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Problem59.py
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Problem59.py
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# Code by @AmirMotefaker
# projecteuler.net
# https://projecteuler.net/problem=59
# XOR decryption
# Problem 59
# Each character on a computer is assigned a unique code and the preferred standard is ASCII (American Standard Code for Information Interchange).
# For example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107.
# A modern encryption method is to take a text file, convert the bytes to ASCII,
# then XOR each byte with a given value, taken from a secret key.
# The advantage with the XOR function is that using the same encryption key on the cipher text, restores the plain text;
# for example, 65 XOR 42 = 107, then 107 XOR 42 = 65.
# For unbreakable encryption, the key is the same length as the plain text message,
# and the key is made up of random bytes. The user would keep the encrypted message
# and the encryption key in different locations, and without both "halves",
# it is impossible to decrypt the message.
# Unfortunately, this method is impractical for most users,
# so the modified method is to use a password as a key.
# If the password is shorter than the message, which is likely,
# the key is repeated cyclically throughout the message.
# The balance for this method is using a sufficiently long password key for security,
# but short enough to be memorable.
# Your task has been made easy, as the encryption key consists of three lower case characters.
# Using p059_cipher.txt (right click and 'Save Link/Target As...'),
# a file containing the encrypted ASCII codes, and the knowledge that the plain text must
# contain common English words, decrypt the message and find the sum of the ASCII values in the original text.
# Solution 1
# import time
# start_time = time.time() #Time at the start of program execution
# def compute():
# bestkey = max(((x, y, z)
# for x in range(97, 123) # ASCII lowercase 'a' to 'z'
# for y in range(97, 123)
# for z in range(97, 123)),
# key=lambda key: get_score(decrypt(CIPHERTEXT, key)))
# ans = sum(decrypt(CIPHERTEXT, bestkey))
# return str(ans)
# # Heuristical function that returns a penalty score, where lower is better.
# def get_score(plaintext):
# result = 0
# for c in plaintext:
# if 65 <= c <= 90: # ASCII uppercase 'A' to 'Z', good
# result += 1
# elif 97 <= c <= 122: # ASCII lowercase 'a' to 'z', excellent
# result += 2
# elif c < 0x20 or c == 0x7F: # ASCII control characters, very bad
# result -= 10
# return result
# # Takes two sequences of integers and returns a list of integers.
