# 使用Z3破解简单的XOR加密

import sys, hexdump
from z3 import *

def xor_strings(s,t):
# https://en.wikipedia.org/wiki/XOR_cipher#Example_implementation
"""将两个字符串进行xor操作"""
return "".join(chr(ord(a)^ord(b)) for a,b in zip(s,t))

file=open(fname, mode='rb')
file.close()
return content

def chunks(l, n):
"""将输入的数据分成n组"""
n = max(1, n)
return [l[i:i + n] for i in range(0, len(l), n)]

def print_model(m, KEY_LEN, key):
# 从model中解析key（model()函数返回的是解
test_key="".join(chr(int(obj_to_string(m[key[i]]))) for i in range(KEY_LEN))
print "key="
hexdump.hexdump(test_key)

# 使用解出来的key解密数据:
tmp=chunks(cipher_file, KEY_LEN)
plain_attempt="".join(map(lambda x: xor_strings(x, test_key), tmp))
print "plain="
hexdump.hexdump(plain_attempt)

def try_len(KEY_LEN, cipher_file):
cipher_len=len(cipher_file)
print "len=", KEY_LEN
s=Optimize()

# key的每一个字节对应一个未知数变量:
key=[BitVec('key_%d' % i, 8) for i in range (KEY_LEN)]
# 输入密文的每一个字节对应一个未知数变量:
cipher=[BitVec('cipher_%d' % i, 8) for i in range (cipher_len)]
# 每一个明文字节对应的未知数变量:
plain=[BitVec('plain_%d' % i, 8) for i in range (cipher_len)]
# 纯文本的每个字节的变量:1如果字节在'a'…“z”范围:
az_in_plain=[Int('az_in_plain_%d' % i) for i in range (cipher_len)]

for i in range(cipher_len):
# 根据输入的密文数据给每一个密文字节变量赋值
# plain text is cipher text XOR-ed with key:
# 明文等于密文xor key
# 明文的每一个字节的应该是可以打印的字符，或CR 或 LF
# 如果是小写字母则为1，否则为0.

# 寻找小写字母个数最多的解。
s.maximize(Sum(*az_in_plain))

if s.check()==unsat:
return
m=s.model()
print_model(m, KEY_LEN, key)

for i in range(1,20):
try_len(i, cipher_file)

#try_len(17, cipher_file)


% python 1.py cipher1.txt
len= 1
len= 2
len= 3
len= 4
len= 5

...

len= 16
len= 17
key=
00000000: 90 A0 21 52 48 84 FB FF  86 83 CF 50 46 12 7A F9  ..!RH......PF.z.
00000010: 36                                                6
plain=
00000000: 4D 72 2E 22 54 63 65 72  6F 6F 63 6D 27 48 6F 6C  Mr."Tceroocm'Hol
00000010: 6A 65 73 2C 22 70 63 6F  20 74 61 73 26 72 73 75  jes,"pco tas&rsu
00000020: 61 6B 6C 79 20 74 62 79  79 20 6F 61 74 63 27 69  akly tbyy oatc'i
00000030: 6E 20 73 68 65 20 6F 68  79 6E 69 6D 67 73 2A 27  n she ohynimgs*'
00000040: 73 61 76 62 0D 0A 75 72  68 65 20 74 6B 6F 73 63  savb..urhe tkosc
00000050: 27 6E 6F 74 27 69 6E 66  70 62 7A 75 65 6D 74 20  'not'infpbzuemt
00000060: 69 64 63 61 73 6E 6F 6E  73 22 70 63 65 6E 23 68  idcasnons"pcen#h
00000070: 65 26 70 61 73 20 72 70  20 61 6E 6B 2B 6E 69 64  e&pas rp ank+nid
00000080: 68 74 2A 27 77 61 73 27  73 65 61 76 62 6F 0D 0A  ht*'was'seavbo..
00000090: 62 74 20 72 6F 65 20 62  75 65 61 6B 64 66 78 74  bt roe bueakdfxt
000000A0: 20 77 61 62 6A 62 2E 20  49 27 73 74 6F 6D 63 2B   wabjb. I'stomc+
000000B0: 75 70 6C 6E 20 72 6F 65  20 68 62 61 72 74 6A 2A  upln roe hbartj*
000000C0: 79 75 67 23 61 6E 62 27  70 69 63 6C 65 64 20 77  yug#anb'picled w
000000D0: 77 2B 74 68 66 0D 0A 75  73 69 63 6B 27 77 68 69  w+thf..usick'whi
000000E0: 61 6F 2B 6F 75 71 20 76  6F 74 69 74 6F 75 20 68  ao+ouq votitou h
000000F0: 61 66 27 67 65 66 77 20  62 63 6F 69 6E 64 27 68  af'gefw bcoind'h
00000100: 69 6D 22 73 63 65 20 6D  69 67 6E 73 20 62 65 61  im"sce migns bea
00000110: 6F 72 65 2C 27 42 74 20  74 61 73 26 66 0D 0A 66  ore,'Bt tas&f..f
00000120: 6E 6E 65 2C 22 73 63 69  63 68 20 70 6F 62 63 65  nne,"scich pobce
00000130: 20 68 66 20 77 6D 68 6F  2C 20 61 75 6C 64 68 75   hf wmho, auldhu
00000140: 73 2D 6F 65 61 64 67 63  27 20 6F 65 20 74 6E 62  s-oeadgc' oe tnb
00000150: 20 73 6F 75 74 20 77 6A  6E 68 68 20 6A 73         sout wjnhh js
len= 18
len= 19


