# -*- coding: utf-8 -*-
# 求兩個數(shù)字的最大公約數(shù)（歐幾里得算法）
def gcd(a, b):
  if b == 0:
    return a
  else:
    return gcd(b, a % b)
'''
擴展歐幾里的算法
計算 ax + by = 1中的x與y的整數(shù)解（a與b互質(zhì)）
'''
def ext_gcd(a, b):
  if b == 0:
    x1 = 1
    y1 = 0
    x = x1
    y = y1
    r = a
    return r, x, y
  else:
    r, x1, y1 = ext_gcd(b, a % b)
    x = y1
    y = x1 - a / b * y1
    return r, x, y

# -*- coding: utf-8 -*-
'''
超大整數(shù)超大次冪然后對超大的整數(shù)取模
(base ^ exponent) mod n
'''
def exp_mode(base, exponent, n):
  bin_array = bin(exponent)[2:][::-1]
  r = len(bin_array)
  base_array = []
  pre_base = base
  base_array.append(pre_base)
  for _ in range(r - 1):
    next_base = (pre_base * pre_base) % n
    base_array.append(next_base)
    pre_base = next_base
  a_w_b = __multi(base_array, bin_array)
  return a_w_b % n
def __multi(array, bin_array):
  result = 1
  for index in range(len(array)):
    a = array[index]
    if not int(bin_array[index]):
      continue
    result *= a
  return result

# -*- coding: utf-8 -*-
from gcd import ext_gcd
from exponentiation import exp_mode
# 生成公鑰私鑰，p、q為兩個超大質(zhì)數(shù)
def gen_key(p, q):
  n = p * q
  fy = (p - 1) * (q - 1)   # 計算與n互質(zhì)的整數(shù)個數(shù) 歐拉函數(shù)
  e = 3889          # 選取e  一般選取65537
  # generate d
  a = e
  b = fy
  r, x, y = ext_gcd(a, b)
  print x  # 計算出的x不能是負數(shù)，如果是負數(shù)，說明p、q、e選取失敗，一般情況下e選取65537
  d = x
  # 返回：  公鑰   私鑰
  return  (n, e), (n, d)
# 加密 m是被加密的信息 加密成為c
def encrypt(m, pubkey):
  n = pubkey[0]
  e = pubkey[1]
  c = exp_mode(m, e, n)
  return c
# 解密 c是密文，解密為明文m
def decrypt(c, selfkey):
  n = selfkey[0]
  d = selfkey[1]
  m = exp_mode(c, d, n)
  return m
if __name__ == "__main__":
  '''公鑰私鑰中用到的兩個大質(zhì)數(shù)p,q'''
  p = 106697219132480173106064317148705638676529121742557567770857687729397446898790451577487723991083173010242416863238099716044775658681981821407922722052778958942891831033512463262741053961681512908218003840408526915629689432111480588966800949428079015682624591636010678691927285321708935076221951173426894836169
  q = 144819424465842307806353672547344125290716753535239658417883828941232509622838692761917211806963011168822281666033695157426515864265527046213326145174398018859056439431422867957079149967592078894410082695714160599647180947207504108618794637872261572262805565517756922288320779308895819726074229154002310375209
  '''生成公鑰私鑰'''
  pubkey, selfkey = gen_key(p, q)
  '''需要被加密的信息轉(zhuǎn)化成數(shù)字，長度小于秘鑰n的長度，如果信息長度大于n的長度，那么分段進行加密，分段解密即可。'''
  m = 1356205320457610288745198967657644166379972189839804389074591563666634066646564410685955217825048626066190866536592405966964024022236587593447122392540038493893121248948780525117822889230574978651418075403357439692743398250207060920929117606033490559159560987768768324823011579283223392964454439904542675637683985296529882973798752471233683249209762843835985174607047556306705224118165162905676610067022517682197138138621344578050034245933990790845007906416093198845798901781830868021761765904777531676765131379495584915533823288125255520904108500256867069512326595285549579378834222350197662163243932424184772115345
  '''信息加密'''
  c = encrypt(m, pubkey)
  print c
  '''信息解密'''
  d = decrypt(c, selfkey)
  print d