import hashlib, re

P = 2**256-2**32-2**9-2**8-2**7-2**6-2**4-1
A = 0
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424
G = (Gx,Gy)

def inv(a,n):
  lm, hm = 1,0
  low, high = a%n,n
  while low > 1:
    r = high/low
    nm, new = hm-lm*r, high-low*r
    lm, low, hm, high = nm, new, lm, low
  return lm % n

def get_code_string(base):
   if base == 2: return '01'
   elif base == 10: return '0123456789'
   elif base == 16: return "0123456789abcdef"
   elif base == 58: return "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"
   elif base == 256: return ''.join([chr(x) for x in range(256)])
   else: raise ValueError("Invalid base!")

def encode(val,base,minlen=0):
   code_string = get_code_string(base)
   result = ""   
   while val > 0:
      result = code_string[val % base] + result
      val /= base
   if len(result) < minlen:
      result = code_string[0]*(minlen-len(result))+result
   return result

def decode(string,base):
   code_string = get_code_string(base)
   result = 0
   if base == 16: string = string.lower()
   while len(string) > 0:
      result *= base
      result += code_string.find(string[0])
      string = string[1:]
   return result

def changebase(string,frm,to,minlen=0):
   return encode(decode(string,frm),to,minlen)

def base10_add(a,b):
  if a == None: return b[0],b[1]
  if b == None: return a[0],a[1]
  if a[0] == b[0]: 
    if a[1] == b[1]: return base10_double(a[0],a[1])
    else: return None
  m = ((b[1]-a[1]) * inv(b[0]-a[0],P)) % P
  x = (m*m-a[0]-b[0]) % P
  y = (m*(a[0]-x)-a[1]) % P
  return (x,y)
  
def base10_double(a):
  if a == None: return None
  m = ((3*a[0]*a[0]+A)*inv(2*a[1],P)) % P
  x = (m*m-2*a[0]) % P
  y = (m*(a[0]-x)-a[1]) % P
  return (x,y)

def base10_multiply(a,n):
  if n == 0: return G
  if n == 1: return a
  if (n%2) == 0: return base10_double(base10_multiply(a,n/2))
  if (n%2) == 1: return base10_add(base10_double(base10_multiply(a,n/2)),a)

def hex_to_point(h): return (decode(h[2:66],16),decode(h[66:],16))

def point_to_hex(p): return '04'+encode(p[0],16,64)+encode(p[1],16,64)

def multiply(privkey,pubkey):
  return point_to_hex(base10_multiply(hex_to_point(pubkey),decode(privkey,16)))

def privtopub(privkey):
  return point_to_hex(base10_multiply(G,decode(privkey,16)))

def add(p1,p2):
  if (len(p1)==32):
    return encode(decode(p1,16) + decode(p2,16) % P,16,32)
  else:
    return point_to_hex(base10_add(hex_to_point(p1),hex_to_point(p2)))

def hash_160(string):
   intermed = hashlib.sha256(string).digest()
   ripemd160 = hashlib.new('ripemd160')
   ripemd160.update(intermed)
   return ripemd160.digest()

def dbl_sha256(string):
   return hashlib.sha256(hashlib.sha256(string).digest()).digest()
  
def bin_to_b58check(inp):
   inp_fmtd = '\x00' + inp
   leadingzbytes = len(re.match('^\x00*',inp_fmtd).group(0))
   checksum = dbl_sha256(inp_fmtd)[:4]
   return '1' * leadingzbytes + changebase(inp_fmtd+checksum,256,58)

#Convert a public key (in hex) to a Bitcoin address
def pubkey_to_address(pubkey):
   return bin_to_b58check(hash_160(changebase(pubkey,16,256)))