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Scalarinversevar #1

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2446b1e
Replace secp256k1_scalar_complement with secp256k1_scalar_sub.
roconnor-blockstream Apr 20, 2020
13e07ab
Remove gotos.
roconnor-blockstream Apr 21, 2020
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37 changes: 12 additions & 25 deletions src/scalar_4x64_impl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -114,6 +114,18 @@ static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int
#endif
}

static void secp256k1_scalar_sub(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
uint128_t t = (uint128_t)a->d[0] - b->d[0];
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; t |= t << 64;
t += (uint128_t)a->d[1] - b->d[1];
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; t |= t << 64;
t += (uint128_t)a->d[2] - b->d[2];
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; t |= t << 64;
t += (uint128_t)a->d[3] - b->d[3];
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
VERIFY_CHECK((t >> 64) == 0);
}

static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
int over;
r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56;
Expand Down Expand Up @@ -181,31 +193,6 @@ static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
return 2 * (mask == 0) - 1;
}

static int secp256k1_scalar_complement(secp256k1_scalar *r, const secp256k1_scalar *a) {
uint128_t t = 1;
t += ~a->d[0];
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += ~a->d[1];
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += ~a->d[2];
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += ~a->d[3];
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
return t;
}

static int secp256k1_scalar_binadd(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
uint128_t t = (uint128_t)a->d[0] + b->d[0];
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[1] + b->d[1];
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[2] + b->d[2];
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[3] + b->d[3];
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
return t;
}

/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */

/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
Expand Down
61 changes: 20 additions & 41 deletions src/scalar_8x32_impl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -162,6 +162,26 @@ static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int
#endif
}

static void secp256k1_scalar_sub(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
uint64_t t = (uint64_t)a->d[0] - b->d[0];
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32; t |= t << 32;
t += (uint64_t)a->d[1] - b->d[1];
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32; t |= t << 32;
t += (uint64_t)a->d[2] - b->d[2];
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32; t |= t << 32;
t += (uint64_t)a->d[3] - b->d[3];
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32; t |= t << 32;
t += (uint64_t)a->d[4] - b->d[4];
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32; t |= t << 32;
t += (uint64_t)a->d[5] - b->d[5];
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32; t |= t << 32;
t += (uint64_t)a->d[6] - b->d[6];
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32; t |= t << 32;
t += (uint64_t)a->d[7] - b->d[7];
r->d[7] = t & 0xFFFFFFFFULL;
VERIFY_CHECK((t >> 32) == 0);
}

static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
int over;
r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
Expand Down Expand Up @@ -259,47 +279,6 @@ static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
return 2 * (mask == 0) - 1;
}

static int secp256k1_scalar_complement(secp256k1_scalar *r, const secp256k1_scalar *a) {
uint64_t t = 1;
t += ~a->d[0];
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
t += ~a->d[1];
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
t += ~a->d[2];
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
t += ~a->d[3];
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
t += ~a->d[4];
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
t += ~a->d[5];
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
t += ~a->d[6];
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
t += ~a->d[7];
r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
return t;
}

static int secp256k1_scalar_binadd(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
uint64_t t = (uint64_t)a->d[0] + b->d[0];
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[1] + b->d[1];
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[2] + b->d[2];
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[3] + b->d[3];
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[4] + b->d[4];
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[5] + b->d[5];
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[6] + b->d[6];
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[7] + b->d[7];
r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
return t;
}

/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */

/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
Expand Down
78 changes: 32 additions & 46 deletions src/scalar_impl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -307,15 +307,25 @@ SECP256K1_INLINE static int secp256k1_scalar_shr_zeros(secp256k1_scalar *r) {
}

static int secp256k1_scalar_eea_inverse(secp256k1_scalar *r, const secp256k1_scalar *n) {
secp256k1_scalar u, v, i, j, acomp, negx;
secp256k1_scalar *a, *b, *x0, *x1, *tmp;
int ka, kb;
secp256k1_scalar u = *n;
secp256k1_scalar v = SECP256K1_SCALAR_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL);
secp256k1_scalar i = secp256k1_scalar_one;
/* a = n */
secp256k1_scalar *a = &u;
/* b = p */
secp256k1_scalar *b = &v;
/* x0 = 1 */
secp256k1_scalar *x0 = &i;
/* x1 = 0 */
secp256k1_scalar *x1 = r;
int k;

secp256k1_scalar_set_int(r, 0);

/* zero is not invertible */
if (secp256k1_scalar_is_zero(n)) {
secp256k1_scalar_set_int(r, 0);
return 0;
}
if (secp256k1_scalar_is_zero(a)) return 0;

/**
* The extended euclidian algorithm compute x, y and gcd(a, b) such as
Expand All @@ -327,66 +337,42 @@ static int secp256k1_scalar_eea_inverse(secp256k1_scalar *r, const secp256k1_sca
* So the equation simplify to a*x = 1, and x = a^-1.
*/

/* a = n */
u = *n;
a = &u;

/* Because 2 is not a common factor between a and b, we can detect
* multiples of 2 using the LSB and eliminate them aggressively. */
ka = secp256k1_scalar_shr_zeros(a);

/* b = p - a */
secp256k1_scalar_negate(&v, a);
b = &v;

/* x0 = 1 */
secp256k1_scalar_set_int(&i, 1);
secp256k1_scalar_negate(&negx, &i);
x0 = &i;

/* x1 = 0 */
secp256k1_scalar_set_int(&j, 0);
x1 = &j;

if (secp256k1_scalar_is_one(a)) {
goto done;
}

/* For a and b, we use 2 comlement math and ensure no overflow happens. */
secp256k1_scalar_complement(&acomp, a);
goto bzero;
k = secp256k1_scalar_shr_zeros(a);
secp256k1_scalar_pow2_div(x0, x0, k);

while (!secp256k1_scalar_is_one(a)) {
secp256k1_scalar_complement(&acomp, a);
secp256k1_scalar negx;
secp256k1_scalar_negate(&negx, x0);

VERIFY_CHECK(secp256k1_scalar_cmp_var(b, a) > 0);
do {
secp256k1_scalar_binadd(b, b, &acomp);
secp256k1_scalar_sub(b, b, a);

bzero:
/* We ensure that a and b are odd, so b must be even after subtracting a. */
VERIFY_CHECK(secp256k1_scalar_is_even(b));
kb = secp256k1_scalar_shr_zeros(b);
k = secp256k1_scalar_shr_zeros(b);
secp256k1_scalar_add(x1, x1, &negx);
secp256k1_scalar_pow2_div(x1, x1, kb);
secp256k1_scalar_pow2_div(x1, x1, k);
} while (secp256k1_scalar_cmp_var(b, a) > 0);

/* a and b can never be equal, so if we exited, it is because a > b. */
VERIFY_CHECK(secp256k1_scalar_cmp_var(a, b) > 0);

/* In order to speed things up, we only swap pointers */
tmp = a;
a = b;
b = tmp;
{
secp256k1_scalar *tmp = a;
a = b;
b = tmp;

tmp = x0;
x0 = x1;
x1 = tmp;
tmp = x0;
x0 = x1;
x1 = tmp;
}
}

done:
secp256k1_scalar_pow2_div(r, x0, ka);
*r = *x0;
return 1;
}
#endif
Expand Down