513: Increase sparsity of pippenger fixed window naf re…
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…presentation

ec0a7b3 Don't touch leading zeros in wnaf_fixed. (Jonas Nick)
9e36d1b Fix bug in wnaf_fixed where the wnaf array is not completely zeroed when given a 0 scalar. (Jonas Nick)
96f68a0 Don't invert scalar in wnaf_fixed when it is even because a caller might intentionally give a scalar with many leading zeros. (Jonas Nick)
6dbb007 Increase sparsity of pippenger fixed window naf representation (Jonas Nick)

Pull request description:

  Fixes bitcoin#506

Tree-SHA512: 49a237a7d09c0c376ba4e6b1f522b9aff2517e420dfef9df810fd5ba920e0b98be8fe3f730b32e41b4aef475bc4cf3b13220024bd8d6f40c2744e6f392ff97a8
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@sipa
sipa committed Apr 5, 2018
2 parents fb9271d + ec0a7b3 commit dbc3ddd
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Showing 2 changed files with 92 additions and 32 deletions.
65 changes: 38 additions & 27 deletions src/ecmult_impl.h
View file
Original file line number Diff line number Diff line change
Expand Up @@ -563,53 +563,66 @@ static size_t secp256k1_strauss_max_points(secp256k1_scratch *scratch) {
* It has the following guarantees:
* - each wnaf[i] is either 0 or an odd integer between -(1 << w) and (1 << w)
* - the number of words set is always WNAF_SIZE(w)
* - the returned skew is 0 without endomorphism, or 0 or 1 with endomorphism
* - the returned skew is 0 or 1
*/
static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) {
int sign = 0;
int skew = 0;
int pos = 1;
#ifndef USE_ENDOMORPHISM
secp256k1_scalar neg_s;
#endif
int pos;
int max_pos;
int last_w;
const secp256k1_scalar *work = s;

if (secp256k1_scalar_is_zero(s)) {
while (pos * w < WNAF_BITS) {
for (pos = 0; pos < WNAF_SIZE(w); pos++) {
wnaf[pos] = 0;
++pos;
}
return 0;
}

if (secp256k1_scalar_is_even(s)) {
#ifdef USE_ENDOMORPHISM
skew = 1;
#else
secp256k1_scalar_negate(&neg_s, s);
work = &neg_s;
sign = -1;
#endif
}

wnaf[0] = (secp256k1_scalar_get_bits_var(work, 0, w) + skew + sign) ^ sign;
wnaf[0] = secp256k1_scalar_get_bits_var(work, 0, w) + skew;
/* Compute last window size. Relevant when window size doesn't divide the
* number of bits in the scalar */
last_w = WNAF_BITS - (WNAF_SIZE(w) - 1) * w;

while (pos * w < WNAF_BITS) {
int now = w;
int val;
if (now + pos * w > WNAF_BITS) {
now = WNAF_BITS - pos * w;
/* Store the position of the first nonzero word in max_pos to allow
* skipping leading zeros when calculating the wnaf. */
for (pos = WNAF_SIZE(w) - 1; pos > 0; pos--) {
int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
if(val != 0) {
break;
}
val = secp256k1_scalar_get_bits_var(work, pos * w, now);
wnaf[pos] = 0;
}
max_pos = pos;
pos = 1;

while (pos <= max_pos) {
int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
if ((val & 1) == 0) {
wnaf[pos - 1] -= ((1 << w) + sign) ^ sign;
wnaf[pos] = (val + 1 + sign) ^ sign;
wnaf[pos - 1] -= (1 << w);
wnaf[pos] = (val + 1);
} else {
wnaf[pos] = (val + sign) ^ sign;
wnaf[pos] = val;
}
/* Set a coefficient to zero if it is 1 or -1 and the proceeding digit
* is strictly negative or strictly positive respectively. Only change
* coefficients at previous positions because above code assumes that
* wnaf[pos - 1] is odd.
*/
if (pos >= 2 && ((wnaf[pos - 1] == 1 && wnaf[pos - 2] < 0) || (wnaf[pos - 1] == -1 && wnaf[pos - 2] > 0))) {
if (wnaf[pos - 1] == 1) {
wnaf[pos - 2] += 1 << w;
} else {
wnaf[pos - 2] -= 1 << w;
}
wnaf[pos - 1] = 0;
}
++pos;
}
VERIFY_CHECK(pos == WNAF_SIZE(w));

return skew;
}
Expand Down Expand Up @@ -665,7 +678,6 @@ static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_wi
secp256k1_ge tmp;
int idx;

