# (Gx,Gy)  is the secp256k1 generator point
Gx=0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
Gy=0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
n=0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
p = 2**256 - 2**32 - 977
import operator
import math

def inverse(x, p):
    """
    Calculate the modular inverse of x ( mod p )   
    the modular inverse is a number such that:   
    (inverse(x, p) * x) % p  ==  1     
    you could think of this as: 1/x
    """
    inv1 = 1
    inv2 = 0
    n=1
    while p != 1 and p!=0:       
        quotient = x // p       
        inv1, inv2 = inv2, inv1 - inv2 * quotient
        x, p = p, x % p     
        n = n+1
   
    return inv2

def dblpt(pt, p):
    """
    Calculate pt+pt = 2*pt
    """
    if pt is None:
        return None
    (x,y)= pt
    if y==0:
        return None         
   
    slope= 3*pow(x,2,p)*pow(2*y,p-2,p)   
    xsum= pow(slope,2,p)-2*x
    ysum= slope*(x-xsum)-y   
   
    return (xsum%p, ysum%p)

def addpt(p1,p2, p):
    """
    Calculate p1+p2
    """
    if p1 is None or p2 is None:
        return None
    (x1,y1)= p1
    (x2,y2)= p2
    if x1==x2:
        return dblpt(p1, p)
       
    # calculate (y1-y2)/(x1-x2)  modulus p
   
    slope=(y1-y2)*pow(x1-x2,p-2,p)   
    xsum= pow(slope,2,p)-(x1+x2)   
    ysum= slope*(x1-xsum)-y1
   
   
    return (xsum%p, ysum%p)

def ptmul(pt,a, p):
    """
    Scalar multiplication: calculate pt*a   
    basically adding pt to itself a times
    """
    scale= pt   
    acc=None
    while a:       
        if a&1:
            if acc is None:
                acc= scale                 
            else:     
                acc= addpt(acc,scale, p)             
               
        scale= dblpt(scale, p)
        a >>= 1
    return acc

def ptdiv(pt,a,p,n):   
    divpt=inverse(a, n)%n
    return ptmul(pt, divpt, p)


def isoncurve(pt,p):
    """
    returns True when pt is on the secp256k1 curve
    """
    (x,y)= pt
    return (y**2 - x**3 - 7)%p == 0


def getuncompressedpub(compressed_key):
    """
    returns uncompressed public key
    """
    y_parity = int(compressed_key[:2]) - 2
    if y_parity>1:
      #it is uncompresse dpub
      x = int(compressed_key[2:66], 16)
      y = int(compressed_key[66:130], 16)
      return (x,y)
   
    x = int(compressed_key[2:], 16)
    a = (pow(x, 3, p) + 7) % p
    y = pow(a, (p+1)//4, p)   
    if y % 2 != y_parity:
        y = -y % p       
    return (x,y)

def compresspub(uncompressed_key):
    """
    returns uncompressed public key
    """
    (x,y)=uncompressed_key
    y_parity = y&1
    head='02'
    if y_parity ==1:
        head='03'   
    compressed_key = head+'{:064x}'.format(x)       
    return compressed_key
   
                                                         
rangeBegin = 0x659756abf6c17ca70e0000000000000000000140be6ddd93e441f8d4b4a85653b20b4cdcc5c748207a0daa16191d07a425d8080c276f9412472e0429e61bc355
rangeEnd =   0x659756abf6c17ca70fffffffffffffffffffff40be6ddd93e441f8d4b4a85653b20b4cdcc5c748207a0daa16191d07a425d8080c276f9412472e0429e61bc355
pub_compressed = '03a61fc84b6429f07fc0edf25265ef7a0ced3cd9a0edea85e9f58b50b5d73f66e7'
Bits = 361

(pubx,puby) = getuncompressedpub(pub_compressed)
(x,y) = ptmul((Gx,Gy),rangeBegin,p)
#substract rangeBegin from public key
(Shiftpubx,Shiftpuby) = addpt((pubx,puby), (x,(p-y)%p), p)
print ("Shifted pub> ",compresspub((Shiftpubx,Shiftpuby)))
#pub / (2**361)
(SPubx,SPuby) = ptdiv((Shiftpubx,Shiftpuby),2**361,p,n)
print ("Pub> ",compresspub((SPubx,SPuby)))

#Convert private key
kangarooPrivKey=0x2d56cbf370cbeef9e80a
RealPrivKey = (kangarooPrivKey * (2**361) + rangeBegin ) % n
print ("Key> %x"% RealPrivKey)