Add modular addition over Fp

constantine/bigints.nim

@@ -5,8 +5,13 @@
 #   * 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.
 
-# Big int internal representation.
+
+# ############################################################
 #
+#                    BigInt representation
+#
+# ############################################################
+
 # To avoid carry issues we don't use the
 # most significant bit of each word.
 # i.e. for a uint64 base we only use 63-bit.
@@ -16,6 +21,10 @@
 #    - https://cryptojedi.org/peter/data/pairing-20131122.pdf
 #    - http://docs.milagro.io/en/amcl/milagro-crypto-library-white-paper.html
 #
+# Note that this might also be beneficial in terms of performance.
+# Due to opcode latency, on Nehalem ADC is 6x times slower than ADD
+# if it has dependencies (i.e the ADC depends on a previous ADC result)
+
 # Control flow should only depends on the static maximum number of bits
 # This number is defined per Finite Field/Prime/Elliptic Curve
 #
@@ -58,8 +67,11 @@ const highLimb* = (not Ct[uint64](0)) shr 1
 # if it is a placebo operation. It stills performs the
 # same memory accesses to be side-channel attack resistant
 
-# For efficiency we define templates and will create functions
-# specialized for runtime and compile-time inputs
+# For efficiency we can define templates and will create functions
+# specialised for runtime and compile-time inputs.
+#
+# We don't specialise for the control word, any optimizing compiler
+# will keep it in registers.
 
 template addImpl[bits](result: CTBool[Limb], a: var BigInt[bits], b: BigInt[bits], ctl: CTBool[Limb]) =
   ## Constant-time big integer in-place addition

constantine/field_arith.nim

@@ -1,8 +0,0 @@
-# Constantine
-# Copyright (c) 2018 Status Research & Development GmbH
-# 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.
-
-

constantine/field_fp.nim

@@ -0,0 +1,60 @@
+# Constantine
+# Copyright (c) 2018 Status Research & Development GmbH
+# 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.
+
+# ############################################################
+#
+#                 Field arithmetic over Fp
+#
+# ############################################################
+
+# We assume that p is prime known at compile-time
+
+import
+  ./word_types, ./bigints
+
+type
+  Fp[P: static BigInt] = object
+    ## P is a prime number
+    ## All operations on a field are modulo P
+    value: type(P)
+
+# ############################################################
+#
+#                         Aliases
+#
+# ############################################################
+
+const
+  True = ctrue(Limb)
+  False = cfalse(Limb)
+
+template add(a: var Fp, b: Fp, ctl: CTBool[Limb]): CTBool[Limb] =
+  add(a.value, b.value, ctl)
+
+template sub(a: var Fp, b: Fp, ctl: CTBool[Limb]): CTBool[Limb] =
+  sub(a.value, b.value, ctl)
+
+# ############################################################
+#
+#                Field arithmetic primitives
+#
+# ############################################################
+
+func `+`*(a, b: Fp): Fp =
+  ## Addition over Fp
+
+  # Non-CT implementation from Stint
+  #
+  # let b_from_p = p - b    # Don't do a + b directly to avoid overflows
+  # if a >= b_from_p:
+  #   return a - b_from_p
+  # return m - b_from_p + a
+
+  result = a
+  var ctl = add(result, b, True)
+  ctl = ctl or not sub(result, Fp.P, False)
+  sub(result, Fp.P, ctl)

constantine/word_types.nim

@@ -15,11 +15,11 @@ type
     ## by conditional branches, we don't use booleans.
     ## We use an int to prevent compiler "optimization" and introduction of branches
 
-func ctrue*(T: type(BaseUint)): auto {.inline.}=
-  (CTBool[Ct[T]])(true)
+func ctrue*(T: type(Ct)): auto {.inline.}=
+  (CTBool[T])(true)
 
-func cfalse*(T: type(BaseUint)): auto {.inline.}=
-  (CTBool[Ct[T]])(false)
+func cfalse*(T: type(Ct)): auto {.inline.}=
+  (CTBool[T])(false)
 
 func ct*[T: BaseUint](x: T): Ct[T] {.inline.}=
   (Ct[T])(x)
@@ -103,6 +103,9 @@ func `not`*(ctl: CTBool): CTBool {.inline.}=
   ## Negate a constant-time boolean
   (type result)(ctl.undistinct xor (type ctl.undistinct)(1))
 
+func `and`*(x, y: CTBool): CTBool {.magic: "BitandI".}
+func `or`*(x, y: CTBool): CTBool {.magic: "BitorI".}
+
 template mux*[T: Ct](ctl: CTBool[T], x, y: T): T =
   ## Multiplexer / selector
   ## Returns x if ctl == 1