From b8741b7680c6d9659a829a72c759e8397534b7c3 Mon Sep 17 00:00:00 2001
From: Óscar Nájera <hi@oscarnajera.com>
Date: Mon, 5 Apr 2021 20:50:34 +0200
Subject: Elliptic Curve on doubles with addition
---
ecc.hs | 54 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 54 insertions(+)
diff --git a/ecc.hs b/ecc.hs
index 282817f..01ef90e 100644
--- a/ecc.hs
+++ b/ecc.hs
@@ -43,3 +43,57 @@ 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)
--
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