diff --git a/src/crypto/crypto-sugar.h b/src/crypto/crypto-sugar.h
index 600fe914..0e48e949 100644
--- a/src/crypto/crypto-sugar.h
+++ b/src/crypto/crypto-sugar.h
@@ -497,7 +497,7 @@ namespace crypto
       zero();
     }
 
-    // as we're using additive notation, zero means identity group element here and after
+    // as we're using additive notation, zero means identity group element (EC point (0, 1)) here and after
     void zero()
     {
       ge_p3_0(&m_p3);
@@ -506,7 +506,11 @@ namespace crypto
     bool is_zero() const
     {
       // (0, 1) ~ (0, z, z, 0)
-      return fe_isnonzero(m_p3.X) * fe_cmp(m_p3.Y, m_p3.Z) == 0;
+      if (fe_isnonzero(m_p3.X) != 0)
+        return false;
+      fe y_minus_z;
+      fe_sub(y_minus_z, m_p3.Y, m_p3.Z);
+      return fe_isnonzero(y_minus_z) == 0;
     }
 
     bool is_in_main_subgroup() const
@@ -669,6 +673,11 @@ namespace crypto
       return true;
     };
 
+    friend bool operator!=(const point_t& lhs, const point_t& rhs)
+    {
+      return !(lhs == rhs);
+    };
+
     friend std::ostream& operator<<(std::ostream& ss, const point_t &v)
     {
       crypto::public_key pk = v.to_public_key();