diff --git a/constantine/tower_field_extensions/fp12_quad_fp6.nim b/constantine/tower_field_extensions/fp12_quad_fp6.nim
index 4ca4856..169ad53 100644
--- a/constantine/tower_field_extensions/fp12_quad_fp6.nim
+++ b/constantine/tower_field_extensions/fp12_quad_fp6.nim
@@ -59,6 +59,7 @@ func `*`(_: typedesc[Gamma], a: Fp6): Fp6 {.noInit, inline.} =
   ## Conveniently γ = v with v the factor in for 𝔽p6 coordinate
   ## and v³ = ξ
   ## (c0 + c1 v + c2 v²) v => ξ c2 + c0 v + c1 v²
+  discard
 
   result.c0 = a.c2 * Xi
   result.c1 = a.c0
@@ -70,7 +71,7 @@ template `*`(a: Fp6, _: typedesc[Gamma]): Fp6 =
 func `*=`(a: var Fp6, _: typedesc[Gamma]) {.inline.} =
   a = Gamma * a
 
-func square*(r: var Fp12, a: Fp12) =
+func square*[C](r: var Fp12[C], a: Fp12[C]) =
   ## Return a² in ``r``
   ## ``r`` is initialized/overwritten
   # (c0, c1)² => (c0 + c1 w)²
@@ -91,17 +92,17 @@ func square*(r: var Fp12, a: Fp12) =
   # Alternative 2:
   #   c0² + γ c1² <=> (c0 + c1)(c0 + γ c1) - γ c0c1 - c0c1
 
-  # r0 <- (c0 - c1)(c0 - γ c1)
-  r.c0.diff(a.c0, a.c1)
-  r.c1.diff(a.c0, Gamma * a.c1)
-  r.c0.prod(r.c0, r.c1)
+  # r0 <- (c0 + c1)(c0 + γ c1)
+  r.c0.sum(a.c0, a.c1)
+  r.c1.sum(a.c0, Gamma * a.c1)
+  r.c0 *= r.c1
 
   # r1 <- c0 c1
   r.c1.prod(a.c0, a.c1)
 
-  # r0 = (c0 - c1)(c0 - γ c1) + γ c0c1 + c0c1
-  r.c0 += Gamma * r.c1
-  r.c0 += r.c1
+  # r0 = (c0 + c1)(c0 + γ c1) - γ c0c1 - c0c1
+  r.c0 -= Gamma * r.c1
+  r.c0 -= r.c1
 
   # r1 = 2 c0c1
   r.c1.double()
diff --git a/constantine/tower_field_extensions/fp6_1_plus_i.nim b/constantine/tower_field_extensions/fp6_1_plus_i.nim
index 0c35e4c..d00434e 100644
--- a/constantine/tower_field_extensions/fp6_1_plus_i.nim
+++ b/constantine/tower_field_extensions/fp6_1_plus_i.nim
@@ -90,6 +90,8 @@ func square*[C](r: var Fp6[C], a: Fp6[C]) =
 
 func prod*[C](r: var Fp6[C], a, b: Fp6[C]) =
   ## Returns r = a * b
+  ##
+  ## r MUST not share a buffer with a
   # Algorithm is Karatsuba
   var v0{.noInit.}, v1{.noInit.}, v2{.noInit.}, t{.noInit.}: Fp2[C]
 
@@ -174,3 +176,11 @@ func inv*[C](r: var Fp6[C], a: Fp6[C]) =
   r.c0 *= v3
   r.c1.prod(v1, v3)
   r.c2.prod(v2, v3)
+
+func `*=`*(a: var Fp6, b: Fp6) {.inline.} =
+  var t: Fp6
+  t.prod(a, b)
+  a = t
+
+func `*`*(a, b: Fp6): Fp6 {.inline.} =
+  result.prod(a, b)
diff --git a/tests/test_fp12.nim b/tests/test_fp12.nim
index dad6aa6..54b2264 100644
--- a/tests/test_fp12.nim
+++ b/tests/test_fp12.nim
@@ -86,13 +86,13 @@ suite "𝔽p12 = 𝔽p6[√∛(1+𝑖)]":
 
         testInstance()
 
-    # test(BN254)
-    # test(BLS12_377)
-    # test(BLS12_381)
-    # test(BN446)
-    # test(FKM12_447)
-    # test(BLS12_461)
-    # test(BN462)
+    test(BN254)
+    test(BLS12_377)
+    test(BLS12_381)
+    test(BN446)
+    test(FKM12_447)
+    test(BLS12_461)
+    test(BN462)
 
   test "Squaring 3 returns 9":
     template test(C: static Curve) =
@@ -124,13 +124,13 @@ suite "𝔽p12 = 𝔽p6[√∛(1+𝑖)]":
 
         testInstance()
 
-    # test(BN254)
-    # test(BLS12_377)
-    # test(BLS12_381)
-    # test(BN446)
-    # test(FKM12_447)
-    # test(BLS12_461)
-    # test(BN462)
+    test(BN254)
+    test(BLS12_377)
+    test(BLS12_381)
+    test(BN446)
+    test(FKM12_447)
+    test(BLS12_461)
+    test(BN462)
 
   test "Squaring -3 returns 9":
     template test(C: static Curve) =
@@ -162,10 +162,10 @@ suite "𝔽p12 = 𝔽p6[√∛(1+𝑖)]":
 
         testInstance()
 
-    # test(BN254)
-    # test(BLS12_377)
-    # test(BLS12_381)
-    # test(BN446)
-    # test(FKM12_447)
-    # test(BLS12_461)
-    # test(BN462)
+    test(BN254)
+    test(BLS12_377)
+    test(BLS12_381)
+    test(BN446)
+    test(FKM12_447)
+    test(BLS12_461)
+    test(BN462)