Merge #1344: group: save normalize_weak calls in secp256k1_ge_is_valid_var/secp256k1_gej_eq_x_var

07c0e8b group: remove unneeded normalize_weak in `secp256k1_gej_eq_x_var` (Sebastian Falbesoner)
efa76c4 group: remove unneeded normalize_weak in `secp256k1_ge_is_valid_var` (Sebastian Falbesoner)

Pull request description:

  This PR removes unneeded normalize_weak calls in two group element functions:
  * `secp256k1_ge_is_valid_var`: After calculating the right-hand side of the elliptic curve equation (x^3 + 7), the field element `x3` has a magnitude of 2 (1 as result of `secp256k1_fe_mul`, then increased by 1 due to `secp256k1_fe_add_int`). This is fine for `secp256k1_fe_equal_var`, as the second parameter only requires the magnitude to not exceed 31, and the normalize_weak call is hence not needed and can be dropped. Note that the interface description for `secp256k1_fe_equal` (which also applies to `secp256k1_fe_equal_var`) once stated that _both_ parameters need to have magnitude 1, but that was corrected in commit 7d7d43c.

  * `secp256k1_gej_eq_x_var`: By requiring that the input group element's X coordinate (`a->x`) has a magnitude of <= 31, the normalize_weak call and also the field element variable `r2` are not needed anymore and hence can be dropped.

ACKs for top commit:
  sipa:
    utACK 07c0e8b
  jonasnick:
    ACK 07c0e8b

Tree-SHA512: 9037e4af881ce7bf3347414d6da06b99e3d318733ba4f70e8b24d2320c2f26d022144e17bd6b95c1a4ef1be3825a4464e56ce2d2b3ae7bbced04257048832b7f

Author: real-or-random

src/group.h

@@ -106,7 +106,8 @@ static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
 /** Check two group elements (jacobian) for equality in variable time. */
 static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b);
 
-/** Compare the X coordinate of a group element (jacobian). */
+/** Compare the X coordinate of a group element (jacobian).
+  * The magnitude of the group element's X coordinate must not exceed 31. */
 static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
 
 /** Set r equal to the inverse of a (i.e., mirrored around the X axis) */

src/group_impl.h

@@ -314,13 +314,17 @@ static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b)
 }
 
 static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
-    secp256k1_fe r, r2;
+    secp256k1_fe r;
+
+#ifdef VERIFY
     secp256k1_fe_verify(x);
+    VERIFY_CHECK(a->x.magnitude <= 31);
     secp256k1_gej_verify(a);
     VERIFY_CHECK(!a->infinity);
+#endif
+
     secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
-    r2 = a->x; secp256k1_fe_normalize_weak(&r2);
-    return secp256k1_fe_equal_var(&r, &r2);
+    return secp256k1_fe_equal_var(&r, &a->x);
 }
 
 static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
@@ -349,7 +353,6 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
     secp256k1_fe_sqr(&y2, &a->y);
     secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
     secp256k1_fe_add_int(&x3, SECP256K1_B);
-    secp256k1_fe_normalize_weak(&x3);
     return secp256k1_fe_equal_var(&y2, &x3);
 }