Solution to Project Euler problem 59
Aaron Schaefer
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! Copyright (c) 2008 Aaron Schaefer, Slava Pestov.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays ascii assocs hashtables io.encodings.ascii io.files kernel math
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math.parser namespaces sequences sequences.lib sequences.private sorting
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splitting strings ;
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IN: project-euler.059
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! http://projecteuler.net/index.php?section=problems&id=59
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! DESCRIPTION
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! -----------
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! Each character on a computer is assigned a unique code and the preferred
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! standard is ASCII (American Standard Code for Information Interchange). For
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! example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107.
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! A modern encryption method is to take a text file, convert the bytes to
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! ASCII, then XOR each byte with a given value, taken from a secret key. The
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! advantage with the XOR function is that using the same encryption key on the
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! cipher text, restores the plain text; for example, 65 XOR 42 = 107, then 107
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! XOR 42 = 65.
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! For unbreakable encryption, the key is the same length as the plain text
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! message, and the key is made up of random bytes. The user would keep the
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! encrypted message and the encryption key in different locations, and without
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! both "halves", it is impossible to decrypt the message.
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! Unfortunately, this method is impractical for most users, so the modified
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! method is to use a password as a key. If the password is shorter than the
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! message, which is likely, the key is repeated cyclically throughout the
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! message. The balance for this method is using a sufficiently long password
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! key for security, but short enough to be memorable.
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! Your task has been made easy, as the encryption key consists of three lower
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! case characters. Using cipher1.txt (right click and 'Save Link/Target
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! As...'), a file containing the encrypted ASCII codes, and the knowledge that
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! the plain text must contain common English words, decrypt the message and
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! find the sum of the ASCII values in the original text.
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! SOLUTION
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! --------
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! Assume that the space character will be the most common, so XOR the input
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! text with a space character then group the text into three "columns" since
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! that's how long our key is. Then do frequency analysis on each column to
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! find out what the most likely candidate is for the key.
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! NOTE: This technique would probably not work well in all cases, but luckily
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! it did for this particular problem.
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<PRIVATE
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: source-059 ( -- seq )
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"extra/project-euler/059/cipher1.txt" resource-path
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ascii file-contents [ blank? ] right-trim "," split
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[ string>number ] map ;
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TUPLE: rollover seq n ;
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C: <rollover> rollover
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M: rollover length rollover-n ;
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M: rollover nth-unsafe rollover-seq [ length mod ] keep nth-unsafe ;
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INSTANCE: rollover immutable-sequence
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: decrypt ( seq key -- seq )
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over length <rollover> swap [ bitxor ] 2map ;
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: frequency-analysis ( seq -- seq )
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dup prune [
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[ 2dup [ = ] curry count 2array , ] each
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] { } make nip ; inline
