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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) =
let slope = ((y q) - (y p)) / ((x q) - (x p))
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)
| (x p) == (x q) && (y p) == 0 = Infinity
| p == q =
let slope = (3 * (x p) ^ 2 + (a p)) / (2 * (y p))
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)
| otherwise = error "Unexpected case of points"
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)
|
