pragma solidity ^0.4.2;

contract EC {

    uint256 constant gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798;
    uint256 constant gy = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8;
    uint256 constant n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F;
    uint256 constant a = 0;
    uint256 constant b = 7;

    function EC(){}

    function _add (uint256 x1,uint256 z1, uint256 x2,uint256 z2) constant returns(uint256 x3,uint256 z3){
        (x3, z3) = (addmod(mulmod(z2, x1, n), mulmod(x2, z1, n), n), mulmod(z1, z2, n));
    }

    function _sub (uint256 x1,uint256 z1, uint256 x2,uint256 z2) constant returns(uint256 x3,uint256 z3){
        (x3, z3) = (addmod(mulmod(z2, x1, n),mulmod(n-x2, z1, n), n), mulmod(z1, z2 , n));
    }

    function _multiply (uint256 x1,uint256 z1, uint256 x2,uint256 z2) constant returns(uint256 x3,uint256 z3){
        (x3, z3) = (mulmod(x1, x2 , n), mulmod(z1, z2 , n));
    }

    function _divide (uint256 x1,uint256 z1, uint256 x2,uint256 z2) constant returns(uint256 x3,uint256 z3){
        (x3, z3) = (mulmod(x1, z2 , n), mulmod(z1 , x2 , n));
    }

    function inv (uint256 a) constant returns(uint256 invA){
        uint256 t=0;
        uint256 newT=1;
        uint256 r=n;
        uint256 newR=a;
        uint256 q;
        while (newR != 0) {
            q = r / newR;

            (t, newT) = (newT, addmod(t , (n - mulmod(q, newT,n)) , n));
            (r, newR) = (newR, r - q * newR );
        }

        return t;
    }

    function Add (uint256 x1,uint256 y1,uint256 z1, uint256 x2,uint256 y2,uint256 z2) constant returns(uint256 x3,uint256 y3,uint256 z3)   {
        uint256 l;
        uint256 lz;
        uint256 da;
        uint256 db;

        if ((x1==0)&&(y1==0)) {
            return (x2,y2,z2);
        }

        if ((x2==0)&&(y2==0)) {
            return (x1,y1,z1);
        }

        if ((x1==x2)&&(y1==y2)) {
            (l,lz) = _multiply(x1, z1, x1, z1);
            (l,lz) = _multiply(l, lz, 3, 1);
            (l,lz) = _add(l, lz, a, 1);

            (da,db) = _multiply(y1, z1, 2, 1);
        }
        else {
            (l,lz) = _sub(y2, z2, y1, z1);
            (da,db)  = _sub(x2, z2, x1, z1);
        }

        (l, lz) = _divide(l, lz, da, db);

        (x3, da) = _multiply(l, lz, l, lz);
        (x3, da) = _sub(x3, da, x1, z1);
        (x3, da) = _sub(x3, da, x2, z2);

        (y3, db) = _sub(x1, z1, x3, da);
        (y3, db) = _multiply(y3, db, l, lz );
        (y3, db) = _sub(y3, db, y1, z1 );


        if (da != db) {
            x3 = mulmod(x3, db, n);
            y3 = mulmod(y3, da, n);
            z3 = mulmod(da, db, n);
        } else {
            z3 = da;
        }

    }

    function Double(uint256 x1,uint256 y1,uint256 z1) constant returns(uint256 x3,uint256 y3,uint256 z3){
        (x3,y3,z3) = Add(x1,y1,z1,x1,y1,z1);
    }

    function Mulultiply(uint256 d, uint256 x1,uint256 y1,uint256 z1) constant returns(uint256 x3,uint256 y3,uint256 z3){
        uint256 remaining = d;
        uint256 px = x1;
        uint256 py = y1;
        uint256 pz = z1;
        uint256 acx = 0;
        uint256 acy = 0;
        uint256 acz = 1;

        if (d==0) {
            return (0,0,1);
        }

        while (remaining != 0) {
            if ((remaining & 1) != 0) {
                (acx,acy,acz) = Add(acx,acy,acz, px,py,pz);
            }
            remaining = remaining / 2;
            (px,py,pz) = Double(px,py,pz);
        }

        (x3,y3,z3) = (acx,acy,acz);
    }

    function privkey_to_public(uint256 privKey) constant returns(uint256 qx, uint256 qy){
        uint256 x;
        uint256 y;
        uint256 z;
        (x,y,z) = Mulultiply(privKey, gx, gy, 1);
        z = inv(z);
        qx = mulmod(x , z ,n);
        qy = mulmod(y , z ,n);
    }
}