diff --git a/constantine/arithmetic/finite_fields.nim b/constantine/arithmetic/finite_fields.nim
index 29585e6..e15675a 100644
--- a/constantine/arithmetic/finite_fields.nim
+++ b/constantine/arithmetic/finite_fields.nim
@@ -91,12 +91,12 @@ func toBig*(src: Fp): auto {.noInit.} =
 
 func setZero*(a: var Fp) =
   ## Set ``a`` to zero
-  a.setZero()
+  a.mres.setZero()
 
 func setOne*(a: var Fp) =
   ## Set ``a`` to one
   # Note: we need 1 in Montgomery residue form
-  a = Fp.C.getMontyOne()
+  a.mres = Fp.C.getMontyOne()
 
 func `+=`*(a: var Fp, b: Fp) =
   ## In-place addition modulo p
diff --git a/constantine/tower_field_extensions/abelian_groups.nim b/constantine/tower_field_extensions/abelian_groups.nim
new file mode 100644
index 0000000..62cb3ac
--- /dev/null
+++ b/constantine/tower_field_extensions/abelian_groups.nim
@@ -0,0 +1,139 @@
+# Constantine
+# Copyright (c) 2018-2019    Status Research & Development GmbH
+# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
+# Licensed and distributed under either of
+#   * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
+#   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
+# at your option. This file may not be copied, modified, or distributed except according to those terms.
+
+import
+  ../config/curves,
+  ../arithmetic/finite_fields
+
+# ############################################################
+#
+#                     Algebraic concepts
+#
+# ############################################################
+# Too heavy on the Nim compiler, we just rely on generic instantiation
+# to complain if the base field procedures don't exist.
+
+# type
+#   AbelianGroup* {.explain.} = concept a, b, var mA, var mR
+#     setZero(mA)
+#     setOne(mA)
+#     `+=`(mA, b)
+#     `-=`(mA, b)
+#     double(mR, a)
+#     sum(mR, a, b)
+#     diff(mR, a, b)
+
+# ############################################################
+#
+#                 Quadratic Extension fields
+#
+# ############################################################
+
+type
+  QuadExtAddGroup*[T] = concept x
+    ## Quadratic extension fields - Abelian Additive Group concept
+    x.c0 is T
+    x.c1 is T
+
+func setZero*(a: var QuadExtAddGroup) =
+  ## Set ``a`` to zero in the extension field
+  ## Coordinates 0 + 0 𝛼
+  ## with 𝛼 the solution of f(x) = x² - µ = 0
+  a.c0.setZero()
+  a.c1.setZero()
+
+func setOne*(a: var QuadExtAddGroup) =
+  ## Set ``a`` to one in the extension field
+  ## Coordinates 1 + 0 𝛼
+  ## with 𝛼 the solution of f(x) = x² - µ = 0
+  a.c0.setOne()
+  a.c1.setZero()
+
+func `+=`*(a: var QuadExtAddGroup, b: QuadExtAddGroup) =
+  ## Addition in the extension field
+  a.c0 += b.c0
+  a.c1 += b.c1
+
+func `-=`*(a: var QuadExtAddGroup, b: QuadExtAddGroup) =
+  ## Substraction in the extension field
+  a.c0 -= b.c0
+  a.c1 -= b.c1
+
+func double*(r: var QuadExtAddGroup, a: QuadExtAddGroup) =
+  ## Double in the extension field
+  r.c0.double(a.c0)
+  r.c1.double(a.c1)
+
+func sum*(r: var QuadExtAddGroup, a, b: QuadExtAddGroup) =
+  ## Sum ``a`` and ``b`` into r
+  r.c0.sum(a.c0, b.c0)
+  r.c1.sum(a.c1, b.c1)
+
+func diff*(r: var QuadExtAddGroup, a, b: QuadExtAddGroup) =
+  ## Difference of ``a`` by `b`` into r
+  r.c0.diff(a.c0, b.c0)
+  r.c1.diff(a.c1, b.c1)
+
+# ############################################################
+#
+#                 Cubic Extension fields
+#
+# ############################################################
+
+type
+  CubicExtAddGroup*[T] = concept x
+    ## Cubic extension fields - Abelian Additive Group concept
+    x.c0 is T
+    x.c1 is T
+    x.c2 is T
+
+func setZero*(a: var CubicExtAddGroup) =
+  ## Set ``a`` to zero in the extension field
+  ## Coordinates 0 + 0 w + 0 w²
+  ## with w the solution of f(x) = x³ - µ = 0
+  a.c0.setZero()
+  a.c1.setZero()
+  a.c2.setZero()
+
+func setOne*(a: var CubicExtAddGroup) =
+  ## Set ``a`` to one in the extension field
+  ## Coordinates 1 + 0 w + 0 w²
+  ## with w the solution of f(x) = x³ - µ = 0
+  a.c0.setOne()
+  a.c1.setZero()
+  a.c2.setZero()
+
+func `+=`*(a: var CubicExtAddGroup, b: CubicExtAddGroup) =
+  ## Addition in the extension field
+  a.c0 += b.c0
+  a.c1 += b.c1
+  a.c2 += b.c2
+
+func `-=`*(a: var CubicExtAddGroup, b: CubicExtAddGroup) =
+  ## Substraction in the extension field
+  a.c0 -= b.c0
+  a.c1 -= b.c1
+  a.c2 -= b.c2
+
+func double*(r: var CubicExtAddGroup, a: CubicExtAddGroup) =
+  ## Double in the extension field
+  r.c0.double(a.c0)
+  r.c1.double(a.c1)
+  r.c2.double(a.c2)
+
+func sum*(r: var CubicExtAddGroup, a, b: CubicExtAddGroup) =
+  ## Sum ``a`` and ``b`` into r
+  r.c0.sum(a.c0, b.c0)
+  r.c1.sum(a.c1, b.c1)
+  r.c2.sum(a.c2, b.c2)
+
+func diff*(r: var CubicExtAddGroup, a, b: CubicExtAddGroup) =
+  ## Difference of ``a`` by `b`` into r
+  r.c0.diff(a.c0, b.c0)
+  r.c1.diff(a.c1, b.c1)
+  r.c2.diff(a.c2, b.c2)
diff --git a/constantine/tower_field_extensions/fp2_complex.nim b/constantine/tower_field_extensions/fp2_complex.nim
index 223aca9..33c9fac 100644
--- a/constantine/tower_field_extensions/fp2_complex.nim
+++ b/constantine/tower_field_extensions/fp2_complex.nim
@@ -43,7 +43,8 @@
 
