Secp256k1

symbolic-base/src/ZkFold/Base/Algebra/EllipticCurve/BLS12_381.hs

@@ -67,18 +67,18 @@ instance EllipticCurve BLS12_381_G1 where
 
     type BaseField BLS12_381_G1 = Fq
 
-    gen = point
+    pointGen = pointXY
         0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb
         0x8b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1
 
     add = addPoints
 
     mul = pointMul
 
-instance StandardEllipticCurve BLS12_381_G1 where
-    aParameter = zero
+instance WeierstrassCurve BLS12_381_G1 where
+    weierstrassA = zero
 
-    bParameter = fromConstant (4 :: Natural)
+    weierstrassB = fromConstant (4 :: Natural)
 
 ------------------------------------ BLS12-381 G2 ------------------------------------
 
@@ -91,7 +91,7 @@ instance EllipticCurve BLS12_381_G2 where
 
     type BaseField BLS12_381_G2 = Fq2
 
-    gen = point
+    pointGen = pointXY
         (Ext2
             0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8
             0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e)
@@ -103,10 +103,10 @@ instance EllipticCurve BLS12_381_G2 where
 
     mul = pointMul
 
-instance StandardEllipticCurve BLS12_381_G2 where
-    aParameter = zero
+instance WeierstrassCurve BLS12_381_G2 where
+    weierstrassA = zero
 
-    bParameter = fromConstant (4 :: Natural)
+    weierstrassB = fromConstant (4 :: Natural)
 
 ------------------------------------ Encoding ------------------------------------
 
@@ -143,7 +143,7 @@ instance Binary (Point BLS12_381_G1) where
             infinite = testBit byte 1
         if infinite then do
             skip (if compressed then 47 else 95)
-            return inf
+            return pointInf
         else do
             let byteXhead = bitReverse8 $ clearBit (clearBit (clearBit byte 0) 1) 2
             bytesXtail <- replicateM 47 getWord8
@@ -153,10 +153,10 @@ instance Binary (Point BLS12_381_G1) where
             else do
                 bytesY <- replicateM 48 getWord8
                 let y = ofBytes bytesY
-                return (point x y)
+                return (pointXY x y)
 
-instance Binary (PointCompressed BLS12_381_G1) where
-    put (PointCompressed x bigY isInf) =
+instance Binary (CompressedPoint BLS12_381_G1) where
+    put (CompressedPoint x bigY isInf) =
         if isInf then foldMap putWord8 (bitReverse8 (bit 0 .|. bit 1) : replicate 47 0) else
         let
             flags = bitReverse8 $ if bigY then bit 0 .|. bit 2 else bit 0
@@ -168,7 +168,7 @@ instance Binary (PointCompressed BLS12_381_G1) where
             infinite = testBit byte 1
         if infinite then do
             skip (if compressed then 47 else 95)
-            return inf
+            return pointInf
         else do
             let byteXhead = bitReverse8 $ clearBit (clearBit (clearBit byte 0) 1) 2
             bytesXtail <- replicateM 47 getWord8
@@ -197,7 +197,7 @@ instance Binary (Point BLS12_381_G2) where
             infinite = testBit byte 1
         if infinite then do
             skip (if compressed then 95 else 191)
-            return inf
+            return pointInf
         else do
             let byteX1head = bitReverse8 $ clearBit (clearBit (clearBit byte 0) 1) 2
             bytesX1tail <- replicateM 47 getWord8
@@ -211,10 +211,10 @@ instance Binary (Point BLS12_381_G2) where
                 bytesY0 <- replicateM 48 getWord8
                 let y0 = ofBytes bytesY0
                     y1 = ofBytes bytesY1
-                return (point (Ext2 x0 x1) (Ext2 y0 y1))
+                return (pointXY (Ext2 x0 x1) (Ext2 y0 y1))
 
-instance Binary (PointCompressed BLS12_381_G2) where
-    put (PointCompressed (Ext2 x0 x1) bigY isInf) =
+instance Binary (CompressedPoint BLS12_381_G2) where
+    put (CompressedPoint (Ext2 x0 x1) bigY isInf) =
         if isInf then foldMap putWord8 (bitReverse8 (bit 0 .|. bit 1) : replicate 95 0) else
         let
             flags = bitReverse8 $ if bigY then bit 0 .|. bit 2 else bit 0
@@ -227,7 +227,7 @@ instance Binary (PointCompressed BLS12_381_G2) where
             infinite = testBit byte 1
         if infinite then do
             skip (if compressed then 95 else 191)
-            return inf
+            return pointInf
         else do
             let byteX1head = bitReverse8 $ clearBit (clearBit (clearBit byte 0) 1) 2
             bytesX1tail <- replicateM 47 getWord8

symbolic-base/src/ZkFold/Base/Algebra/EllipticCurve/BN254.hs

@@ -70,13 +70,13 @@ data BN254_G1
 instance EllipticCurve BN254_G1 where
   type ScalarField BN254_G1 = Fr
   type BaseField BN254_G1 = Fp
-  gen = point 1 2
+  pointGen = pointXY 1 2
   add = addPoints
   mul = pointMul
 