# def decrypt(ciphertext, key):
# return [(c ^ key[i % len(key)]) for (i, c) in enumerate(ciphertext)]
# CIPHERTEXT = [
# 36, 22, 80, 0, 0, 4, 23, 25, 19, 17, 88, 4, 4, 19, 21, 11, 88, 22, 23, 23,
# 29, 69, 12, 24, 0, 88, 25, 11, 12, 2, 10, 28, 5, 6, 12, 25, 10, 22, 80, 10,
# 30, 80, 10, 22, 21, 69, 23, 22, 69, 61, 5, 9, 29, 2, 66, 11, 80, 8, 23, 3,
# 17, 88, 19, 0, 20, 21, 7, 10, 17, 17, 29, 20, 69, 8, 17, 21, 29, 2, 22, 84,
# 80, 71, 60, 21, 69, 11, 5, 8, 21, 25, 22, 88, 3, 0, 10, 25, 0, 10, 5, 8,
# 88, 2, 0, 27, 25, 21, 10, 31, 6, 25, 2, 16, 21, 82, 69, 35, 63, 11, 88, 4,
# 13, 29, 80, 22, 13, 29, 22, 88, 31, 3, 88, 3, 0, 10, 25, 0, 11, 80, 10, 30,
# 80, 23, 29, 19, 12, 8, 2, 10, 27, 17, 9, 11, 45, 95, 88, 57, 69, 16, 17, 19,
# 29, 80, 23, 29, 19, 0, 22, 4, 9, 1, 80, 3, 23, 5, 11, 28, 92, 69, 9, 5,
# 12, 12, 21, 69, 13, 30, 0, 0, 0, 0, 27, 4, 0, 28, 28, 28, 84, 80, 4, 22,
# 80, 0, 20, 21, 2, 25, 30, 17, 88, 21, 29, 8, 2, 0, 11, 3, 12, 23, 30, 69,
# 30, 31, 23, 88, 4, 13, 29, 80, 0, 22, 4, 12, 10, 21, 69, 11, 5, 8, 88, 31,
# 3, 88, 4, 13, 17, 3, 69, 11, 21, 23, 17, 21, 22, 88, 65, 69, 83, 80, 84, 87,
# 68, 69, 83, 80, 84, 87, 73, 69, 83, 80, 84, 87, 65, 83, 88, 91, 69, 29, 4, 6,
# 86, 92, 69, 15, 24, 12, 27, 24, 69, 28, 21, 21, 29, 30, 1, 11, 80, 10, 22, 80,
# 17, 16, 21, 69, 9, 5, 4, 28, 2, 4, 12, 5, 23, 29, 80, 10, 30, 80, 17, 16,
# 21, 69, 27, 25, 23, 27, 28, 0, 84, 80, 22, 23, 80, 17, 16, 17, 17, 88, 25, 3,
# 88, 4, 13, 29, 80, 17, 10, 5, 0, 88, 3, 16, 21, 80, 10, 30, 80, 17, 16, 25,
# 22, 88, 3, 0, 10, 25, 0, 11, 80, 12, 11, 80, 10, 26, 4, 4, 17, 30, 0, 28,
# 92, 69, 30, 2, 10, 21, 80, 12, 12, 80, 4, 12, 80, 10, 22, 19, 0, 88, 4, 13,
# 29, 80, 20, 13, 17, 1, 10, 17, 17, 13, 2, 0, 88, 31, 3, 88, 4, 13, 29, 80,
# 6, 17, 2, 6, 20, 21, 69, 30, 31, 9, 20, 31, 18, 11, 94, 69, 54, 17, 8, 29,
# 28, 28, 84, 80, 44, 88, 24, 4, 14, 21, 69, 30, 31, 16, 22, 20, 69, 12, 24, 4,
# 12, 80, 17, 16, 21, 69, 11, 5, 8, 88, 31, 3, 88, 4, 13, 17, 3, 69, 11, 21,
# 23, 17, 21, 22, 88, 25, 22, 88, 17, 69, 11, 25, 29, 12, 24, 69, 8, 17, 23, 12,
# 80, 10, 30, 80, 17, 16, 21, 69, 11, 1, 16, 25, 2, 0, 88, 31, 3, 88, 4, 13,
# 29, 80, 21, 29, 2, 12, 21, 21, 17, 29, 2, 69, 23, 22, 69, 12, 24, 0, 88, 19,
# 12, 10, 19, 9, 29, 80, 18, 16, 31, 22, 29, 80, 1, 17, 17, 8, 29, 4, 0, 10,
# 80, 12, 11, 80, 84, 67, 80, 10, 10, 80, 7, 1, 80, 21, 13, 4, 17, 17, 30, 2,
# 88, 4, 13, 29, 80, 22, 13, 29, 69, 23, 22, 69, 12, 24, 12, 11, 80, 22, 29, 2,
# 12, 29, 3, 69, 29, 1, 16, 25, 28, 69, 12, 31, 69, 11, 92, 69, 17, 4, 69, 16,
# 17, 22, 88, 4, 13, 29, 80, 23, 