 import
   ../arithmetic/finite_fields,
-  ../config/curves
+  ../config/curves,
+  ./abelian_groups
 
 type
   Fp2[C: static Curve] = object
@@ -55,29 +56,7 @@ type
     ##
     ## This requires 𝑖² = -1 to not
     ## be a square (mod p)
-    c0, c1: Fp[Curve]
-
-func setZero*(a: var Fp2) =
-  ## Set ``a`` to zero in 𝔽p2
-  ## Coordinates 0 + 0𝑖
-  a.c0.setZero()
-  a.c1.setZero()
-
-func setOne*(a: var Fp2) =
-  ## Set ``a`` to one in 𝔽p2
-  ## Coordinates 1 + 0𝑖
-  a.c0.setOne()
-  a.c1.setZero()
-
-func `+=`*(a: var Fp2, b: Fp2) =
-  ## Addition over 𝔽p2
-  a.c0 += b.c0
-  a.c1 += b.c1
-
-func `-=`*(a: var Fp2, b: Fp2) =
-  ## Substraction over 𝔽p2
-  a.c0 -= b.c0
-  a.c1 -= b.c1
+    c0*, c1*: Fp[C]
 
 func square*(a: Fp2): Fp2 {.noInit.} =
   ## Return a^2 in 𝔽p2