-instance StandardEllipticCurve BN254_G1 where
-  aParameter = 0
-  bParameter = 3
+instance WeierstrassCurve BN254_G1 where
+  weierstrassA = 0
+  weierstrassB = 3
 
 ------------------------------- bn254 G2 ---------------------------------------
 
@@ -85,17 +85,17 @@ data BN254_G2
 instance EllipticCurve BN254_G2 where
   type ScalarField BN254_G2 = Fr
   type BaseField BN254_G2 = Fp2
-  gen = point
+  pointGen = pointXY
     (Ext2 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed
           0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2)
     (Ext2 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa
           0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b)
   add = addPoints
   mul = pointMul
 
-instance StandardEllipticCurve BN254_G2 where
-  aParameter = zero
-  bParameter =
+instance WeierstrassCurve BN254_G2 where
+  weierstrassA = zero
+  weierstrassB =
     Ext2 0x2b149d40ceb8aaae81be18991be06ac3b5b4c5e559dbefa33267e6dc24a138e5
          0x9713b03af0fed4cd2cafadeed8fdf4a74fa084e52d1852e4a2bd0685c315d2
 
@@ -133,22 +133,22 @@ instance Pairing BN254_G1 BN254_G2 where
 
 instance Binary (Point BN254_G1) where
   put (Point xp yp isInf) =
-    if isInf then put @(Point BN254_G1) (point zero zero) else put xp >> put yp
+    if isInf then put @(Point BN254_G1) (pointXY zero zero) else put xp >> put yp
   get = do
     xp <- get
     yp <- get
     return $
       if xp == zero && yp == zero
-      then inf
-      else point xp yp
+      then pointInf
+      else pointXY xp yp
 
 instance Binary (Point BN254_G2) where
   put (Point xp yp isInf) =
-    if isInf then put @(Point BN254_G2) (point zero zero) else put xp >> put yp
+    if isInf then put @(Point BN254_G2) (pointXY zero zero) else put xp >> put yp
   get = do
     xp <- get
     yp <- get
     return $
       if xp == zero && yp == zero
-      then inf
-      else point xp yp
+      then pointInf
+      else pointXY xp yp

symbolic-base/src/ZkFold/Base/Algebra/EllipticCurve/Class.hs

@@ -58,31 +58,31 @@ instance
   ) => SymbolicData (Point curve)
 
 class Planar field plane where
-  point :: field -> field -> plane
+  pointXY :: field -> field -> plane
 
 instance
   ( field ~ BaseField curve
   , bool ~ BooleanOf curve
   , BoolType bool
   ) => Planar field (Point curve) where
-  point x y = Point x y false
+  pointXY x y = Point x y false
 
 class ProjectivePlanar plane where
-  inf :: plane
+  pointInf :: plane
 
 instance
   ( field ~ BaseField curve
   , BoolType (BooleanOf curve)
   , AdditiveMonoid field
   ) => ProjectivePlanar (Point curve) where
-  inf = Point zero zero true
+  pointInf = Point zero zero true
 
 instance
   ( field ~ BaseField curve
   , BoolType (BooleanOf curve)
   , AdditiveMonoid field
-  ) => ProjectivePlanar (PointCompressed curve) where
-  inf = PointCompressed zero false true
+  ) => ProjectivePlanar (CompressedPoint curve) where
+  pointInf = CompressedPoint zero false true
 
 class
     ( BoolType (BooleanOf curve)
@@ -98,7 +98,7 @@ class
     type BooleanOf curve :: Type
     type BooleanOf curve = P.Bool
 
-    gen :: Point curve
+    pointGen :: Point curve
 
     add :: Point curve -> Point curve -> Point curve
 
@@ -127,7 +127,7 @@ instance EllipticCurve curve => Scale Natural (Point curve) where
     scale = natScale
 
 instance EllipticCurve curve => AdditiveMonoid (Point curve) where
-    zero = inf
+    zero = pointInf
 
 instance (EllipticCurve curve, AdditiveGroup (BaseField curve)) => Scale Integer (Point curve) where
     scale = intScale
@@ -136,7 +136,7 @@ instance (EllipticCurve curve, AdditiveGroup (BaseField curve)) => AdditiveGroup
     negate = pointNegate
 
 instance (EllipticCurve curve, Arbitrary (ScalarField curve)) => Arbitrary (Point curve) where
-    arbitrary = arbitrary <&> (`mul` gen)
+    arbitrary = arbitrary <&> (`mul` pointGen)
 