25, 4, 12, 23, 80, 22, 9, 2, 17, 80, 70, 76,
# 88, 29, 16, 20, 4, 12, 8, 28, 12, 29, 20, 69, 26, 9, 69, 11, 80, 17, 23, 80,
# 84, 88, 31, 3, 88, 4, 13, 29, 80, 21, 29, 2, 12, 21, 21, 17, 29, 2, 69, 12,
# 31, 69, 12, 24, 0, 88, 20, 12, 25, 29, 0, 12, 21, 23, 86, 80, 44, 88, 7, 12,
# 20, 28, 69, 11, 31, 10, 22, 80, 22, 16, 31, 18, 88, 4, 13, 25, 4, 69, 12, 24,
# 0, 88, 3, 16, 21, 80, 10, 30, 80, 17, 16, 25, 22, 88, 3, 0, 10, 25, 0, 11,
# 80, 17, 23, 80, 7, 29, 80, 4, 8, 0, 23, 23, 8, 12, 21, 17, 17, 29, 28, 28,
# 88, 65, 75, 78, 68, 81, 65, 67, 81, 72, 70, 83, 64, 68, 87, 74, 70, 81, 75, 70,
# 81, 67, 80, 4, 22, 20, 69, 30, 2, 10, 21, 80, 8, 13, 28, 17, 17, 0, 9, 1,
# 25, 11, 31, 80, 17, 16, 25, 22, 88, 30, 16, 21, 18, 0, 10, 80, 7, 1, 80, 22,
# 17, 8, 73, 88, 17, 11, 28, 80, 17, 16, 21, 11, 88, 4, 4, 19, 25, 11, 31, 80,
# 17, 16, 21, 69, 11, 1, 16, 25, 2, 0, 88, 2, 10, 23, 4, 73, 88, 4, 13, 29,
# 80, 11, 13, 29, 7, 29, 2, 69, 75, 94, 84, 76, 65, 80, 65, 66, 83, 77, 67, 80,
# 64, 73, 82, 65, 67, 87, 75, 72, 69, 17, 3, 69, 17, 30, 1, 29, 21, 1, 88, 0,
# 23, 23, 20, 16, 27, 21, 1, 84, 80, 18, 16, 25, 6, 16, 80, 0, 0, 0, 23, 29,
# 3, 22, 29, 3, 69, 12, 24, 0, 88, 0, 0, 10, 25, 8, 29, 4, 0, 10, 80, 10,
# 30, 80, 4, 88, 19, 12, 10, 19, 9, 29, 80, 18, 16, 31, 22, 29, 80, 1, 17, 17,
# 8, 29, 4, 0, 10, 80, 12, 11, 80, 84, 86, 80, 35, 23, 28, 9, 23, 7, 12, 22,
# 23, 69, 25, 23, 4, 17, 30, 69, 12, 24, 0, 88, 3, 4, 21, 21, 69, 11, 4, 0,
# 8, 3, 69, 26, 9, 69, 15, 24, 12, 27, 24, 69, 49, 80, 13, 25, 20, 69, 25, 2,
# 23, 17, 6, 0, 28, 80, 4, 12, 80, 17, 16, 25, 22, 88, 3, 16, 21, 92, 69, 49,
# 80, 13, 25, 6, 0, 88, 20, 12, 11, 19, 10, 14, 21, 23, 29, 20, 69, 12, 24, 4,
# 12, 80, 17, 16, 21, 69, 11, 5, 8, 88, 31, 3, 88, 4, 13, 29, 80, 22, 29, 2,
# 12, 29, 3, 69, 73, 80, 78, 88, 65, 74, 73, 70, 69, 83, 80, 84, 87, 72, 84, 88,
# 91, 69, 73, 95, 87, 77, 70, 69, 83, 80, 84, 87, 70, 87, 77, 80, 78, 88, 21, 17,
# 27, 94, 69, 25, 28, 22, 23, 80, 1, 29, 0, 0, 22, 20, 22, 88, 31, 11, 88, 4,
# 13, 29, 80, 20, 13, 17, 1, 10, 17, 17, 13, 2, 0, 88, 31, 3, 88, 4, 13, 29,
# 80, 6, 17, 2, 6, 20, 21, 75, 88, 62, 4, 21, 21, 9, 1, 92, 69, 12, 24, 0,
# 88, 3, 16, 21, 80, 10, 30, 80, 17, 16, 25, 22, 88, 29, 16, 20, 4, 12, 8, 28,
# 12, 29, 20, 69, 26, 9, 69, 65, 64, 69, 31, 25, 19, 29, 3, 69, 12, 24, 0, 88,
# 18, 12, 9, 5, 4, 28, 2, 4, 12, 21, 69, 80, 22, 10, 13, 2, 17, 16, 80, 21,
# 23, 7, 0, 10, 89, 69, 23, 22, 69, 12, 24, 0, 88, 19, 12, 10, 19, 16, 21, 22,
# 0, 10, 21, 11, 27, 21, 69, 23, 22, 69, 12, 24, 0, 88, 0, 0, 10, 25, 8, 29,
# 4, 0, 10, 80, 10, 30, 80, 4, 88, 19, 12, 10, 19, 9, 29, 80, 18, 16, 