Introduce Fr type: finite field over curve order. Need workaround for n…

…im-lang/Nim#16774

constantine/arithmetic/finite_fields.nim

@@ -26,7 +26,7 @@
 
 import
   ../primitives,
-  ../config/[common, type_fp, curves],
+  ../config/[common, type_fp, type_fr, curves],
   ./bigints, ./limbs_montgomery
 
 when UseASM_X86_64:
@@ -37,7 +37,7 @@ when nimvm:
 else:
   discard
 
-export Fp
+export Fp, Fr
 
 # No exceptions allowed
 {.push raises: [].}

constantine/config/curves.nim

@@ -32,6 +32,7 @@ template getCurveBitwidth*(C: Curve): int =
   CurveBitWidth[C]
 
 template matchingBigInt*(C: static Curve): untyped =
+  # Workaround: https://github.com/nim-lang/Nim/issues/16774
   BigInt[CurveBitWidth[C]]
 
 template family*(C: Curve): CurveFamily =
@@ -60,6 +61,10 @@ macro getCurveOrderBitwidth*(C: static Curve): untyped =
     ident"bits"
   )
 
+template matchingOrderBigInt*(C: static Curve): untyped =
+  # Workaround: https://github.com/nim-lang/Nim/issues/16774
+  BigInt[CurveOrderBitWidth[C]]
+
 macro getEquationForm*(C: static Curve): untyped =
   ## Returns the equation form
   ## (ShortWeierstrass, Montgomery, Twisted Edwards, Weierstrass, ...)

constantine/config/curves_parser.nim

@@ -237,8 +237,12 @@ template getCoef(c: CurveCoef, width: NimNode): untyped {.dirty.}=
 proc genMainConstants(defs: var seq[CurveParams]): NimNode =
   ## Generate curves and fields main constants
 
+  # MapCurveBitWidth & MapCurveOrderBitWidth
+  # are workaround for https://github.com/nim-lang/Nim/issues/16774
+
   var Curves: seq[NimNode]
   var MapCurveBitWidth = nnkBracket.newTree()
+  var MapCurveOrderBitWidth = nnkBracket.newTree()
   var MapCurveFamily = nnkBracket.newTree()
   var curveModStmts = newStmtList()
   var curveEllipticStmts = newStmtList()
@@ -290,6 +294,14 @@ proc genMainConstants(defs: var seq[CurveParams]): NimNode =
           curveDef.order
         )
       )
+      MapCurveOrderBitWidth.add nnkExprColonExpr.newTree(
+        curve, curveDef.orderBitwidth
+      )
+    else: # Dummy
+      MapCurveOrderBitWidth.add nnkExprColonExpr.newTree(
+        curve, newLit 0
+      )
+
     if curveDef.coef_A.kind != NoCoef and curveDef.coef_B.kind != NoCoef:
       curveEllipticStmts.add newConstStmt(
         exported($curve & "_coef_A"),
@@ -347,6 +359,10 @@ proc genMainConstants(defs: var seq[CurveParams]): NimNode =
   result.add newConstStmt(
     exported("CurveFamilies"), MapCurveFamily
   )
+  # const CurveOrderBitSize: array[Curve, int] = ...
+  result.add newConstStmt(
+    exported("CurveOrderBitWidth"), MapCurveOrderBitWidth
+  )
 
   result.add curveModStmts
   result.add curveEllipticStmts

constantine/config/type_fp.nim

@@ -12,7 +12,7 @@ import
 
 type
   Fp*[C: static Curve] = object
-    ## All operations on a field are modulo P
+    ## All operations on a Fp field are modulo P
     ## P being the prime modulus of the Curve C
     ## Internally, data is stored in Montgomery n-residue form
     ## with the magic constant chosen for convenient division (a power of 2 depending on P bitsize)

constantine/config/type_fr.nim

@@ -0,0 +1,28 @@
+# 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
+  ./common,
+  ./curves_declaration
+
+type
+  Fr*[C: static Curve] = object
+    ## All operations on a field are modulo `r`
+    ## `r` being the prime curve order or subgroup order
+    ## Internally, data is stored in Montgomery n-residue form
+    ## with the magic constant chosen for convenient division (a power of 2 depending on P bitsize)
+    mres: matchingOrderBigInt(C)
+
+debug:
+  import ./type_bigint
+
+  func `$`*[C: static Curve](a: Fr[C]): string =
+    result = "Fr[" & $C
+    result.add "]("
+    result.add $a.mres
+    result.add ')'

tests/t_fr.nim

@@ -0,0 +1,14 @@
+# 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  std/unittest,
+        ../constantine/arithmetic,
+        ../constantine/io/io_fields,
+        ../constantine/config/curves
+
+var x: Fr[BLS12_381]