refactor deriver (#7)

* refactor deriver

* removed unused function

src/Deriver.sol

@@ -6,6 +6,7 @@ import {EllipticCurve} from "../lib/elliptic-curve-solidity/contracts/EllipticCu
 import {Bech32m} from "./Bech32m.sol";
 
 library Deriver {
+
     // BEGIN SECP256k1 CONSTANTS
     uint256 public constant GX =
         0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798;
@@ -15,54 +16,52 @@ library Deriver {
     uint256 public constant BB = 7;
     uint256 public constant PP =
         0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F;
-
     // END SECP256k1 CONSTANTS
 
-    // https://ethereum.stackexchange.com/questions/884/how-to-convert-an-address-to-bytes-in-solidity
-    function toBytes(address a) public pure returns (bytes memory) {
-        return abi.encodePacked(a);
-    }
-
     // TODO(mkl): use tagged hashes
     function getCoefficient(
         uint256 x1,
         uint256 y1,
         address a
-    ) public pure returns (uint256) {
+    ) internal pure returns (uint256) {
         uint256 c = uint256(sha256(abi.encode(x1, y1, a)));
         return c;
     }
 
+    // pubkey add operation
     function addPubkeys(
         uint256 x1,
         uint256 y1,
         uint256 x2,
         uint256 y2
-    ) public pure returns (uint256, uint256) {
+    ) internal pure returns (uint256, uint256) {
         return EllipticCurve.ecAdd(x1, y1, x2, y2, AA, PP);
     }
 
+    // pubkey multiplication by scalar operation
     function mulPubkey(
         uint256 x,
         uint256 y,
         uint256 scalar
-    ) public pure returns (uint256, uint256) {
+    ) internal pure returns (uint256, uint256) {
         return EllipticCurve.ecMul(scalar, x, y, AA, PP);
     }
 
+    // linear combination of two pubkeys
     function getCombinedPubkey(
         uint256 p1x,
         uint256 p1y,
         uint256 p2x,
         uint256 p2y,
         uint256 c1,
         uint256 c2
-    ) public pure returns (uint256, uint256) {
+    ) internal pure returns (uint256, uint256) {
         (uint256 x1, uint256 y1) = mulPubkey(p1x, p1y, c1);
         (uint256 x2, uint256 y2) = mulPubkey(p2x, p2y, c2);
         return addPubkeys(x1, y1, x2, y2);
     }
 
+    // derive pubkey from Validators' pubkeys and user's Ethereum address
     function getPubkeyFromAddress(
         uint256 p1x,
         uint256 p1y,
@@ -75,6 +74,7 @@ library Deriver {
         return getCombinedPubkey(p1x, p1y, p2x, p2y, c1, c2);
     }
 
+    // derive Bitcoin address from user's Ethereum address and validators' pubkeys
     function getBtcAddressFromEth(
         uint256 p1x,
         uint256 p1y,
@@ -93,8 +93,8 @@ library Deriver {
         return string(Bech32m.encodeSegwitAddress(hrp, 1, abi.encodePacked(x)));
     }
 
+    // calculate y coordinate from x coordinate
     function liftX(uint256 x) public pure returns (uint256) {
-        uint256 y = EllipticCurve.deriveY(0x02, x, AA, BB, PP);
-        return y;
+        return EllipticCurve.deriveY(0x02, x, AA, BB, PP);
     }
 }