diff --git a/constantine/arithmetic/assembly/limbs_asm_montred_x86_adx_bmi2.nim b/constantine/arithmetic/assembly/limbs_asm_montred_x86_adx_bmi2.nim
index f2ac174..eb2cb18 100644
--- a/constantine/arithmetic/assembly/limbs_asm_montred_x86_adx_bmi2.nim
+++ b/constantine/arithmetic/assembly/limbs_asm_montred_x86_adx_bmi2.nim
@@ -20,8 +20,6 @@ import
 #
 # ############################################################
 
-# TODO, MCL has an implementation about 14% faster
-
 static: doAssert UseASM_X86_64
 
 # MULX/ADCX/ADOX
@@ -140,6 +138,17 @@ macro montyRedc2x_adx_gen*[N: static int](
   # Code generation
   result.add ctx.generate()
 
+func montRed_asm_adx_bmi2_impl*[N: static int](
+       r: var array[N, SecretWord],
+       a: array[N*2, SecretWord],
+       M: array[N, SecretWord],
+       m0ninv: BaseType,
+       hasSpareBit: static bool
+      ) =
+  ## Constant-time Montgomery reduction
+  ## Inline-version
+  montyRedc2x_adx_gen(r, a, M, m0ninv, hasSpareBit)
+
 func montRed_asm_adx_bmi2*[N: static int](
        r: var array[N, SecretWord],
        a: array[N*2, SecretWord],
@@ -148,4 +157,4 @@ func montRed_asm_adx_bmi2*[N: static int](
        hasSpareBit: static bool
       ) =
   ## Constant-time Montgomery reduction
-  montyRedc2x_adx_gen(r, a, M, m0ninv, hasSpareBit)
+  montRed_asm_adx_bmi2_impl(r, a, M, m0ninv, hasSpareBit)
diff --git a/constantine/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim b/constantine/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim
index 3a7fde1..844a38c 100644
--- a/constantine/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim
+++ b/constantine/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim
@@ -168,11 +168,18 @@ macro mulx_gen[rLen, aLen, bLen: static int](rx: var Limbs[rLen], ax: Limbs[aLen
   # Codegen
   result.add ctx.generate
 
-func mul_asm_adx_bmi2*[rLen, aLen, bLen: static int](r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen]) =
+func mul_asm_adx_bmi2_impl*[rLen, aLen, bLen: static int](
+       r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen]) {.inline.} =
   ## Multi-precision Multiplication
   ## Assumes r doesn't alias a or b
+  ## Inline version
   mulx_gen(r, a, b)
 
+func mul_asm_adx_bmi2*[rLen, aLen, bLen: static int](
+       r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen]) =
+  ## Multi-precision Multiplication
+  ## Assumes r doesn't alias a or b
+  mul_asm_adx_bmi2_impl(r, a, b)
 
