From 49ee0dbe167b54e92ed4602cc5c9372d1e619849 Mon Sep 17 00:00:00 2001 From: Peter Dettman Date: Sat, 13 Dec 2014 17:14:26 +0700 Subject: [PATCH] Add _normalizes_to_zero_var variant --- src/field.h | 4 ++++ src/field_10x26_impl.h | 38 ++++++++++++++++++++++++++++++++++++++ src/field_5x52_impl.h | 31 +++++++++++++++++++++++++++++++ src/field_impl.h | 3 +-- src/group_impl.h | 8 ++++---- 5 files changed, 78 insertions(+), 6 deletions(-) diff --git a/src/field.h b/src/field.h index ed34c965d9d..14e2b813c17 100644 --- a/src/field.h +++ b/src/field.h @@ -58,6 +58,10 @@ static void secp256k1_fe_normalize_var(secp256k1_fe_t *r); * implementation may optionally normalize the input, but this should not be relied upon. */ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r); +/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field + * implementation may optionally normalize the input, but this should not be relied upon. */ +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r); + /** Set a field element equal to a small integer. Resulting field element is normalized. */ static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a); diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h index 7778ac3d5a4..8f5d15c729e 100644 --- a/src/field_10x26_impl.h +++ b/src/field_10x26_impl.h @@ -219,6 +219,44 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) { return (z0 == 0) | (z1 == 0x3FFFFFFUL); } +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) { + uint32_t t0 = r->n[0], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t x = t9 >> 22; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + uint32_t z0 = t0 & 0x3FFFFFFUL, z1 = z0 ^ 0x3D0UL; + + /* Fast return path should catch the majority of cases */ + if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) + return 0; + + uint32_t t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8]; + t9 &= 0x03FFFFFUL; + t1 += (x << 6); + + t1 += (t0 >> 26); t0 = z0; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8; + z0 |= t9; z1 &= t9 ^ 0x3C00000UL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + return (z0 == 0) | (z1 == 0x3FFFFFFUL); +} + SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) { r->n[0] = a; r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0; diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h index 45f61e0d7e3..33597c446f2 100644 --- a/src/field_5x52_impl.h +++ b/src/field_5x52_impl.h @@ -191,6 +191,37 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) { return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); } +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) { + uint64_t t0 = r->n[0], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t x = t4 >> 48; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + uint64_t z0 = t0 & 0xFFFFFFFFFFFFFULL, z1 = z0 ^ 0x1000003D0ULL; + + /* Fast return path should catch the majority of cases */ + if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) + return 0; + + uint64_t t1 = r->n[1], t2 = r->n[2], t3 = r->n[3]; + t4 &= 0x0FFFFFFFFFFFFULL; + + t1 += (t0 >> 52); t0 = z0; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; + z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); +} + SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) { r->n[0] = a; r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0; diff --git a/src/field_impl.h b/src/field_impl.h index d1b6cd6f330..484e67310c5 100644 --- a/src/field_impl.h +++ b/src/field_impl.h @@ -64,12 +64,11 @@ static int secp256k1_fe_set_hex(secp256k1_fe_t *r, const char *a, int alen) { return secp256k1_fe_set_b32(r, tmp); } -/* TODO Not actually var currently */ SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) { secp256k1_fe_t na; secp256k1_fe_negate(&na, a, 1); secp256k1_fe_add(&na, b); - return secp256k1_fe_normalizes_to_zero(&na); + return secp256k1_fe_normalizes_to_zero_var(&na); } static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) { diff --git a/src/group_impl.h b/src/group_impl.h index e62d3209ee3..fef06df2892 100644 --- a/src/group_impl.h +++ b/src/group_impl.h @@ -257,8 +257,8 @@ static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z); secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); secp256k1_fe_t i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2); - if (secp256k1_fe_normalizes_to_zero(&h)) { - if (secp256k1_fe_normalizes_to_zero(&i)) { + if (secp256k1_fe_normalizes_to_zero_var(&h)) { + if (secp256k1_fe_normalizes_to_zero_var(&i)) { secp256k1_gej_double_var(r, a); } else { r->infinity = 1; @@ -296,8 +296,8 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t * secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z); secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); secp256k1_fe_t i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2); - if (secp256k1_fe_normalizes_to_zero(&h)) { - if (secp256k1_fe_normalizes_to_zero(&i)) { + if (secp256k1_fe_normalizes_to_zero_var(&h)) { + if (secp256k1_fe_normalizes_to_zero_var(&i)) { secp256k1_gej_double_var(r, a); } else { r->infinity = 1;