diff --git a/constantine/config/curves.nim b/constantine/config/curves.nim
index e4ea71c..6a1424e 100644
--- a/constantine/config/curves.nim
+++ b/constantine/config/curves.nim
@@ -55,6 +55,9 @@ when not defined(testingCurves):
     curve P256: # secp256r1 / NIST P-256
       bitsize: 256
       modulus: "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
+    curve Secp256k1: # Bitcoin curve
+      bitsize: 256
+      modulus: "0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F"
 else:
   # Fake curve for testing field arithmetic
   declareCurves:
diff --git a/tests/test_fp2.nim b/tests/test_fp2.nim
index a0fb799..3f7f703 100644
--- a/tests/test_fp2.nim
+++ b/tests/test_fp2.nim
@@ -8,7 +8,7 @@
 
 import
   # Standard library
-  unittest, times,
+  unittest, times, random,
   # Internals
   ../constantine/tower_field_extensions/[abelian_groups, fp2_complex],
   ../constantine/config/[common, curves],
@@ -16,8 +16,114 @@ import
   # Test utilities
   ./prng
 
+const Iters = 1
 
 var rng: RngState
 let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
 rng.seed(seed)
 echo "test_fp2 xoshiro512** seed: ", seed
+
+# Import: wrap in field element tests in small procedures
+#         otherwise they will become globals,
+#         and will create binary size issues.
+#         Also due to Nim stack scanning,
+#         having too many elements on the stack (a couple kB)
+#         will significantly slow down testing (100x is possible)
+
+suite "𝔽p2 = 𝔽p[𝑖] (irreducible polynomial x²+1)":
+  test "Squaring 1 returns 1":
+    template test(C: static Curve) =
+      block:
+        proc testInstance() =
+          let One {.inject.} = block:
+            var O{.noInit.}: Fp2[C]
+            O.setOne()
+            O
+          block:
+            var r{.noinit.}: Fp2[C]
+            r.square(One)
+            check: bool(r == One)
+          block:
+            var r{.noinit.}: Fp2[C]
+            r.prod(One, One)
+            check: bool(r == One)
+
+        testInstance()
+
+    test(BN254)
+    test(BLS12_381)
+    test(P256)
+    test(Secp256k1)
+
+  test "Multiplication by 0 and 1":
+    template test(C: static Curve, body: untyped) =
+      block:
+        proc testInstance() =
+          let Zero {.inject.} = block:
+            var Z{.noInit.}: Fp2[C]
+            Z.setZero()
+            Z
+          let One {.inject.} = block:
+            var O{.noInit.}: Fp2[C]
+            O.setOne()
+            O
+
+          for i in 0 ..< Iters:
+            let x {.inject.} = rng.random(Fp2[C])
+            var r{.noinit, inject.}: Fp2[C]
+            body
+
+        testInstance()
+
+    test(BN254):
+      r.prod(x, Zero)
+      check: bool(r == Zero)
+    test(BN254):
+      r.prod(Zero, x)
+      check: bool(r == Zero)
+    # test(BN254):
+    #   r.prod(x, One)
+    #   echo "r: ", r
+    #   echo "x: ", x
+    #   check: bool(r == x)
+    # test(BN254):
+    #   r.prod(One, x)
+    #   echo "r: ", r
+    #   echo "x: ", x
+    #   check: bool(r == x)
+    test(BLS12_381):
+      r.prod(x, Zero)
+      check: bool(r == Zero)
+    test(BLS12_381):
+      r.prod(Zero, x)
+      check: bool(r == Zero)
+    # test(BLS12_381):
+    #   r.prod(x, One)
+    #   check: bool(r == x)
+    # test(BLS12_381):
+    #   r.prod(One, x)
+    #   check: bool(r == x)
+    test(P256):
+      r.prod(x, Zero)
+      check: bool(r == Zero)
+    test(P256):
+      r.prod(Zero, x)
+      check: bool(r == Zero)
+    # test(P256):
+    #   r.prod(x, One)
+    #   check: bool(r == x)
+    # test(P256):
+    #   r.prod(One, x)
+    #   check: bool(r == x)
+    test(Secp256k1):
+      r.prod(x, Zero)
+      check: bool(r == Zero)
+    test(Secp256k1):
+      r.prod(Zero, x)
+      check: bool(r == Zero)
+    # test(Secp256k1):
+    #   r.prod(x, One)
+    #   check: bool(r == x)
+    # test(Secp256k1):
+    #   r.prod(One, x)
+    #   check: bool(r == x)