diff --git a/benchmarks/bench_finite_fields.nim b/benchmarks/bench_fields_template.nim
similarity index 74%
rename from benchmarks/bench_finite_fields.nim
rename to benchmarks/bench_fields_template.nim
index d670c93..eac7944 100644
--- a/benchmarks/bench_finite_fields.nim
+++ b/benchmarks/bench_fields_template.nim
@@ -18,25 +18,16 @@ import
   ../constantine/arithmetic,
   ../constantine/io/[io_bigints, io_fields],
   ../constantine/primitives,
+  ../constantine/tower_field_extensions/[abelian_groups, fp2_complex, fp6_1_plus_i],
   # Helpers
   ../helpers/[timers, prng, static_for],
   # Standard library
   std/[monotimes, times, strformat, strutils, macros]
 
-const Iters = 1_000_000
-const InvIters = 1000
-const AvailableCurves = [
-  P224,
-  BN254,
-  P256,
-  Secp256k1,
-  BLS12_381
-]
-
 var rng: RngState
 let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
 rng.seed(seed)
-echo "bench_finite_field xoshiro512** seed: ", seed
+echo "bench xoshiro512** seed: ", seed
 
 # warmup
 proc warmup*() =
@@ -82,9 +73,6 @@ macro fixFieldDisplay(T: typedesc): untyped =
   name.add "[" & $Curve(instantiated[1][1].intVal) & "]"
   result = newLit name
 
-# Compilers are smart with dead code (but not with multiprecision arithmetic :/)
-var globalsAreNotOptimizedAway: Word
-
 template bench(op: string, T: typedesc, iters: int, body: untyped): untyped =
   let start = getMonotime()
   let startClk = getTicks()
@@ -95,63 +83,43 @@ template bench(op: string, T: typedesc, iters: int, body: untyped): untyped =
 
   report(op, fixFieldDisplay(T), start, stop, startClk, stopClk, iters)
 
-proc addBench(T: typedesc) =
+proc addBench*(T: typedesc, iters: int) =
   var x = rng.random(T)
   let y = rng.random(T)
-  bench("Addition", T, Iters):
+  bench("Addition", T, iters):
     x += y
-  globalsAreNotOptimizedAway += x.mres.limbs[^1]
 
-proc subBench(T: typedesc) =
+proc subBench*(T: typedesc, iters: int) =
   var x = rng.random(T)
   let y = rng.random(T)
   preventOptimAway(x)
-  bench("Substraction", T, Iters):
+  bench("Substraction", T, iters):
     x -= y
-  globalsAreNotOptimizedAway += x.mres.limbs[^1]
 
-proc negBench(T: typedesc) =
+proc negBench*(T: typedesc, iters: int) =
   var r: T
   let x = rng.random(T)
-  bench("Negation", T, Iters):
+  bench("Negation", T, iters):
     r.neg(x)
-  globalsAreNotOptimizedAway += r.mres.limbs[^1]
 
-proc mulBench(T: typedesc) =
+proc mulBench*(T: typedesc, iters: int) =
   var r: T
   let x = rng.random(T)
   let y = rng.random(T)
   preventOptimAway(r)
-  bench("Multiplication", T, Iters):
+  bench("Multiplication", T, iters):
     r.prod(x, y)
 
-proc sqrBench(T: typedesc) =
+proc sqrBench*(T: typedesc, iters: int) =
   var r: T
   let x = rng.random(T)
   preventOptimAway(r)
-  bench("Squaring", T, Iters):
+  bench("Squaring", T, iters):
     r.square(x)
 
