MCMC 破译密码 http://mlwhiz.com/blog/2015/08/21/MCMC_Algorithms_Cryptography/

# AIM: To Decrypt a text using MCMC approach. i.e. find decryption key which we will call cipher from now on.
import string
import math
import random

# This function takes as input a decryption key and creates a dict for key where each letter in the decryption key
# maps to a alphabet For example if the decryption key is "DGHJKL...." this function will create a dict like {D:A,G:B,H:C....}
def create_cipher_dict(cipher):
    cipher_dict = {}
    alphabet_list = list(string.ascii_uppercase)
    for i in range(len(cipher)):
        cipher_dict[alphabet_list[i]] = cipher[i]
    return cipher_dict

# This function takes a text and applies the cipher/key on the text and returns text.
def apply_cipher_on_text(text,cipher):
    cipher_dict = create_cipher_dict(cipher)
    text = list(text)
    newtext = ""
    for elem in text:
        if elem.upper() in cipher_dict:
            newtext+=cipher_dict[elem.upper()]
        else:
            newtext+=" "
    return newtext

# This function takes as input a path to a long text and creates scoring_params dict which contains the
# number of time each pair of alphabet appears together
# Ex. {‘AB‘:234,‘TH‘:2343,‘CD‘:23 ..}
def create_scoring_params_dict(longtext_path):
    scoring_params = {}
    alphabet_list = list(string.ascii_uppercase)
    with open(longtext_path) as fp:
        for line in fp:
            data = list(line.strip())
            for i in range(len(data)-1):
                alpha_i = data[i].upper()
                alpha_j = data[i+1].upper()
                if alpha_i not in alphabet_list and alpha_i != " ":
                    alpha_i = " "
                if alpha_j not in alphabet_list and alpha_j != " ":
                    alpha_j = " "
                key = alpha_i+alpha_j
                if key in scoring_params:
                    scoring_params[key]+=1
                else:
                    scoring_params[key]=1
    return scoring_params

# This function takes as input a text and creates scoring_params dict which contains the
# number of time each pair of alphabet appears together
# Ex. {‘AB‘:234,‘TH‘:2343,‘CD‘:23 ..}

def score_params_on_cipher(text):
    scoring_params = {}
    alphabet_list = list(string.ascii_uppercase)
    data = list(text.strip())
    for i in range(len(data)-1):
        alpha_i =data[i].upper()
        alpha_j = data[i+1].upper()
        if alpha_i not in alphabet_list and alpha_i != " ":
            alpha_i = " "
        if alpha_j not in alphabet_list and alpha_j != " ":
            alpha_j = " "
        key = alpha_i+alpha_j
        if key in scoring_params:
            scoring_params[key]+=1
        else:
            scoring_params[key]=1
    return scoring_params

# This function takes the text to be decrypted and a cipher to score the cipher.
# This function returns the log(score) metric

def get_cipher_score(text,cipher,scoring_params):
    cipher_dict = create_cipher_dict(cipher)
    decrypted_text = apply_cipher_on_text(text,cipher)
    scored_f = score_params_on_cipher(decrypted_text)
    cipher_score = 0
    for k,v in scored_f.iteritems():
        if k in scoring_params:
            cipher_score += v*math.log(scoring_params[k])
    return cipher_score

# Generate a proposal cipher by swapping letters at two random location
def generate_cipher(cipher):
    pos1 = random.randint(0, len(list(cipher))-1)
    pos2 = random.randint(0, len(list(cipher))-1)
    if pos1 == pos2:
        return generate_cipher(cipher)
    else:
        cipher = list(cipher)
        pos1_alpha = cipher[pos1]
        pos2_alpha = cipher[pos2]
        cipher[pos1] = pos2_alpha
        cipher[pos2] = pos1_alpha
        return "".join(cipher)

# Toss a random coin with robability of head p. If coin comes head return true else false.
def random_coin(p):
    unif = random.uniform(0,1)
    if unif>=p:
        return False
    else:
        return True

# Takes as input a text to decrypt and runs a MCMC algorithm for n_iter. Returns the state having maximum score and also
# the last few states
def MCMC_decrypt(n_iter,cipher_text,scoring_params):
    current_cipher = string.ascii_uppercase # Generate a random cipher to start
    state_keeper = set()
    best_state = ‘‘
    score = 0
    for i in range(n_iter):
        state_keeper.add(current_cipher)
        proposed_cipher = generate_cipher(current_cipher)
        score_current_cipher = get_cipher_score(cipher_text,current_cipher,scoring_params)
        score_proposed_cipher = get_cipher_score(cipher_text,proposed_cipher,scoring_params)
        acceptance_probability = min(1,math.exp(score_proposed_cipher-score_current_cipher))
        if score_current_cipher>score:
            best_state = current_cipher
        if random_coin(acceptance_probability):
            current_cipher = proposed_cipher
        if i%500==0:
            print "iter",i,":",apply_cipher_on_text(cipher_text,current_cipher)[0:99]
    return state_keeper,best_state

## Run the Main Program:

scoring_params = create_scoring_params_dict(‘war_and_peace.txt‘)

plain_text = "As Oliver gave this first proof of the free and proper action of his lungs, the patchwork coverlet which was carelessly flung over the iron bedstead, rustled; the pale face of a young woman was raised feebly from the pillow; and a faint voice imperfectly articulated the words, Let me see the child, and die. The surgeon had been sitting with his face turned towards the fire: giving the palms of his hands a warm and a rub alternately. As the young woman spoke, he rose, and advancing to the bed‘s head, said, with more kindness than might have been expected of him: "

encryption_key = "XEBPROHYAUFTIDSJLKZMWVNGQC"
cipher_text = apply_cipher_on_text(plain_text,encryption_key)
decryption_key = "ICZNBKXGMPRQTWFDYEOLJVUAHS"

print"Text To Decode:", cipher_text
print "\n"
states,best_state = MCMC_decrypt(10000,cipher_text,scoring_params)
print "\n"
print "Decoded Text:",apply_cipher_on_text(cipher_text,best_state)
print "\n"
print "MCMC KEY FOUND:",best_state
print "ACTUAL DECRYPTION KEY:",decryption_key