...
# 定义变量
# 对于每一个明文的字节变量: 1 如果这个字节是数字符号:
digits_in_plain=[Int('digits_in_plain_%d' % i) for i in range (cipher_len)]
# 对于每一个明文的字节变量: 1 如果当前字节 + 下一字节恰好等于‘th’:
th_in_plain=[Int('th_in_plain_%d' % i) for i in range (cipher_len-1)]
# ... 同理 ‘he’:
he_in_plain=[Int('he_in_plain_%d' % i) for i in range (cipher_len-1)]
in_in_plain=[Int('in_in_plain_%d' % i) for i in range (cipher_len-1)]
er_in_plain=[Int('er_in_plain_%d' % i) for i in range (cipher_len-1)]

...

for i in range(cipher_len-1):
# 约束条件
# ... 对于每一个明文的字节变量: 1 如果当前字节 + 下一字节恰好等于‘th’:
# ... etc:

# 寻找小写字母个数最多的解。
s.maximize(Sum(*az_in_plain))
# ... 且数字出现次数最少的解
s.minimize(Sum(*digits_in_plain))

# "th", "he", "in" , "er" 出现次数最多的解
s.maximize(Sum(*th_in_plain))
s.maximize(Sum(*he_in_plain))
s.maximize(Sum(*in_in_plain))
s.maximize(Sum(*er_in_plain))

...


len= 17
key=
00000000: 90 A0 22 50 4F 8F FB FF  85 83 CF 56 41 12 7A FE  .."PO......VA.z.
00000010: 31                                                1
plain=
00000000: 4D 72 2D 20 53 68 65 72  6C 6F 63 6B 20 48 6F 6B  Mr- Sherlock Hok
00000010: 6D 65 73 2F 20 77 68 6F  20 77 61 73 20 75 73 75  mes/ who was usu
00000020: 66 6C 6C 79 23 76 65 72  79 20 6C 61 74 65 20 69  flly#very late i
00000030: 6E 27 74 68 65 23 6D 6F  72 6E 69 6E 67 73 2C 20  n'the#mornings,
00000040: 73 61 71 65 0D 0A 76 70  6F 6E 20 74 68 6F 73 65  saqe..vpon those
00000050: 20 6E 6F 73 20 69 6E 65  72 65 71 75 65 6E 74 20   nos inerequent
00000060: 6F 63 63 61 74 69 6F 6E  70 20 77 68 65 6E 20 68  occationp when h
00000070: 65 20 77 61 73 27 75 70  20 62 6C 6C 20 6E 69 67  e was'up bll nig
00000080: 68 74 2C 20 77 61 74 20  73 65 62 74 65 64 0D 0A  ht, wat sebted..
00000090: 61 74 20 74 68 65 20 65  72 65 61 68 66 61 73 74  at the ereahfast
000000A0: 20 74 61 62 6C 65 2E 20  4E 20 73 74 6C 6F 64 20   table. N stlod
000000B0: 75 70 6F 6E 20 74 68 65  20 6F 65 61 72 77 68 2D  upon the oearwh-
000000C0: 72 75 67 20 61 6E 64 20  70 69 64 6B 65 64 23 75  rug and pidked#u
000000D0: 70 20 74 68 65 0D 0A 73  74 69 63 6C 20 77 68 6A  p the..sticl whj
000000E0: 63 68 20 6F 75 72 20 76  69 73 69 74 68 72 20 68  ch our visithr h
000000F0: 62 64 20 6C 65 66 74 20  62 65 68 69 6E 63 20 68  bd left behinc h
00000100: 69 6E 20 74 68 65 20 6E  69 67 68 74 20 62 62 66  in the night bbf
00000110: 6F 72 66 2E 20 49 74 20  77 61 73 20 61 0D 0A 61  orf. It was a..a
00000120: 69 6E 65 2F 20 74 68 69  63 6B 20 70 69 65 63 65  ine/ thick piece
00000130: 27 6F 66 20 74 6F 6F 64  2C 20 62 75 6C 62 6F 75  'of tood, bulbou
00000140: 73 2A 68 65 61 67 65 64  2C 20 6F 66 20 74 68 65  s*heaged, of the


