Fix point at infinity verification in signature and public key

Sources/starkbank-ecdsa/Curve.swift

@@ -35,7 +35,16 @@ public class CurveFp {
     - Returns: boolean
     */
     func contains(p: Point) -> Bool {
-        return (p.y.power(2) - (p.x.power(3) + self.A * p.x + self.B)) % self.P == 0
+        if (p.x < 0 || p.x >= self.P) {
+            return false
+        }
+        if (p.y < 0 || p.y >= self.P) {
+            return false
+        }
+        if ((p.y.power(2) - (p.x.power(3) + self.A * p.x + self.B)) % self.P != 0) {
+            return false
+        }
+        return true
     }
 
     func length() -> Int {

Sources/starkbank-ecdsa/Ecdsa.swift

@@ -39,8 +39,10 @@ public class Ecdsa {
         let inv = Math.inv(s, curve.N)
         let u1 = Math.multiply(curve.G, (numberMessage * inv).modulus(curve.N), curve.N, curve.A, curve.P)
         let u2 = Math.multiply(publicKey.point, (r * inv).modulus(curve.N), curve.N, curve.A, curve.P)
-        let add = Math.add(u1, u2, curve.A, curve.P)
-        let modX = add.x.modulus(curve.N)
-        return r == modX
+        let v = Math.add(u1, u2, curve.A, curve.P)
+        if (v.isAtInfinity()) {
+            return false
+        }
+        return v.x.modulus(curve.N) == r
     }
 }

Sources/starkbank-ecdsa/Point.swift

@@ -20,4 +20,8 @@ public class Point {
         self.y = y
         self.z = z
     }
+
+    func isAtInfinity() -> Bool {
+        return self.y == BigInt(0)
+    }
 }

Sources/starkbank-ecdsa/PublicKey.swift

@@ -76,13 +76,26 @@ public class PublicKey {
 
         let point = Point(BinaryAscii.intFromHex(xs), BinaryAscii.intFromHex(ys))
 
-        if (validatePoint && !curve.contains(p: point)) {
+        let publicKey = PublicKey(point: point, curve: curve)
+        if (!validatePoint) {
+            return publicKey
+        }
+        if (point.isAtInfinity()) {
+            throw Error.infinityError("Public Key point is at infinity")
+        }
+        if (!curve.contains(p: point)) {
             throw Error.pointError("Point ({x},{y}) is not valid for curve {name}"
                                     .replacingOccurrences(of: "{x}", with: String(point.x))
-                                    .replacingOccurrences(of:"{y}", with: String(point.y))
-                                    .replacingOccurrences(of:"{name}", with: curve.name))
+                                    .replacingOccurrences(of: "{y}", with: String(point.y))
+                                    .replacingOccurrences(of: "{name}", with: curve.name))
+        }
+        if (!Math.multiply(point, curve.N, curve.N, curve.A, curve.P).isAtInfinity()) {
+            throw Error.pointError("Point ({x},{y}) * {name}.N is not at infinity"
+                                    .replacingOccurrences(of: "{x}", with: String(point.x))
+                                    .replacingOccurrences(of: "{y}", with: String(point.y))
+                                    .replacingOccurrences(of: "{name}", with: curve.name))
         }
-        return PublicKey(point: point, curve: curve)
+        return publicKey
     }
 }
 

Sources/starkbank-ecdsa/Utils/Error.swift

@@ -15,4 +15,5 @@ enum Error: Swift.Error {
     case pointError(String)
     case generationError(String)
     case invalidPath(String)
+    case infinityError(String)
 }

Tests/starkbank-ecdsaTests/EcdsaTests.swift

@@ -33,4 +33,12 @@ class EcdsaTests: XCTestCase {
 
         XCTAssertFalse(Ecdsa.verify(message: message2, signature: signature, publicKey: publicKey))
     }
+
+    func testSignatureZero() throws {
+        let privateKey = try PrivateKey()
+        let publicKey = privateKey.publicKey()
+        let message = "This is a text message"
+
+        XCTAssertFalse(Ecdsa.verify(message: message, signature: Signature(0, 0), publicKey: publicKey))
+    }
 }