# 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.

# Below are the public specs for Bitcoin's curve - the secp256k1

Pcurve = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 -1 # The proven prime
N=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 # Number of points in the field
Acurve = 0; Bcurve = 7 # These two defines the elliptic curve. y^2 = x^3 + Acurve * x + Bcurve
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424
GPoint = (Gx,Gy) # This is our generator point. Trillions of dif ones possible

#Individual Transaction/Personal Information
privKey = 0xA0DC65FFCA799873CBEA0AC274015B9526505DAAAED385155425F7337704883E #replace with any private key

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): # Not true addition, invented for EC. Could have been called anything.
    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): # This is called point doubling, also invented for EC.
    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): #Double & add. Not true multiplication
    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)): # This is invented EC multiplication.
        Q=ECdouble(Q); # print "DUB", Q[0]; print
        if ScalarBin[i] == "1":
            Q=ECadd(Q,GenPoint); # print "ADD", Q[0]; print
    return (Q)

print; print "******* Public Key Generation *********";
print
PublicKey = EccMultiply(GPoint,privKey)
print "the private key:";
print privKey; print
print "the uncompressed public key (not address):";
print PublicKey; print
print "the uncompressed public key (HEX):";
print "04" + "%064x" % PublicKey[0] + "%064x" % PublicKey[1];
print;
print "the official Public Key - compressed:";
if PublicKey[1] % 2 == 1: # If the Y value for the Public Key is odd.
    print "03"+str(hex(PublicKey[0])[2:-1]).zfill(64)
else: # Or else, if the Y value is even.
    print "02"+str(hex(PublicKey[0])[2:-1]).zfill(64)