Initialize field elements when resulting in infinity

Summary:
 * Added test with additions resulting in infinity

 * Clear field elements when writing infinity

This is a backport of secp256k1 [[bitcoin-core/secp256k1#699 | PR699]]

Test Plan:
  ninja check-secp256k1

Reviewers: #bitcoin_abc, jasonbcox

Reviewed By: #bitcoin_abc, jasonbcox

Subscribers: jasonbcox

Differential Revision: https://reviews.bitcoinabc.org/D7611

Author: elichai

src/secp256k1/src/group_impl.h

@@ -399,7 +399,7 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
             if (rzr != NULL) {
                 secp256k1_fe_set_int(rzr, 0);
             }
-            r->infinity = 1;
+            secp256k1_gej_set_infinity(r);
         }
         return;
     }
@@ -449,7 +449,7 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
             if (rzr != NULL) {
                 secp256k1_fe_set_int(rzr, 0);
             }
-            r->infinity = 1;
+            secp256k1_gej_set_infinity(r);
         }
         return;
     }
@@ -508,7 +508,7 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
             secp256k1_gej_double_var(r, a, NULL);
         } else {
-            r->infinity = 1;
+            secp256k1_gej_set_infinity(r);
         }
         return;
     }

src/secp256k1/src/tests.c

@@ -2307,6 +2307,39 @@ void test_ge(void) {
     free(zinv);
 }
 
+
+void test_intialized_inf(void) {
+    secp256k1_ge p;
+    secp256k1_gej pj, npj, infj1, infj2, infj3;
+    secp256k1_fe zinv;
+
+    /* Test that adding P+(-P) results in a fully initalized infinity*/
+    random_group_element_test(&p);
+    secp256k1_gej_set_ge(&pj, &p);
+    secp256k1_gej_neg(&npj, &pj);
+
+    secp256k1_gej_add_var(&infj1, &pj, &npj, NULL);
+    CHECK(secp256k1_gej_is_infinity(&infj1));
+    CHECK(secp256k1_fe_is_zero(&infj1.x));
+    CHECK(secp256k1_fe_is_zero(&infj1.y));
+    CHECK(secp256k1_fe_is_zero(&infj1.z));
+
+    secp256k1_gej_add_ge_var(&infj2, &npj, &p, NULL);
+    CHECK(secp256k1_gej_is_infinity(&infj2));
+    CHECK(secp256k1_fe_is_zero(&infj2.x));
+    CHECK(secp256k1_fe_is_zero(&infj2.y));
+    CHECK(secp256k1_fe_is_zero(&infj2.z));
+
+    secp256k1_fe_set_int(&zinv, 1);
+    secp256k1_gej_add_zinv_var(&infj3, &npj, &p, &zinv);
+    CHECK(secp256k1_gej_is_infinity(&infj3));
+    CHECK(secp256k1_fe_is_zero(&infj3.x));
+    CHECK(secp256k1_fe_is_zero(&infj3.y));
+    CHECK(secp256k1_fe_is_zero(&infj3.z));
+
+
+}
+
 void test_add_neg_y_diff_x(void) {
     /* The point of this test is to check that we can add two points
      * whose y-coordinates are negatives of each other but whose x
@@ -2380,6 +2413,7 @@ void run_ge(void) {
         test_ge();
     }
     test_add_neg_y_diff_x();
+    test_intialized_inf();
 }
 
 void test_ec_combine(void) {