# Super simple Elliptic Curve Presentation. No imported libraries, wrappers, nothing. 
# For educational purposes only. Remember to use Python 2.7.6 or lower. You'll need to make changes for Python 3.
# Original source: https://github.com/wobine/blackboard101/blob/master/EllipticCurvesPart4-PrivateKeyToPublicKey.py

# secp256k1 domain parameters
Pcurve = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 -1 # The proven prime
Acurve = 0; # These two defines the elliptic curve. y^2 = x^3 + Acurve * x + Bcurve
Bcurve = 7;
Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798 
Gy = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
GPoint = (int(Gx),int(Gy)) # This is our generator point.
N=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 # Number of points in the field

# Replace with any private key
privKey = 0x79FE45D61339181238E49424E905446A35497A8ADEA8B7D5241A1E7F2C95A04D

def modinv(a,n=Pcurve): #Extended Euclidean Algorithm/'division' in elliptic curves
    lm, hm = 1,0
    low, high = a%n,n
    while low > 1:
        ratio = high/low
        nm, new = hm-lm*ratio, high-low*ratio
        lm, low, hm, high = nm, new, lm, low
    return lm % n

def ECadd(a,b): # EC Addition
    LamAdd = ((b[1]-a[1]) * modinv(b[0]-a[0],Pcurve)) % Pcurve
    x = (LamAdd*LamAdd-a[0]-b[0]) % Pcurve
    y = (LamAdd*(a[0]-x)-a[1]) % Pcurve
    return (x,y)

def ECdouble(a): # EC Doubling
    Lam = ((3*a[0]*a[0]+Acurve) * modinv((2*a[1]),Pcurve)) % Pcurve
    x = (Lam*Lam-2*a[0]) % Pcurve
    y = (Lam*(a[0]-x)-a[1]) % Pcurve
    return (x,y)

def EccMultiply(GenPoint,ScalarHex): # Doubling & Addition
    if ScalarHex == 0 or ScalarHex >= N: raise Exception("Invalid Scalar/Private Key")
    ScalarBin = str(bin(ScalarHex))[2:]
    Q=GenPoint
    for i in range (1, len(ScalarBin)):
        Q=ECdouble(Q); 
        if ScalarBin[i] == "1":
            Q=ECadd(Q,GenPoint);
    return (Q)

print; print "******* Bitcoin Public Key Generation *********"; 
print
PublicKey = EccMultiply(GPoint,privKey)
print "the private key:"; 
print hex(privKey); print

print "the public key x-value (Hex):"; 
print "0x" + "%064x" % PublicKey[0];
print;

print "the public key y-value (Hex):"; 
print "0x" + "%064x" % PublicKey[1];
print;

print "the public key (Hex):"; 
print "0x" + "%064x" % PublicKey[0] + "%064x" % PublicKey[1];
print;