 # Squaring
 # -----------------------------------------------------------------------------------------------
diff --git a/constantine/tower_field_extensions/assembly/fp2_asm_x86_adx_bmi2.nim b/constantine/tower_field_extensions/assembly/fp2_asm_x86_adx_bmi2.nim
new file mode 100644
index 0000000..3a1c7d7
--- /dev/null
+++ b/constantine/tower_field_extensions/assembly/fp2_asm_x86_adx_bmi2.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
+  # Internal
+  ../../config/[common, curves],
+  ../../primitives,
+  ../../arithmetic,
+  ../../arithmetic/assembly/[
+    limbs_asm_mul_x86_adx_bmi2,
+    limbs_asm_montmul_x86_adx_bmi2,
+    limbs_asm_montred_x86_adx_bmi2
+  ]
+
+
+# ############################################################
+#                                                            #
+#             Assembly implementation of 𝔽p2                 #
+#                                                            #
+# ############################################################
+
+static: doAssert UseASM_X86_64
+
+# MULX/ADCX/ADOX
+{.localPassC:"-madx -mbmi2".}
+# Necessary for the compiler to find enough registers (enabled at -O1)
+{.localPassC:"-fomit-frame-pointer".}
+
+# No exceptions allowed
+{.push raises: [].}
+
+template c0*(a: array): auto =
+  a[0]
+template c1*(a: array): auto =
+  a[1]
+
+func has1extraBit(F: type Fp): bool =
+  ## We construct extensions only on Fp (and not Fr)
+  getSpareBits(F) >= 1
+
+func has2extraBits(F: type Fp): bool =
+  ## We construct extensions only on Fp (and not Fr)
+  getSpareBits(F) >= 2
+
+# 𝔽p2 squaring
+# ------------------------------------------------------------
+
+func sqrx2x_complex_asm_adx_bmi2*(
+        r: var array[2, FpDbl],
+        a: array[2, Fp]
+      ) =
+  ## Complex squaring on 𝔽p2
+  # This specialized proc inlines all calls and avoids many ADX support checks.
+  # and push/pop for paramater passing.
+
+  var t0 {.noInit.}, t1 {.noInit.}: typeof(a.c0)
+
+  when Fp.has1extraBit():
+    t0.sumUnr(a.c1, a.c1)
+    t1.sumUnr(a.c0, a.c1)
+  else:
+    t0.double(a.c1)
+    t1.sum(a.c0, a.c1)
+
+  r.c1.mul_asm_adx_bmi2_impl(t0, a.c0)
+  t0.diff(a.c0, a.c1)
+  r.c0.mul_asm_adx_bmi2_impl(t0, t1)
+
+func sqrx_complex_asm_adx_bmi2*(
+        r: var array[2, Fp],
+        a: array[2, Fp]
+      ) =
+  ## Complex squaring on 𝔽p2
+  # This specialized proc inlines all calls and avoids many ADX support checks.
+  # and push/pop for paramater passing.
+  # Staying in 𝔽p and not using double-precision is faster for squaring
+
+  static: doAssert Fp.has1extraBit()
+
+  var v0 {.noInit.}, v1 {.noInit.}: typeof(r.c0)
+  v0.diff(a.c0, a.c1)
+  v1.sum(a.c0, a.c1)
+  r.c1.mres.limbs.montMul_CIOS_nocarry_asm_adx_bmi2(a.c0.mres.limbs, a.c1.mres.limbs, Fp.fieldMod().limbs, Fp.getNegInvModWord())
+  # aliasing: a unneeded now
+  r.c1.double()
+  r.c0.mres.limbs.montMul_CIOS_nocarry_asm_adx_bmi2(v0.mres.limbs, v1.mres.limbs, Fp.fieldMod().limbs, Fp.getNegInvModWord())
+
+# 𝔽p2 multiplication
+# ------------------------------------------------------------
+
+func mulx2x_complex_asm_adx_bmi2*(
+        r: var array[2, FpDbl],
+        a, b: array[2, Fp]
+      ) =
+  ## Complex multiplication on 𝔽p2
+  var D {.noInit.}: typeof(r.c0)
+  var t0 {.noInit.}, t1 {.noInit.}: typeof(a.c0)
+
+  r.c0.limbs2x.mul_asm_adx_bmi2_impl(a.c0.mres.limbs, b.c0.mres.limbs)
+  D.limbs2x.mul_asm_adx_bmi2_impl(a.c1.mres.limbs, b.c1.mres.limbs)
+  when Fp.has1extraBit():
+    t0.sumUnr(a.c0, a.c1)
+    t1.sumUnr(b.c0, b.c1)
+  else:
+    t0.sum(a.c0, a.c1)
+    t1.sum(b.c0, b.c1)
+  r.c1.limbs2x.mul_asm_adx_bmi2_impl(t0.mres.limbs, t1.mres.limbs)
+  when Fp.has1extraBit():
+    r.c1.diff2xUnr(r.c1, r.c0)
+    r.c1.diff2xUnr(r.c1, D)
+  else:
+    r.c1.diff2xMod(r.c1, r.c0)
+    r.c1.diff2xMod(r.c1, D)
+  r.c0.diff2xMod(r.c0, D)
+
+func mulx_complex_asm_adx_bmi2*(
+        r: var array[2, Fp],
+        a, b: array[2, Fp]
+      ) =
+  ## Complex multiplication on 𝔽p2
+  var d {.noInit.}: array[2,doublePrec(Fp)]
+  d.mulx2x_complex_asm_adx_bmi2(a, b)
+  r.c0.mres.limbs.montRed_asm_adx_bmi2_impl(
+    d.c0.limbs2x,
+    Fp.fieldMod().limbs,
+    Fp.getNegInvModWord(),
+    Fp.has1extraBit()
+  )
+  r.c1.mres.limbs.montRed_asm_adx_bmi2_impl(
+    d.c1.limbs2x,
+    Fp.fieldMod().limbs,
+    Fp.getNegInvModWord(),
+    Fp.has1extraBit()
+  )
diff --git a/constantine/tower_field_extensions/extension_fields.nim b/constantine/tower_field_extensions/extension_fields.nim
index c20ec65..4c64198 100644
--- a/constantine/tower_field_extensions/extension_fields.nim
+++ b/constantine/tower_field_extensions/extension_fields.nim
@@ -12,6 +12,10 @@ import
   ../arithmetic,
   ../io/io_fields
 
