Add _fe_normalizes_to_zero method

src/field.h

@@ -54,6 +54,10 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r);
 /** Normalize a field element, without constant-time guarantee. */
 static void secp256k1_fe_normalize_var(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(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);
 

src/field_10x26_impl.h

@@ -122,6 +122,9 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
     t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
     t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
 
+    /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t9 >> 23 == 0);
+
     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
     r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
 
@@ -187,6 +190,35 @@ static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
 #endif
 }
 
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
+    uint32_t t0 = r->n[0], 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 = 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; t9 &= 0x03FFFFFUL;
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    uint32_t z0, z1;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x3D1UL; t1 += (x << 6);
+    t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0  = t0; z1  = t0 ^ 0x3D0UL;
+    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;

src/field_5x52_impl.h

@@ -168,6 +168,29 @@ static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
 #endif
 }
 
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], 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; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    uint64_t z0, z1;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0  = t0; z1  = t0 ^ 0x1000003D0ULL;
+    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;

src/field_impl.h

@@ -64,12 +64,12 @@ 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);
-    secp256k1_fe_normalize_var(&na);
+    return secp256k1_fe_normalizes_to_zero(&na);
-    return secp256k1_fe_is_zero(&na);
 }
 
 static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {

src/group_impl.h

@@ -160,9 +160,7 @@ static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
 static int secp256k1_gej_eq_x_var(const secp256k1_fe_t *x, const secp256k1_gej_t *a) {
     VERIFY_CHECK(!a->infinity);
     secp256k1_fe_t r; secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
-    secp256k1_fe_t r2 = a->x;
+    secp256k1_fe_t r2 = a->x; secp256k1_fe_normalize_weak(&r2);
-    secp256k1_fe_normalize_weak(&r);
-    secp256k1_fe_normalize_weak(&r2);
     return secp256k1_fe_equal_var(&r, &r2);
 }
 
@@ -257,16 +255,16 @@ static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a,
     secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
     secp256k1_fe_t s1; secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
     secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
-    if (secp256k1_fe_equal_var(&u1, &u2)) {
+    secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-        if (secp256k1_fe_equal_var(&s1, &s2)) {
+    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)) {
             secp256k1_gej_double_var(r, a);
         } else {
             r->infinity = 1;
         }
         return;
     }
-    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);
     secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
     secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
     secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2);
@@ -296,16 +294,16 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *
     secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
     secp256k1_fe_t s1 = a->y; secp256k1_fe_normalize_weak(&s1);
     secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
-    if (secp256k1_fe_equal_var(&u1, &u2)) {
+    secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-        if (secp256k1_fe_equal_var(&s1, &s2)) {
+    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)) {
             secp256k1_gej_double_var(r, a);
         } else {
             r->infinity = 1;
         }
         return;
     }
-    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);
     secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
     secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
     secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2);
@@ -360,8 +358,7 @@ static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, c
     secp256k1_fe_add(&rr, &t);                                      /* rr = R = T^2-U1*U2 (3) */
     secp256k1_fe_sqr(&t, &rr);                                      /* t = R^2 (1) */
     secp256k1_fe_mul(&r->z, &m, &z);                                /* r->z = M*Z (1) */
-    secp256k1_fe_normalize(&r->z);
+    int infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
-    int infinity = secp256k1_fe_is_zero(&r->z) * (1 - a->infinity);
     secp256k1_fe_mul_int(&r->z, 2 * (1 - a->infinity)); /* r->z = Z3 = 2*M*Z (2) */
     r->x = t;                                           /* r->x = R^2 (1) */
     secp256k1_fe_negate(&q, &q, 1);                     /* q = -Q (2) */