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data FieldElement =
FieldElement
{ number :: Int
, prime :: Int
}
deriving (Eq)
instance Show FieldElement where
show a = "FieldElement_" ++ show (prime a) ++ " " ++ show (number a)
instance Num FieldElement where
(FieldElement a b) + (FieldElement c d)
| b /= d = error "Distinct Fields"
| otherwise = FieldElement (mod (a + c) b) b
(FieldElement a b) * (FieldElement c d)
| b /= d = error "Distinct Fields"
| otherwise = FieldElement (mod (a * c) b) b
abs a = a
signum _ = 1
negate (FieldElement a b) = FieldElement (mod (b - a) b) b
fromInteger _ = error "can't transform"
instance Fractional FieldElement where
recip a = a ^ (prime a - 2)
fromRational _ = error "can't transform"
assert :: Bool -> Bool
assert False = error "WRONG"
assert x = x
aa =
let a = FieldElement 2 31
b = FieldElement 15 31
in assert
(and
[ a + b == FieldElement 17 31
, a /= b
, a - b == FieldElement 18 31
])
bb =
let a = FieldElement 19 31
b = FieldElement 24 31
in a * b
data ECPoint
= Infinity
| ECPoint
{ x :: Double
, y :: Double
, a :: Double
, b :: Double
}
deriving (Eq)
instance Show ECPoint where
show Infinity = "ECPoint(Infinity)"
show p =
"ECPoint(" ++
show (x p) ++ ", " ++ show (y p) ++ ")_" ++ show (a p) ++ "_" ++ show (b p)
validECPoint :: ECPoint -> Bool
validECPoint Infinity = True
validECPoint p = y p ^ 2 == x p ^ 3 + a p * x p + b p
add :: ECPoint -> ECPoint -> ECPoint
add Infinity p = p
add p Infinity = p
add p q
| a p /= a q || b p /= b q = error "point not on same curve"
| x p == x q && y p /= y q = Infinity
| x p /= x q = new_point $ (y q - y p) / (x q - x p)
| x p == x q && y p == 0 = Infinity
| p == q = new_point $ (3 * x p ^ 2 + a p) / (2 * y p)
| otherwise = error "Unexpected case of points"
where
new_point slope =
let new_x = slope ^ 2 - x p - x q
new_y = slope * (x p - new_x) - y p
in ECPoint new_x new_y (a p) (b p)
cc =
let a = ECPoint 3 (-7) 5 7
b = ECPoint 18 77 5 7
c = ECPoint (-1) (-1) 5 7
in ( validECPoint a
, validECPoint b
, validECPoint c
, a /= b
, a == a
, add Infinity a
, add a (ECPoint 3 7 5 7)
, add (ECPoint 3 7 5 7) c
, add c c)
|