-proc invBench(T: typedesc) =
+proc invBench*(T: typedesc, iters: int) =
   var r: T
   let x = rng.random(T)
   preventOptimAway(r)
-  bench("Inversion", T, InvIters):
+  bench("Inversion", T, iters):
     r.inv(x)
-
-proc main() =
-  echo "-".repeat(80)
-  staticFor i, 0, AvailableCurves.len:
-    const curve = AvailableCurves[i]
-    addBench(Fp[curve])
-    subBench(Fp[curve])
-    negBench(Fp[curve])
-    mulBench(Fp[curve])
-    sqrBench(Fp[curve])
-    invBench(Fp[curve])
-    echo "-".repeat(80)
-
-main()
-
-echo "Notes:"
-echo "  GCC is significantly slower than Clang on multiprecision arithmetic."
diff --git a/benchmarks/bench_fp.nim b/benchmarks/bench_fp.nim
new file mode 100644
index 0000000..f8d7a60
--- /dev/null
+++ b/benchmarks/bench_fp.nim
@@ -0,0 +1,51 @@
+# 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
+  # Internals
+  ../constantine/config/curves,
+  # Helpers
+  ../helpers/static_for,
+  ./bench_fields_template,
+  # Standard library
+  std/strutils
+
+# ############################################################
+#
+#                  Benchmark of 𝔽p
+#
+# ############################################################
+
+
+const Iters = 1_000_000
+const InvIters = 1000
+const AvailableCurves = [
+  P224,
+  BN254,
+  P256,
+  Secp256k1,
+  BLS12_381
+]
+
+proc main() =
+  echo "-".repeat(80)
+  staticFor i, 0, AvailableCurves.len:
+    const curve = AvailableCurves[i]
+    addBench(Fp[curve], Iters)
+    subBench(Fp[curve], Iters)
+    negBench(Fp[curve], Iters)
+    mulBench(Fp[curve], Iters)
+    sqrBench(Fp[curve], Iters)
+    invBench(Fp[curve], InvIters)
+    echo "-".repeat(80)
+
+main()
+
+echo "Notes:"
+echo "  GCC is significantly slower than Clang on multiprecision arithmetic."
+echo "  The simplest operations might be optimized away by the compiler."
diff --git a/benchmarks/bench_fp2.nim b/benchmarks/bench_fp2.nim
new file mode 100644
index 0000000..71796b6
--- /dev/null
+++ b/benchmarks/bench_fp2.nim
@@ -0,0 +1,48 @@
+# 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
+  # Internals
+  ../constantine/config/curves,
+  ../constantine/tower_field_extensions/[abelian_groups, fp2_complex],
+  # Helpers
+  ../helpers/static_for,
+  ./bench_fields_template,
+  # Standard library
+  std/strutils
+
+# ############################################################
+#
+#               Benchmark of 𝔽p2 = 𝔽p[𝑖]
+#
+# ############################################################
+
+
+const Iters = 1_000_000
+const InvIters = 1000
+const AvailableCurves = [
+  BN254,
+  BLS12_381
+]
+
+proc main() =
+  echo "-".repeat(80)
+  staticFor i, 0, AvailableCurves.len:
+    const curve = AvailableCurves[i]
+    addBench(Fp2[curve], Iters)
+    subBench(Fp2[curve], Iters)
+    negBench(Fp2[curve], Iters)
+    mulBench(Fp2[curve], Iters)
+    sqrBench(Fp2[curve], Iters)
+    invBench(Fp2[curve], InvIters)
+    echo "-".repeat(80)
+
+main()
+
+echo "Notes:"
+echo "  GCC is significantly slower than Clang on multiprecision arithmetic."
diff --git a/benchmarks/bench_fp6.nim b/benchmarks/bench_fp6.nim
new file mode 100644
index 0000000..633b74c
--- /dev/null
+++ b/benchmarks/bench_fp6.nim
@@ -0,0 +1,48 @@
+# 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
+  # Internals
+  ../constantine/config/curves,
+  ../constantine/tower_field_extensions/[abelian_groups, fp6_1_plus_i],
+  # Helpers
+  ../helpers/static_for,
+  ./bench_fields_template,
+  # Standard library
+  std/strutils
+
+# ############################################################
+#
+#               Benchmark of 𝔽p2 = 𝔽p[𝑖]
+#
+# ############################################################
+
+
+const Iters = 1_000_000
+const InvIters = 1000
+const AvailableCurves = [
+  BN254,
+  BLS12_381
+]
+
+proc main() =
+  echo "-".repeat(80)
+  staticFor i, 0, AvailableCurves.len:
+    const curve = AvailableCurves[i]
+    # addBench(Fp6[curve], Iters)
+    # subBench(Fp6[curve], Iters)
+    # negBench(Fp6[curve], Iters)
+    # mulBench(Fp6[curve], Iters)
+    sqrBench(Fp6[curve], Iters)
+    # invBench(Fp6[curve], InvIters)
+    echo "-".repeat(80)
+
+main()
+
+echo "Notes:"
+echo "  GCC is significantly slower than Clang on multiprecision arithmetic."
diff --git a/constantine.nimble b/constantine.nimble
index 83267e7..f4f35e5 100644
--- a/constantine.nimble
+++ b/constantine.nimble
@@ -111,17 +111,40 @@ task test_no_gmp, "Run tests that don't require GMP":
     # 𝔽p2
     test "", "tests/test_fp2.nim"
 
