diff --git a/constantine/arithmetic/bigints_checked.nim b/constantine/arithmetic/bigints_checked.nim
index 2880789..1f5339c 100644
--- a/constantine/arithmetic/bigints_checked.nim
+++ b/constantine/arithmetic/bigints_checked.nim
@@ -113,24 +113,77 @@ func setOne*(a: var BigInt) =
   when a.limbs.len > 1:
     zeroMem(a.limbs[1].unsafeAddr, (a.limbs.len-1) * sizeof(Word))
 
-func cadd*[bits](a: var BigInt[bits], b: BigInt[bits], ctl: CTBool[Word]): CTBool[Word] =
+func cadd*(a: var BigInt, b: BigInt, ctl: CTBool[Word]): CTBool[Word] =
   ## Constant-time in-place conditional addition
   ## The addition is only performed if ctl is "true"
   ## The result carry is always computed.
   cadd(a.view, b.view, ctl)
 
-func csub*[bits](a: var BigInt[bits], b: BigInt[bits], ctl: CTBool[Word]): CTBool[Word] =
+func csub*(a: var BigInt, b: BigInt, ctl: CTBool[Word]): CTBool[Word] =
   ## Constant-time in-place conditional addition
   ## The addition is only performed if ctl is "true"
   ## The result carry is always computed.
   csub(a.view, b.view, ctl)
 
-func cdouble*[bits](a: var BigInt[bits], ctl: CTBool[Word]): CTBool[Word] =
+func cdouble*(a: var BigInt, ctl: CTBool[Word]): CTBool[Word] =
   ## Constant-time in-place conditional doubling
   ## The doubling is only performed if ctl is "true"
   ## The result carry is always computed.
   cadd(a.view, a.view, ctl)
 
+# ############################################################
+#
+#          BigInt Primitives Optimized for speed
+#
+# ############################################################
+#
+# TODO: fallback to cadd / csub with a "size" compile-option
+
+func add*(a: var BigInt, b: BigInt): CTBool[Word] =
+  ## Constant-time in-place addition
+  ## Returns the carry
+  add(a.view, b.view)
+
+func sub*(a: var BigInt, b: BigInt): CTBool[Word] =
+  ## Constant-time in-place substraction
+  ## Returns the borrow
+  sub(a.view, b.view)
+
+func double*(a: var BigInt): CTBool[Word] =
+  ## Constant-time in-place doubling
+  ## Returns the carry
+  add(a.view, a.view)
+
+func sum*(r: var BigInt, a, b: BigInt): CTBool[Word] =
+  ## Sum `a` and `b` into `r`.
+  ## `r` is initialized/overwritten
+  ##
+  ## Returns the carry
+  sum(r.view, a.view, b.view)
+
+func diff*(r: var BigInt, a, b: BigInt): CTBool[Word] =
+  ## Substract `b` from `a` and store the result into `r`.
+  ## `r` is initialized/overwritten
+  ##
+  ## Returns the borrow
+  diff(r.view, a.view, b.view)
+
+# ############################################################
+#
+#                    Comparisons
+#
+# ############################################################
+
+# Use "csub", which unfortunately requires the first operand to be mutable.
+# for example for a <= b, we now that if a-b borrows then b > a and so a<=b is false
+# This can be tested with "not csub(a, b, CtFalse)"
+
+# ############################################################
+#
+#                   Modular BigInt
+#
+# ############################################################
+
 func reduce*[aBits, mBits](r: var BigInt[mBits], a: BigInt[aBits], M: BigInt[mBits]) =
   ## Reduce `a` modulo `M` and store the result in `r`
   ##
@@ -143,7 +196,7 @@ func reduce*[aBits, mBits](r: var BigInt[mBits], a: BigInt[aBits], M: BigInt[mBi
   # pass a pointer+length to a fixed session of the BSS.
   reduce(r.view, a.view, M.view)
 
-func montyResidue*[mBits](mres: var BigInt[mBits], a, N, r2modN: BigInt[mBits], negInvModWord: static BaseType) =
+func montyResidue*(mres: var BigInt, a, N, r2modN: BigInt, negInvModWord: static BaseType) =
   ## Convert a BigInt from its natural representation
   ## to the Montgomery n-residue form
   ##
@@ -168,14 +221,20 @@ func redc*[mBits](r: var BigInt[mBits], a, N: BigInt[mBits], negInvModWord: stat
     one
   redc(r.view, a.view, one.view, N.view, Word(negInvModWord))
 