...
# 3 known characters of plain text:
...


len= 17
key=
00000000: 90 A0 21 50 4F 8F FB FF  85 83 CF 56 41 12 7A F9  ..!PO......VA.z.
00000010: 31                                                1
plain=
00000000: 4D 72 2E 20 53 68 65 72  6C 6F 63 6B 20 48 6F 6C  Mr. Sherlock Hol
00000010: 6D 65 73 2C 20 77 68 6F  20 77 61 73 20 75 73 75  mes, who was usu
00000020: 61 6C 6C 79 20 76 65 72  79 20 6C 61 74 65 20 69  ally very late i
00000030: 6E 20 74 68 65 20 6D 6F  72 6E 69 6E 67 73 2C 20  n the mornings,
00000040: 73 61 76 65 0D 0A 75 70  6F 6E 20 74 68 6F 73 65  save..upon those
00000050: 20 6E 6F 74 20 69 6E 66  72 65 71 75 65 6E 74 20   not infrequent
00000060: 6F 63 63 61 73 69 6F 6E  73 20 77 68 65 6E 20 68  occasions when h
00000070: 65 20 77 61 73 20 75 70  20 61 6C 6C 20 6E 69 67  e was up all nig
00000080: 68 74 2C 20 77 61 73 20  73 65 61 74 65 64 0D 0A  ht, was seated..
00000090: 61 74 20 74 68 65 20 62  72 65 61 6B 66 61 73 74  at the breakfast
000000A0: 20 74 61 62 6C 65 2E 20  49 20 73 74 6F 6F 64 20   table. I stood
000000B0: 75 70 6F 6E 20 74 68 65  20 68 65 61 72 74 68 2D  upon the hearth-
000000C0: 72 75 67 20 61 6E 64 20  70 69 63 6B 65 64 20 75  rug and picked u
000000D0: 70 20 74 68 65 0D 0A 73  74 69 63 6B 20 77 68 69  p the..stick whi
000000E0: 63 68 20 6F 75 72 20 76  69 73 69 74 6F 72 20 68  ch our visitor h
000000F0: 61 64 20 6C 65 66 74 20  62 65 68 69 6E 64 20 68  ad left behind h
00000100: 69 6D 20 74 68 65 20 6E  69 67 68 74 20 62 65 66  im the night bef
00000110: 6F 72 65 2E 20 49 74 20  77 61 73 20 61 0D 0A 66  ore. It was a..f
00000120: 69 6E 65 2C 20 74 68 69  63 6B 20 70 69 65 63 65  ine, thick piece
00000130: 20 6F 66 20 77 6F 6F 64  2C 20 62 75 6C 62 6F 75   of wood, bulbou
00000140: 73 2D 68 65 61 64 65 64  2C 20 6F 66 20 74 68 65  s-headed, of the
00000150: 20 73 6F 72 74 20 77 68  69 63 68 20 69 73         sort which is