#ifdef USE_ENDOMORPHISM
if (i == 0) {
/* correct for wnaf skew */
int skew = point_state.skew_na;
Expand All @@ -674,7 +686,6 @@ static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_wi
secp256k1_gej_add_ge_var(&buckets[0], &buckets[0], &tmp, NULL);
}
}
#endif
if (n > 0) {
idx = (n - 1)/2;
secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &pt[point_state.input_pos], NULL);
Expand Down
59 changes: 54 additions & 5 deletions src/tests.c
View file
Original file line number Diff line number Diff line change
Expand Up @@ -3022,8 +3022,7 @@ void test_fixed_wnaf(const secp256k1_scalar *number, int w) {
for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
secp256k1_scalar t;
int v = wnaf[i];
CHECK(v != 0); /* check nonzero */
CHECK(v & 1); /* check parity */
CHECK(v == 0 || v & 1); /* check parity */
CHECK(v > -(1 << w)); /* check range above */
CHECK(v < (1 << w)); /* check range below */

Expand All @@ -3041,20 +3040,70 @@ void test_fixed_wnaf(const secp256k1_scalar *number, int w) {
CHECK(secp256k1_scalar_eq(&x, &num));
}

void test_fixed_wnaf_zero(int w) {
/* Checks that the first 8 elements of wnaf are equal to wnaf_expected and the
* rest is 0.*/
void test_fixed_wnaf_small_helper(int *wnaf, int *wnaf_expected, int w) {
int i;
for (i = WNAF_SIZE(w)-1; i >= 8; --i) {
CHECK(wnaf[i] == 0);
}
for (i = 7; i >= 0; --i) {
CHECK(wnaf[i] == wnaf_expected[i]);
}
}

void test_fixed_wnaf_small(void) {
int w = 4;
int wnaf[256] = {0};
int i;
int skew;
secp256k1_scalar num;

secp256k1_scalar_set_int(&num, 0);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);

for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
int v = wnaf[i];
CHECK(v == 0);
}
CHECK(skew == 0);

secp256k1_scalar_set_int(&num, 1);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
for (i = WNAF_SIZE(w)-1; i >= 1; --i) {
int v = wnaf[i];
CHECK(v == 0);
}
CHECK(wnaf[0] == 1);
CHECK(skew == 0);

{
int wnaf_expected[8] = { 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf };
secp256k1_scalar_set_int(&num, 0xffffffff);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
CHECK(skew == 0);
}
{
int wnaf_expected[8] = { -1, -1, -1, -1, -1, -1, -1, 0xf };
secp256k1_scalar_set_int(&num, 0xeeeeeeee);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
CHECK(skew == 1);
}
{
int wnaf_expected[8] = { 1, 0, 1, 0, 1, 0, 1, 0 };
secp256k1_scalar_set_int(&num, 0x01010101);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
CHECK(skew == 0);
}
{
int wnaf_expected[8] = { -0xf, 0, 0xf, -0xf, 0, 0xf, 1, 0 };
secp256k1_scalar_set_int(&num, 0x01ef1ef1);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
CHECK(skew == 0);
}
}

void run_wnaf(void) {
Expand All @@ -3068,7 +3117,7 @@ void run_wnaf(void) {
n.d[0] = 2;
test_constant_wnaf(&n, 4);
/* Test 0 */
test_fixed_wnaf_zero(4);
test_fixed_wnaf_small();
/* Random tests */
for (i = 0; i < count; i++) {
random_scalar_order(&n);
Expand Down

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