-func montyMul*[mBits](r: var BigInt[mBits], a, b, M: BigInt[mBits], negInvModWord: static BaseType) =
+# ############################################################
+#
+#                 Montgomery Arithmetic
+#
+# ############################################################
+
+func montyMul*(r: var BigInt, a, b, M: BigInt, negInvModWord: static BaseType) =
   ## Compute r <- a*b (mod M) in the Montgomery domain
   ##
   ## This resets r to zero before processing. Use {.noInit.}
   ## to avoid duplicating with Nim zero-init policy
   montyMul(r.view, a.view, b.view, M.view, Word(negInvModWord))
 
-func montySquare*[mBits](r: var BigInt[mBits], a, M: BigInt[mBits], negInvModWord: static BaseType) =
+func montySquare*(r: var BigInt, a, M: BigInt, negInvModWord: static BaseType) =
   ## Compute r <- a^2 (mod M) in the Montgomery domain
   ##
   ## This resets r to zero before processing. Use {.noInit.}
diff --git a/constantine/arithmetic/bigints_raw.nim b/constantine/arithmetic/bigints_raw.nim
index ff9a23f..159081d 100644
--- a/constantine/arithmetic/bigints_raw.nim
+++ b/constantine/arithmetic/bigints_raw.nim
@@ -299,6 +299,71 @@ func shiftRight*(a: BigIntViewMut, k: int) =
     a[i] = (a[i] shr k) or mask(a[i+1] shl (WordBitSize - k))
   a[len-1] = a[len-1] shr k
 
+# ############################################################
+#
+#          BigInt Primitives Optimized for speed
+#
+# ############################################################
+#
+# This section implements primitives that improve the speed
+# of common use-cases at the expense of a slight increase in code-size.
+# Where code size is a concern, the high-level API should use
+# copy and/or the conditional operations.
+
+func add*(a: BigIntViewMut, b: BigIntViewAny): CTBool[Word] =
+  ## Constant-time in-place addition
+  ## Returns the carry
+  ##
+  ## a and b MAY be the same buffer
+  ## a and b MUST have the same announced bitlength (i.e. `bits` static parameters)
+  checkMatchingBitlengths(a, b)
+
+  for i in 0 ..< a.numLimbs():
+    a[i] = a[i] + b[i] + Word(result)
+    result = a[i].isMsbSet()
+    a[i] = a[i].mask()
+
+func sub*(a: BigIntViewMut, b: BigIntViewAny): CTBool[Word] =
+  ## Constant-time in-place substraction
+  ## Returns the borrow
+  ##
+  ## a and b MAY be the same buffer
+  ## a and b MUST have the same announced bitlength (i.e. `bits` static parameters)
+  checkMatchingBitlengths(a, b)
+
+  for i in 0 ..< a.numLimbs():
+    a[i] = a[i] - b[i] - Word(result)
+    result = a[i].isMsbSet()
+    a[i] = a[i].mask()
+
+func sum*(r: BigIntViewMut, a, b: BigIntViewAny): CTBool[Word] =
+  ## Sum `a` and `b` into `r`.
+  ## `r` is initialized/overwritten
+  ##
+  ## Returns the carry
+  checkMatchingBitlengths(a, b)
+
+  r.setBitLength(bitSizeof(M))
+
+  for i in 0 ..< a.numLimbs():
+    r[i] = a[i] + b[i] + Word(result)
+    result = a[i].isMsbSet()
+    r[i] = r[i].mask()
+
+func diff*(r: BigIntViewMut, a, b: BigIntViewAny): CTBool[Word] =
+  ## Substract `b` from `a` and store the result into `r`.
+  ## `r` is initialized/overwritten
+  ##
+  ## Returns the borrow
+  checkMatchingBitlengths(a, b)
+
+  r.setBitLength(bitSizeof(M))
+
+  for i in 0 ..< a.numLimbs():
+    r[i] = a[i] - b[i] - Word(result)
+    result = a[i].isMsbSet()
+    r[i] = r[i].mask()
+
 # ############################################################
 #
 #                   Modular BigInt
@@ -550,7 +615,7 @@ func montyResidue*(
 
   montyMul(r, a, r2ModN, N, negInvModWord)
 
