Caesar cipher decoder using chi-squared values

chi-caesar.py

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## DECODE CAESAR CIPHER USING CHI-SQUARED VALUES ##
##        COPYRIGHT (C) 2018 HENRY FRANKS        ##
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phrase = "AOLJHLZHYJPWOLYPZVULZMAOLLHYSPLZARUVDUHUKZPTWSLZAJPWOLYZPAPZHAFWLVMZBIZAPABAPVUJPWOLYPUDOPJOLHJOSLAALYPUAOLWSHPUALEAPZZOPMALKHJLYAHPUUBTILYVMWSHJLZKVDUAOLHSWOHILA" # Phrase to decode

expected = [13.2345, 2.4138, 4.5036, 6.885, 19.602, 3.6126, 3.2724, 9.8658, 11.2914, 0.243, 1.2474, 6.5286, 3.9042, 10.935, 12.1662, 3.1226, 0.162, 9.7038, 10.2546, 14.6772, 4.4712, 1.5876, 3.8232, 0.243, 3.1914, 0.1134] # Expected frequencies for 162 letters

observed = [18, 3, 0, 3, 1, 1, 0, 12, 3, 8, 3, 22, 4, 0, 12, 17, 0, 1, 6, 2, 11, 7, 8, 0, 8, 12] # Observed letter frequencies

chi_values = {} # Dictionary will store shift as key and X^2 as value

for shift in range(26):
	shifted = observed[-shift:] + observed[:-shift] # Shift list by shift
	chi_squared = sum([(o-e)**2 / e for (e, o) in zip(expected, shifted)]) # Calculate X^2 for shifted list

	print('Shift: %02d | X^2: %d' % (shift, chi_squared))
	chi_values[shift] = chi_squared # Add shift and X^2 to dictionary

best_shift = min(chi_values, key=chi_values.get) # Get the shift for the lowest X^2

# Apply shift to string
values = [ord(c) + best_shift for c in phrase.upper()] # Convert character to number
decoded = ''.join([chr(n) if n < 91 else chr(n-26) for n in values]) # Shift number and convert back to character


print('\nBest shift: %d | Decoded: %s' % (best_shift, decoded))