-task bench, "Run benchmark with your default compiler":
+proc runBench(benchName: string, compiler = "") =
   if not dirExists "build":
     mkDir "build"
-  exec "nim c -d:danger --verbosity:0 -o:build/bench_finite_fields_default -r --hints:off --warnings:off benchmarks/bench_finite_fields"
 
-task bench_gcc, "Run benchmark with gcc":
-  if not dirExists "build":
-    mkDir "build"
-  exec "nim c --cc:gcc -d:danger --verbosity:0 -o:build/bench_finite_fields_gcc -r --hints:off --warnings:off benchmarks/bench_finite_fields"
+  var cc = ""
+  if compiler != "":
+    cc = "--cc:" & compiler
+  exec "nim c " & cc &
+       " -d:danger --verbosity:0 -o:build/" & benchName & "_" & compiler &
+       " -r --hints:off --warnings:off benchmarks/" & benchName & ".nim"
 
-task bench_clang, "Run benchmark with clang":
-  if not dirExists "build":
-    mkDir "build"
-  exec "nim c --cc:clang -d:danger --verbosity:0 -o:build/bench_finite_fields_clang -r --hints:off --warnings:off benchmarks/bench_finite_fields"
+task bench_fp, "Run benchmark 𝔽p with your default compiler":
+  runBench("bench_fp")
+
+task bench_fp_gcc, "Run benchmark 𝔽p with gcc":
+  runBench("bench_fp", "gcc")
+
+task bench_fp_clang, "Run benchmark 𝔽p with clang":
+  runBench("bench_fp", "clang")
+
+task bench_fp2, "Run benchmark with 𝔽p2 your default compiler":
+  runBench("bench_fp2")
+
+task bench_fp2_gcc, "Run benchmark 𝔽p2 with gcc":
+  runBench("bench_fp2", "gcc")
+
+task bench_fp2_clang, "Run benchmark 𝔽p2 with clang":
+  runBench("bench_fp2", "clang")
+
+task bench_fp6, "Run benchmark with 𝔽p6 your default compiler":
+  runBench("bench_fp6")
+
+task bench_fp6_gcc, "Run benchmark 𝔽p6 with gcc":
+  runBench("bench_fp6", "gcc")
+
+task bench_fp6_clang, "Run benchmark 𝔽p6 with clang":
+  runBench("bench_fp6", "clang")
diff --git a/constantine/arithmetic/finite_fields_inversion.nim b/constantine/arithmetic/finite_fields_inversion.nim
index d6f2004..feafb5e 100644
--- a/constantine/arithmetic/finite_fields_inversion.nim
+++ b/constantine/arithmetic/finite_fields_inversion.nim
@@ -8,6 +8,7 @@
 
 import
   ../config/[common, curves],
+  ./bigints,
   ./finite_fields
 
 # ############################################################