Foobar password decryption

xor_dec.py

#!/usr/bin/env python3
from functools import lru_cache

"""
  The encryption equation is given as:
  
    D_i = (129M_i) XOR (M_(i-1)) (mod 256)
      where D denotes a encrypted string, M is the message.
    
  Thus, the message equation derived from the original equation should be:
  
    M_i = 256c_i * (D_i XOR (M_(i-1))) / 129
      where c_i is an integer that makes M_i closed under the integer field
  
"""

digest = lambda i: [0, 129, 3, 129, 7, 129, 3, 129, 15, 129, 3, 129, 7, 129, 3, 129][i]
selInt = lru_cache()(lambda x, y: \
    int(x) if int(x) == x else y())
message = lru_cache()(lambda i, c: \
    selInt(
        (256.0*c + (digest(i) ^ message(i-1, 0))) / 129.0,
        lambda: message(i, c+1)
    ) if i >= 0 else 0)

print([digest(x) for x in range(16)])
print([message(x, 0) for x in range(16)])