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: most-frequent ( seq -- elt )
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frequency-analysis sort-values keys peek ;
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: crack-key ( seq key-length -- key )
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[ " " decrypt ] dip group 1 head-slice*
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flip [ most-frequent ] map ;
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PRIVATE>
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: euler059 ( -- answer )
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source-059 dup 3 crack-key decrypt sum ;
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! [ euler059 ] 100 ave-time
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! 13 ms run / 0 ms GC ave time - 100 trials
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MAIN: euler059
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@ -0,0 +1 @@
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79,59,12,2,79,35,8,28,20,2,3,68,8,9,68,45,0,12,9,67,68,4,7,5,23,27,1,21,79,85,78,79,85,71,38,10,71,27,12,2,79,6,2,8,13,9,1,13,9,8,68,19,7,1,71,56,11,21,11,68,6,3,22,2,14,0,30,79,1,31,6,23,19,10,0,73,79,44,2,79,19,6,28,68,16,6,16,15,79,35,8,11,72,71,14,10,3,79,12,2,79,19,6,28,68,32,0,0,73,79,86,71,39,1,71,24,5,20,79,13,9,79,16,15,10,68,5,10,3,14,1,10,14,1,3,71,24,13,19,7,68,32,0,0,73,79,87,71,39,1,71,12,22,2,14,16,2,11,68,2,25,1,21,22,16,15,6,10,0,79,16,15,10,22,2,79,13,20,65,68,41,0,16,15,6,10,0,79,1,31,6,23,19,28,68,19,7,5,19,79,12,2,79,0,14,11,10,64,27,68,10,14,15,2,65,68,83,79,40,14,9,1,71,6,16,20,10,8,1,79,19,6,28,68,14,1,68,15,6,9,75,79,5,9,11,68,19,7,13,20,79,8,14,9,1,71,8,13,17,10,23,71,3,13,0,7,16,71,27,11,71,10,18,2,29,29,8,1,1,73,79,81,71,59,12,2,79,8,14,8,12,19,79,23,15,6,10,2,28,68,19,7,22,8,26,3,15,79,16,15,10,68,3,14,22,12,1,1,20,28,72,71,14,10,3,79,16,15,10,68,3,14,22,12,1,1,20,28,68,4,14,10,71,1,1,17,10,22,71,10,28,19,6,10,0,26,13,20,7,68,14,27,74,71,89,68,32,0,0,71,28,1,9,27,68,45,0,12,9,79,16,15,10,68,37,14,20,19,6,23,19,79,83,71,27,11,71,27,1,11,3,68,2,25,1,21,22,11,9,10,68,6,13,11,18,27,68,19,7,1,71,3,13,0,7,16,71,28,11,71,27,12,6,27,68,2,25,1,21,22,11,9,10,68,10,6,3,15,27,68,5,10,8,14,10,18,2,79,6,2,12,5,18,28,1,71,0,2,71,7,13,20,79,16,2,28,16,14,2,11,9,22,74,71,87,68,45,0,12,9,79,12,14,2,23,2,3,2,71,24,5,20,79,10,8,27,68,19,7,1,71,3,13,0,7,16,92,79,12,2,79,19,6,28,68,8,1,8,30,79,5,71,24,13,19,1,1,20,28,68,19,0,68,19,7,1,71,3,13,0,7,16,73,79,93,71,59,12,2,79,11,9,10,68,16,7,11,71,6,23,71,27,12,2,79,16,21,26,1,71,3,13,0,7,16,75,79,19,15,0,68,0,6,18,2,28,68,11,6,3,15,27,68,19,0,68,2,25,1,21,22,11,9,10,72,71,24,5,20,79,3,8,6,10,0,79,16,8,79,7,8,2,1,71,6,10,19,0,68,19,7,1,71,24,11,21,3,0,73,79,85,87,79,38,18,27,68,6,3,16,15,0,17,0,7,68,19,7,1,71,24,11,21,3,0,71,24,5,20,79,9,6,11,1,71,27,12,21,0,17,0,7,68,15,6,9,75,79,16,15,10,68,16,0,22,11,11,68,3,6,0,9,72,16,71,29,1,4,0,3,9,6,30,2,79,12,14,2,68,16,7,1,9,79,12,2,79,7,6,2,1,73,79,85,86,79,33,17,10,10,71,6,10,71,7,13,20,79,11,16,1,68,11,14,10,3,79,5,9,11,68,6,2,11,9,8,68,15,6,23,71,0,19,9,79,20,2,0,20,11,10,72,71,7,1,71,24,5,20,79,10,8,27,68,6,12,7,2,31,16,2,11,74,71,94,86,71,45,17,19,79,16,8,79,5,11,3,68,16,7,11,71,13,1,11,6,1,17,10,0,71,7,13,10,79,5,9,11,68,6,12,7,2,31,16,2,11,68,15,6,9,75,79,12,2,79,3,6,25,1,71,27,12,2,79,22,14,8,12,19,79,16,8,79,6,2,12,11,10,10,68,4,7,13,11,11,22,2,1,68,8,9,68,32,0,0,73,79,85,84,79,48,15,10,29,71,14,22,2,79,22,2,13,11,21,1,69,71,59,12,14,28,68,14,28,68,9,0,16,71,14,68,23,7,29,20,6,7,6,3,68,5,6,22,19,7,68,21,10,23,18,3,16,14,1,3,71,9,22,8,2,68,15,26,9,6,1,68,23,14,23,20,6,11,9,79,11,21,79,20,11,14,10,75,79,16,15,6,23,71,29,1,5,6,22,19,7,68,4,0,9,2,28,68,1,29,11,10,79,35,8,11,74,86,91,68,52,0,68,19,7,1,71,56,11,21,11,68,5,10,7,6,2,1,71,7,17,10,14,10,71,14,10,3,79,8,14,25,1,3,79,12,2,29,1,71,0,10,71,10,5,21,27,12,71,14,9,8,1,3,71,26,23,73,79,44,2,79,19,6,28,68,1,26,8,11,79,11,1,79,17,9,9,5,14,3,13,9,8,68,11,0,18,2,79,5,9,11,68,1,14,13,19,7,2,18,3,10,2,28,23,73,79,37,9,11,68,16,10,68,15,14,18,2,79,23,2,10,10,71,7,13,20,79,3,11,0,22,30,67,68,19,7,1,71,8,8,8,29,29,71,0,2,71,27,12,2,79,11,9,3,29,71,60,11,9,79,11,1,79,16,15,10,68,33,14,16,15,10,22,73
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@ -14,9 +14,10 @@ USING: definitions io io.files kernel math math.parser project-euler.ave-time
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project-euler.037 project-euler.038 project-euler.039 project-euler.040
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project-euler.041 project-euler.042 project-euler.043 project-euler.044
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project-euler.045 project-euler.046 project-euler.047 project-euler.048
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project-euler.052 project-euler.053 project-euler.056 project-euler.067
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project-euler.075 project-euler.079 project-euler.092 project-euler.097
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project-euler.134 project-euler.169 project-euler.173 project-euler.175 ;
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project-euler.052 project-euler.053 project-euler.056 project-euler.059
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project-euler.067 project-euler.075 project-euler.079 project-euler.092
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project-euler.097 project-euler.134 project-euler.169 project-euler.173
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project-euler.175 ;
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IN: project-euler
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<PRIVATE
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