31, 22,
# 29, 80, 1, 17, 17, 8, 29, 4, 0, 10, 80, 12, 11, 80, 84, 86, 80, 36, 22, 20,
# 69, 26, 9, 69, 11, 25, 8, 17, 28, 4, 10, 80, 23, 29, 17, 22, 23, 30, 12, 22,
# 23, 69, 49, 80, 13, 25, 6, 0, 88, 28, 12, 19, 21, 18, 17, 3, 0, 88, 18, 0,
# 29, 30, 69, 25, 18, 9, 29, 80, 17, 23, 80, 1, 29, 4, 0, 10, 29, 12, 22, 21,
# 69, 12, 24, 0, 88, 3, 16, 21, 3, 69, 23, 22, 69, 12, 24, 0, 88, 3, 16, 26,
# 3, 0, 9, 5, 0, 22, 4, 69, 11, 21, 23, 17, 21, 22, 88, 25, 11, 88, 7, 13,
# 17, 19, 13, 88, 4, 13, 29, 80, 0, 0, 0, 10, 22, 21, 11, 12, 3, 69, 25, 2,
# 0, 88, 21, 19, 29, 30, 69, 22, 5, 8, 26, 21, 23, 11, 94,
# ]
# if __name__ == "__main__":
# print(compute())
# end_time = time.time() #Time at the end of execution
# print ("Time of program execution:", (end_time - start_time)) #Time of program execution
# Solution 2
# It suffices to check all 26*26*26 = 17,576 possible 3-letter keys and store the ones that
# decrypt the cipher text(Problem59_cipher.txt) into a reasonable deciphered text.
# It takes a bit of guessing and checking to determine what characters are acceptable
# in a reasonable deciphered text, but after going through the most common characters
# in typical English text, we can find that only one key provides a reasonable answer.
import time
start_time = time.time() #Time at the start of program execution
f = open("Problem59_cipher.txt", "r")
if(f.mode == "r"):
contents = f.readlines()
realContents = []
for x in contents:
realContents.append(x.split(","))
else:
raise ValueError("Cannot read from file")
finalContents = []
for x in realContents[0]:
finalContents.append(int(x))
def isAcceptable(myChar):
return 'a'<=myChar<='z' or 'A'<=myChar<='Z' or myChar == ' ' or myChar == '\'' or myChar == ',' or myChar == '"' or myChar == '[' or myChar == ']' or myChar == ':' or '0'<=myChar<='9' or myChar == '/' or myChar == '.' or myChar == '(' or myChar == ')' or myChar == ';' or myChar=='+'
def problem59(cipherText):
tl = len(cipherText)
alphabet = "abcdefghijklmnopqrstuvwxyz"
possible = []
for a in alphabet:
for b in alphabet:
for c in alphabet:
myGuess = a+b+c
asciiIndices = [ord(a),ord(b),ord(c)]
s = ""
bad = False
for x in range(tl):
myChar = chr(cipherText[x] ^ asciiIndices[x%3])
if not isAcceptable(myChar):
bad = True
break
s+=myChar
if not bad:
possible.append(s)
total = -1
for x in possible:
subTotal = 0
for y in x:
subTotal+=ord(y)
if(total==-1):
total = subTotal
return total
print (problem59(finalContents))
end_time = time.time() #Time at the end of execution
print ("Time of program execution:", (end_time - start_time)) #Time of program execution
#### Answer: 129448