Test demonstrating discrepancy in sqr output

src/field.h

@@ -42,6 +42,10 @@ void static secp256k1_fe_start(void);
 /** Unload field element precomputation data. */
 void static secp256k1_fe_stop(void);
 
+#ifdef VERIFY
+int  static secp256k1_fe_verify(const secp256k1_fe_t * a);
+#endif
+
 /** Normalize a field element. */
 void static secp256k1_fe_normalize(secp256k1_fe_t *r);
 

src/field_5x52_impl.h

@@ -33,6 +33,25 @@
 void static secp256k1_fe_inner_start(void) {}
 void static secp256k1_fe_inner_stop(void) {}
 
+#ifdef VERIFY
+int static secp256k1_fe_verify(const secp256k1_fe_t * a) {
+    const uint64_t *d = a->n;
+    int m = a->magnitude, r = 1;
+    r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
+    if (a->normalized) {
+        r &= (m == 1);
+        if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
+            r &= (d[0] < 0xFFFFEFFFFFC2FULL);
+        }
+    }
+    return r;
+}
+#endif
+
 void static secp256k1_fe_normalize(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];
 

src/tests.c

@@ -312,6 +312,29 @@ void run_field_inv_all_var() {
     }
 }
 
+void run_sqr() {
+    secp256k1_fe_t x, s;
+
+#if defined(USE_FIELD_5X52)
+    // Known issue with reduction part of sqr. For simplicity, we trigger the problem here
+    // with "negative" powers of 2, but the problem exists for large ranges of values.
+    {
+        secp256k1_fe_set_int(&x, 1);
+        secp256k1_fe_negate(&x, &x, 1);
+
+        for (int i=1; i<=512; ++i) {
+            secp256k1_fe_mul_int(&x, 2);
+            secp256k1_fe_normalize(&x);
+            secp256k1_fe_sqr(&s, &x);
+            if (!secp256k1_fe_verify(&s)) {
+                printf("%4i: %016llx %016llx %016llx %016llx %016llx\n",
+                    i, s.n[4], s.n[3], s.n[2], s.n[1], s.n[0]);
+            }
+        }
+    }
+#endif
+}
+
 void test_sqrt(const secp256k1_fe_t *a, const secp256k1_fe_t *k) {
     secp256k1_fe_t r1, r2;
     int v = secp256k1_fe_sqrt(&r1, a);
@@ -609,6 +632,7 @@ int main(int argc, char **argv) {
     run_field_inv_var();
     run_field_inv_all();
     run_field_inv_all_var();
+    run_sqr();
     run_sqrt();
 
     // ecmult tests