diff --git a/tests/test_bigints.nim b/tests/test_bigints.nim
index 9010d1d..af3240d 100644
--- a/tests/test_bigints.nim
+++ b/tests/test_bigints.nim
@@ -441,21 +441,36 @@ proc mainModularInverse() =
 
       check: bool(r == expected)
 
-    test "0^-1 (mod 0) = 0 (need for tower of extension fields)":
-      let a = BigInt[16].fromUint(0'u16)
-      let M = BigInt[16].fromUint(2017'u16)
+    test "0^-1 (mod any) = 0 (need for tower of extension fields)":
+      block:
+        let a = BigInt[16].fromUint(0'u16)
+        let M = BigInt[16].fromUint(2017'u16)
 
-      var mp1div2 = M
-      mp1div2.shiftRight(1)
-      discard mp1div2.add(Word 1)
+        var mp1div2 = M
+        mp1div2.shiftRight(1)
+        discard mp1div2.add(Word 1)
 
-      let expected = BigInt[16].fromUint(0'u16)
-      var r {.noInit.}: BigInt[16]
+        let expected = BigInt[16].fromUint(0'u16)
+        var r {.noInit.}: BigInt[16]
 
-      r.invmod(a, M, mp1div2)
+        r.invmod(a, M, mp1div2)
 
-      check: bool(r == expected)
+        check: bool(r == expected)
 
+      block:
+        let a = BigInt[381].fromUint(0'u16)
+        let M = BigInt[381].fromHex("0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab")
+
+        var mp1div2 = M
+        mp1div2.shiftRight(1)
+        discard mp1div2.add(Word 1)
+
+        let expected = BigInt[381].fromUint(0'u16)
+        var r {.noInit.}: BigInt[381]
+
+        r.invmod(a, M, mp1div2)
+
+        check: bool(r == expected)
 
 mainArith()
 mainNeg()
diff --git a/tests/test_finite_fields_powinv.nim b/tests/test_finite_fields_powinv.nim
index 7e966b5..79dce00 100644
--- a/tests/test_finite_fields_powinv.nim
+++ b/tests/test_finite_fields_powinv.nim
@@ -153,18 +153,31 @@ proc main() =
           computed == expected
 
   suite "Modular inversion over prime fields":
-    test "Specific test on Fp[BLS12_381]":
-      var r, x: Fp[BLS12_381]
+    test "Specific tests on Fp[BLS12_381]":
+      block: # No inverse exist for 0 --> should return 0 for projective/jacobian to affine coordinate conversion
+        var r, x: Fp[BLS12_381]
+        x.setZero()
+        r.inv(x)
+        check: bool r.isZero()
 
-      # BN254 field modulus
-      x.fromHex("0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47")
+      block:
+        var r, x: Fp[BLS12_381]
+        x.setOne()
+        r.inv(x)
+        check: bool r.isOne()
 
-      let expected = "0x0636759a0f3034fa47174b2c0334902f11e9915b7bd89c6a2b3082b109abbc9837da17201f6d8286fe6203caa1b9d4c8"
-      r.inv(x)
-      let computed = r.toHex()
+      block:
+        var r, x: Fp[BLS12_381]
 
-      check:
-        computed == expected
+        # BN254 field modulus
+        x.fromHex("0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47")
+
+        let expected = "0x0636759a0f3034fa47174b2c0334902f11e9915b7bd89c6a2b3082b109abbc9837da17201f6d8286fe6203caa1b9d4c8"
+        r.inv(x)
+        let computed = r.toHex()
+
+        check:
+          computed == expected
 
     test "Specific tests on Fp[BN254_Snarks]":
       block: