diff --git a/src/crypto/crypto-sugar.h b/src/crypto/crypto-sugar.h
index 6ecdf713..7e0d881f 100644
--- a/src/crypto/crypto-sugar.h
+++ b/src/crypto/crypto-sugar.h
@@ -612,9 +612,13 @@ namespace crypto
 
     bool is_zero() const
     {
-      // (0, 1) ~ (0, z, z, 0)
+      // (0, 1) ~ (0, z, z, 0) for any non-zero z           https://www.rfc-editor.org/rfc/rfc8032#page-17
       if (fe_isnonzero(m_p3.X) != 0)
-        return false;
+        return false; // x != 0
+      if (fe_isnonzero(m_p3.Z) == 0)
+        return false; // z == 0
+      if (fe_isnonzero(m_p3.T) != 0)
+        return false; // t != 0
       fe y_minus_z;
       fe_sub(y_minus_z, m_p3.Y, m_p3.Z);
       return fe_isnonzero(y_minus_z) == 0;
diff --git a/tests/functional_tests/crypto_tests.cpp b/tests/functional_tests/crypto_tests.cpp
index 41ea0a03..efa4aab0 100644
--- a/tests/functional_tests/crypto_tests.cpp
+++ b/tests/functional_tests/crypto_tests.cpp
@@ -1466,6 +1466,37 @@ TEST(crypto, point_is_zero)
 
   ASSERT_TRUE(p.is_zero());
 
+  
+  memset(&p.m_p3, 0, sizeof p.m_p3);
+  memcpy(&p.m_p3.Y, f_x, sizeof p.m_p3.Y);
+  memcpy(&p.m_p3.Z, f_x, sizeof p.m_p3.Z);
+  memcpy(&p.m_p3.T, fancy_p, sizeof p.m_p3.T);
+  // {0, x, x, P} == {0, 1} (still the identity point)
+
+  ASSERT_TRUE(p.is_zero());
+
+  //
+  // negative tests
+  //
+
+  memset(&p.m_p3, 0, sizeof p.m_p3);
+  // {0, 0, 0, 0} is not a point at all
+
+  ASSERT_FALSE(p.is_zero());
+
+
+  memset(&p.m_p3, 0, sizeof p.m_p3);
+  memcpy(&p.m_p3.Y, f_x, sizeof p.m_p3.Y);
+  memcpy(&p.m_p3.Z, f_x, sizeof p.m_p3.Z);
+  memcpy(&p.m_p3.T, fancy_p_plus_1, sizeof p.m_p3.T);
+  // {0, x, x, !0} is not a valid point (incorrect non-zero T) 
+
+  ASSERT_FALSE(p.is_zero());
+
+  memcpy(&p.m_p3.T, f_x, sizeof p.m_p3.T);
+  // {0, x, x, x}, while x != 0 is still incorrect point representation
+  ASSERT_FALSE(p.is_zero());
+
   return true;
 }