-func montySquare(
+func montySquare*(
        r: BigIntViewMut, a: BigIntViewAny,
        M: BigIntViewConst, negInvModWord: Word) {.inline.} =
   ## Compute r <- a^2 (mod M) in the Montgomery domain
@@ -598,13 +663,6 @@ func montySquare(
 #     of the exponent, leaking this to cache attacks
 #   - in contrast BearSSL touches the whole table to
 #     hide the actual selection
-#
-# Directly using the Hamming weight would probably
-# significantly improve pairing-friendly curves as
-# they are chosen for their low Hamming-Weight (see BLS12-381 x factor)
-# --> Expose an exponent-leaky powMod?
-#     If so, create distinct type for leaked bits and BigInt
-#     so that sensitive data use is compiler-checked
 
 func getWindowLen(bufLen: int): uint =
   ## Compute the maximum window size that fits in the scratchspace buffer
diff --git a/constantine/arithmetic/finite_fields.nim b/constantine/arithmetic/finite_fields.nim
index 585fde0..233ebf9 100644
--- a/constantine/arithmetic/finite_fields.nim
+++ b/constantine/arithmetic/finite_fields.nim
@@ -75,30 +75,6 @@ func toBig*(src: Fp): auto {.noInit.} =
   r.redc(src.mres, Fp.C.Mod.mres, Fp.C.getNegInvModWord())
   return r
 
-# ############################################################
-#
-#                         Aliases
-#
-# ############################################################
-
-template cadd(a: var Fp, b: Fp, ctl: CTBool[Word]): CTBool[Word] =
-  ## Constant-time in-place conditional addition
-  ## The addition is only performed if ctl is "true"
-  ## The result carry is always computed.
-  ##
-  ## a and b MAY be the same buffer
-  ## a and b MUST have the same announced bitlength (i.e. `bits` static parameters)
-  cadd(a.mres, b.mres, ctl)
-
-template csub(a: var Fp, b: Fp, ctl: CTBool[Word]): CTBool[Word] =
-  ## Constant-time in-place conditional substraction
-  ## The substraction is only performed if ctl is "true"
-  ## The result carry is always computed.
-  ##
-  ## a and b MAY be the same buffer
-  ## a and b MUST have the same announced bitlength (i.e. `bits` static parameters)
-  csub(a.mres, b.mres, ctl)
-
 # ############################################################
 #
 #                Field arithmetic primitives
@@ -124,20 +100,20 @@ func setOne*(a: var Fp) =
 
 func `+=`*(a: var Fp, b: Fp) =
   ## Addition modulo p
-  var ctl = cadd(a, b, CtTrue)
-  ctl = ctl or not csub(a, Fp.C.Mod, CtFalse)
-  discard csub(a, Fp.C.Mod, ctl)
+  var overflowed = add(a.mres, b.mres)
+  overflowed = overflowed or not csub(a.mres, Fp.C.Mod.mres, CtFalse) # a >= P
+  discard csub(a.mres, Fp.C.Mod.mres, overflowed)
 
 func `-=`*(a: var Fp, b: Fp) =
   ## Substraction modulo p
-  let ctl = csub(a, b, CtTrue)
-  discard cadd(a, Fp.C.Mod, ctl)
+  let underflowed = sub(a.mres, b.mres)
+  discard cadd(a.mres, Fp.C.Mod.mres, underflowed)
 
 func double*(a: var Fp) =
   ## Double ``a`` modulo p
-  var ctl = cdouble(a, CtTrue)
-  ctl = ctl or not csub(a, Fp.C.Mod, CtFalse)
-  discard csub(a, Fp.C.Mod, ctl)
+  var overflowed = double(a.mres)
+  overflowed = overflowed or not csub(a.mres, Fp.C.Mod.mres, CtFalse) # a >= P
+  discard csub(a.mres, Fp.C.Mod.mres, overflowed)
 
 func `*`*(a, b: Fp): Fp {.noInit.} =
   ## Multiplication modulo p
diff --git a/constantine/arithmetic/precomputed.nim b/constantine/arithmetic/precomputed.nim
index c635f06..47f2537 100644
--- a/constantine/arithmetic/precomputed.nim
+++ b/constantine/arithmetic/precomputed.nim
@@ -34,7 +34,7 @@ func isMsbSet(x: BaseType): bool =
   const msb_pos = BaseType.sizeof * 8 - 1
   bool(x shr msb_pos)
 
-func double(a: var BigInt): bool =
+func dbl(a: var BigInt): bool =
   ## In-place multiprecision double
   ##   a -> 2a
   for i in 0 ..< a.limbs.len:
@@ -61,7 +61,7 @@ func doubleMod(a: var BigInt, M: BigInt) =
   ## It is NOT constant-time and is intended
   ## only for compile-time precomputation
   ## of non-secret data.
-  var ctl = double(a)
+  var ctl = dbl(a)
   ctl = ctl or not sub(a, M, false)
   discard sub(a, M, ctl)