+when UseASM_X86_64:
+  import
+    ./assembly/fp2_asm_x86_adx_bmi2
+
 # Note: to avoid burdening the Nim compiler, we rely on generic extension
 # to complain if the base field procedures don't exist
 
@@ -807,8 +811,8 @@ func prod2x_complex(r: var QuadraticExt2x, a, b: Fp2) =
     t1.sum(b.c0, b.c1)
   r.c1.prod2x(t0, t1)            # r1 = (b0 + b1)(a0 + a1)
   when Fp2.has1extraBit():
-    r.c1.diff2xUnr(r.c1, r.c0) # r1 = (b0 + b1)(a0 + a1) - a0 b0
-    r.c1.diff2xUnr(r.c1, D)    # r1 = (b0 + b1)(a0 + a1) - a0 b0 - a1b1
+    r.c1.diff2xUnr(r.c1, r.c0)   # r1 = (b0 + b1)(a0 + a1) - a0 b0
+    r.c1.diff2xUnr(r.c1, D)      # r1 = (b0 + b1)(a0 + a1) - a0 b0 - a1b1
   else:
     r.c1.diff2xMod(r.c1, r.c0)
     r.c1.diff2xMod(r.c1, D)
@@ -1227,7 +1231,13 @@ func square2x*(r: var QuadraticExt2x, a: QuadraticExt) =
 func square*(r: var QuadraticExt, a: QuadraticExt) =
   when r.fromComplexExtension():
     when true:
-      r.square_complex(a)
+      when UseASM_X86_64 and a.c0.mres.limbs.len <= 6:
+        if ({.noSideEffect.}: hasAdx()):
+          r.coords.sqrx_complex_asm_adx_bmi2(a.coords)
+        else:
+          r.square_complex(a)
+      else:
+        r.square_complex(a)
     else: # slower
       var d {.noInit.}: doublePrec(typeof(r))
       d.square2x_complex(a)
@@ -1259,10 +1269,19 @@ func prod*(r: var QuadraticExt, a, b: QuadraticExt) =
     when false:
       r.prod_complex(a, b)
     else: # faster
-      var d {.noInit.}: doublePrec(typeof(r))
-      d.prod2x_complex(a, b)
-      r.c0.redc2x(d.c0)
-      r.c1.redc2x(d.c1)
+      when UseASM_X86_64 and a.c0.mres.limbs.len <= 6:
+        if ({.noSideEffect.}: hasAdx()):
+          r.coords.mulx_complex_asm_adx_bmi2(a.coords, b.coords)
+        else:
+          var d {.noInit.}: doublePrec(typeof(r))
+          d.prod2x_complex(a, b)
+          r.c0.redc2x(d.c0)
+          r.c1.redc2x(d.c1)
+      else:
+        var d {.noInit.}: doublePrec(typeof(r))
+        d.prod2x_complex(a, b)
+        r.c0.redc2x(d.c0)
+        r.c1.redc2x(d.c1)
   else:
     when r.typeof.F.C == BW6_761 or typeof(r.c0) is Fp:
       # BW6-761 requires too many registers for Dbl width path
@@ -1287,7 +1306,13 @@ func prod2x_disjoint*[Fdbl, F](
 func prod2x*(r: var QuadraticExt2x, a, b: QuadraticExt) =
   ## Double-precision multiplication r <- a*b
   when a.fromComplexExtension():
-    r.prod2x_complex(a, b)
+    when UseASM_X86_64 and a.c0.mres.limbs.len <= 6:
+      if ({.noSideEffect.}: hasAdx()):
+        r.coords.mulx2x_complex_asm_adx_bmi2(a.coords, b.coords)
+      else:
+        r.prod2x_complex(a, b)
+    else:
+      r.prod2x_complex(a, b)
   else:
     r.prod2x_disjoint(a.c0, a.c1, b.c0, b.c1)