 class (EllipticCurve curve1, EllipticCurve curve2, ScalarField curve1 ~ ScalarField curve2,
         P.Eq (TargetGroup curve1 curve2), MultiplicativeGroup (TargetGroup curve1 curve2),
@@ -153,8 +153,8 @@ pointAdd
 pointAdd p@(Point x1 y1 isInf1) q@(Point x2 y2 isInf2) =
   if isInf2 then p
   else if isInf1 then q
-  else if x1 == x2 then inf
-  else point x3 y3
+  else if x1 == x2 then pointInf
+  else pointXY x3 y3
   where
     slope  = (y1 - y2) // (x1 - x2)
     x3 = slope * slope - x1 - x2
@@ -164,7 +164,7 @@ pointDouble
     :: EllipticCurve curve
     => Field (BaseField curve)
     => Point curve -> Point curve
-pointDouble (Point x y isInf) = if isInf then inf else point x' y'
+pointDouble (Point x y isInf) = if isInf then pointInf else pointXY x' y'
   where
     slope = (x * x + x * x + x * x) // (y + y)
     x' = slope * slope - x - x
@@ -182,7 +182,7 @@ pointNegate
     :: EllipticCurve curve
     => AdditiveGroup (BaseField curve)
     => Point curve -> Point curve
-pointNegate (Point x y isInf) = if isInf then inf else point x (negate y)
+pointNegate (Point x y isInf) = if isInf then pointInf else pointXY x (negate y)
 
 pointMul
     :: forall curve s
@@ -196,76 +196,76 @@ pointMul
 pointMul = natScale . fromBinary . castBits . binaryExpansion
 
 -- An elliptic curve in standard form, y^2 = x^3 + a * x + b
-class EllipticCurve curve => StandardEllipticCurve curve where
-    aParameter :: BaseField curve
-    bParameter :: BaseField curve
-
-data PointCompressed curve = PointCompressed
-  { _x    :: BaseField curve
-  , _bigY :: BooleanOf curve
-  , _inf  :: BooleanOf curve
+class EllipticCurve curve => WeierstrassCurve curve where
+  weierstrassA :: BaseField curve
+  weierstrassB :: BaseField curve
+
+data CompressedPoint curve = CompressedPoint
+  { _x     :: BaseField curve
+  , _bigY  :: BooleanOf curve
+  , _isInf :: BooleanOf curve
   } deriving Generic
 
-pointCompressed :: BoolType (BooleanOf curve) => BaseField curve -> BooleanOf curve -> PointCompressed curve
-pointCompressed x bigY = PointCompressed x bigY false
+pointCompressed :: BoolType (BooleanOf curve) => BaseField curve -> BooleanOf curve -> CompressedPoint curve
+pointCompressed x bigY = CompressedPoint x bigY false
 
 instance
   ( EllipticCurve curve
   , bool ~ BooleanOf curve
-  ) => Conditional bool (PointCompressed curve)
+  ) => Conditional bool (CompressedPoint curve)
 
 instance
   ( EllipticCurve curve
   , bool ~ BooleanOf curve
-  ) => Eq bool (PointCompressed curve)
+  ) => Eq bool (CompressedPoint curve)
 
 instance
   ( EllipticCurve curve
   , BooleanOf curve ~ P.Bool
-  ) => P.Eq (PointCompressed curve) where
+  ) => P.Eq (CompressedPoint curve) where
   (==) = (==)
   (/=) = (/=)
 
 instance
   ( Show (BaseField curve)
   , Conditional (BooleanOf curve) P.String
   , Show (BooleanOf curve)
-  ) => Show (PointCompressed curve) where
-    show (PointCompressed x bigY isInf) =
+  ) => Show (CompressedPoint curve) where
+    show (CompressedPoint x bigY isInf) =
       if isInf then "InfCompressed" else "(" ++ show x ++ ", " ++ show bigY ++ ")"
 
 instance
   ( EllipticCurve curve
   , AdditiveGroup (BaseField curve)
   , Ord (BooleanOf curve) (BaseField curve)
   , Arbitrary (ScalarField curve)
-  ) => Arbitrary (PointCompressed curve) where
+  ) => Arbitrary (CompressedPoint curve) where
     arbitrary = compress <$> arbitrary
 
 compress
   :: ( AdditiveGroup (BaseField curve)
      , EllipticCurve curve
      , Ord (BooleanOf curve) (BaseField curve)
      )
-  => Point curve -> PointCompressed curve
+  => Point curve -> CompressedPoint curve
 compress = \case
-  Point x y isInf -> if isInf then inf else PointCompressed x (y > negate y) false
+  Point x y isInf -> if isInf then pointInf else CompressedPoint x (y > negate y) false
 
 decompress
   :: forall curve .
-     ( StandardEllipticCurve curve
+     ( WeierstrassCurve curve
      , FiniteField (BaseField curve)
      , Ord (BooleanOf curve) (BaseField curve)
      )
-  => PointCompressed curve -> Point curve
-decompress (PointCompressed x bigY isInf) =
-  if isInf then inf else
-    let a = aParameter @curve
-        b = bParameter @curve
+  => CompressedPoint curve -> Point curve
+decompress (CompressedPoint x bigY isInf) =
+  if isInf then pointInf else
+    let a = weierstrassA @curve
+        b = weierstrassB @curve
         p = order @(BaseField curve)
         sqrt_ z = z ^ ((p + 1) `P.div` 2)
         y' = sqrt_ (x * x * x + a * x + b)
         y'' = negate y'
         y = if bigY then max @(BooleanOf curve) y' y'' else min @(BooleanOf curve) y' y''
     in
-        point x y
+        pointXY x y