Jun-Wang-2018

# From public key to address
# Reference: https://medium.freecodecamp.org/how-to-create-a-bitcoin-wallet-address-from-a-private-key-eca3ddd9c05f
#            https://docs.python.org/2/library/hashlib.html
import codecs  #If not installed: "pip3 install codecs"
import hashlib
# UK0 is a demo public key.
UK0 = ['3a56bd64573c28050bfe202c57e56b46c63744a253d1430e2b737876fa883b19','73c2f565444dc62151562993ff4b566c826010befb289fa2fc749293266066c0']
UK1 = "04" + UK0[0] + UK0[1]
UK2 = hashlib.sha256(codecs.decode(UK1, 'hex'))
h = hashlib.new('ripemd160')

Jun-Wang-2018

# From private key(hex) to Wallet Import Format(WIF)
# Reference: https://medium.freecodecamp.org/how-to-create-a-bitcoin-wallet-address-from-a-private-key-eca3ddd9c05f
#            https://docs.python.org/2/library/hashlib.html
import codecs  #If not installed: "pip3 install codecs"
import hashlib
# PK0 is a demo private key.
PK0 = "841846de7afbe32ee7ded837872c6e0825db095275b8afed0000000000000000"
PK1 = '80'+ PK0
PK2 = hashlib.sha256(codecs.decode(PK1, 'hex'))
PK3 = hashlib.sha256(PK2.digest())

Jun-Wang-2018

#These are Bitcoin parameters. See [Recommended Elliptic Curve Domain Parameters: page 15](http://www.secg.org/SEC2-Ver-1.0.pdf).
a = 0; b = 7  # Define a elliptic curve. y**2 = a*x**3 + b*x
P = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 -1  # A prime.
x1 = int("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798",16) 
y1 = int("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8",16)
G = (x1,y1)  # Base point
N = int("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",16)  # The order of the base point which is equal to the order of the curve in this case.

# Note: A and P must share no factor greater than 1.
def modular_inverse(A,P):

Jun-Wang-2018

# a,b define a elliptic curve. y**2 = a*x**3 + b*x   
# G(x1,y1) is the base point.
# P is a large prime. N is the order of the base point and usually equals to the order of the curve.

def ECMultiplication(G,a,b,P,N,privateKey):
    #if privateKey < 1 or privateKey >= N: raise Exception("ECMultiplication(G,a,b,P,privateKey), privateKey should >0 and <N.")
    n_binary = str(bin(privateKey))[2:]
    D = G
    for i in range (1, len(n_binary)):
        D = ECdouble(D,a,b,P)

Jun-Wang-2018

# Predfined parameters (x1,y1,x2,y2 are integers)
A = (x1,y1); B = (x2,y2)

# Function
def ECadd(A,B):
    lambda_mod = (B[1]-A[1])% P * modular_inverse(B[0]-A[0], P)
    x3 = (lambda_mod * lambda_mod - A[0] - B[0]) % P
    y3 = (lambda_mod * (A[0] - x3) - A[1]) % P
    return (x3,y3)

Jun-Wang-2018

# An example of predfined parameters
a = 1; b = 1
P = 23
x1 = 0; y1 = 1
G = (x1,y1)

# Function
def ECdouble(G,a,b,P):  # G = (x1,y1) where x1,y1 are integers.
    lambda_mod = (3*G[0]** 2 + a)% P * modular_inverse(2*G[1],P) 
    x3 = (lambda_mod * lambda_mod - G[0] - G[0]) % P

Jun-Wang-2018

# Note: A and P must share no factor greater than 1.
def modular_inverse(A,P):
    p0, a0 = 1, 0
    p1, a1 = 0, 1
    R0, R1 = P, A%P
    while R1 != 1 and R1 != 0:
        n, R2 = divmod(R0, R1)
        p2 = p0 - n*p1 ; a2 = a0 - n*a1
        p0 = p1; a0 = a1; p1 = p2; a1 = a2
        R0 = R1; R1 = R2