Editing Autokey cipher (section)

==Cryptanalysis==
Autokey ciphers are somewhat more secure than polyalphabetic ciphers that use fixed keys since the key does not repeat within a single message. Therefore, methods like the [[Kasiski examination]] or [[index of coincidence]] analysis will not work on the ciphertext, unlike for similar ciphers that use a single repeated key.<ref name="hoffstein" >{{cite book |title=An Introduction to Mathematical Cryptography |first1=Jeffrey |last1=Hoffstein |first2=Jill |last2=Pipher |first3=Joseph |last3=Silverman |publisher=Springer |url=https://books.google.com/books?id=cbl_BAAAQBAJ&pg=PA288 |date=2014|isbn=9781493917112
| page=288
}}</ref>

A crucial weakness of the system, however, is that the plaintext is part of the key. That means that the key will likely contain common words at various points. The key can be attacked by using a dictionary of common words, [[bigram]]s, [[trigram]]s etc. and by attempting the decryption of the message by moving that word through the key until potentially-readable text appears.

Consider an example message <code>meet at the fountain</code> encrypted with the primer keyword <code>KILT</code>:<ref>{{cite web|url=http://asecuritysite.com/security/Coding/autokey?word=meetatthefountain%2Ckilt |title=Autokey Calculator |publisher=Asecuritysite.com |access-date=2012-12-26 |url-status=dead |archive-url=https://web.archive.org/web/20131203104209/http://asecuritysite.com/security/Coding/autokey?word=meetatthefountain%2Ckilt |archive-date=2013-12-03 }}</ref> To start, the autokey would be constructed by placing the primer at the front of the message:

 plaintext:  meetatthefountain
 primer:     KILT
 autokey:    KILTMEETATTHEFOUN

The message is then encrypted by using the key and the substitution alphabets, here a tabula recta:

 plaintext:  meetatthefountain
 key:        KILTMEETATTHEFOUN
 ciphertext: WMPMMXXAEYHBRYOCA

The attacker receives only the ciphertext and can attack the text by selecting a word that is likely to appear in the plaintext. In this example, the attacker selects the word <code>the</code> as a potential part of the original message and then attempts to decode it by placing <code>THE</code> at every possible location in the key:

 cipher: WMP MMX XAE YHB RYO CA 
 key:    THE THE THE THE THE ..
 plain:  dfl tft eta fax yrk ..
 
 cipher: W MPM MXX AEY HBR YOC A
 key:    . THE THE THE THE THE .
 plain:  . tii tqt hxu oun fhy .
 
 cipher: WM PMM XXA EYH BRY OCA
 key:    .. THE THE THE THE THE
 plain:  .. wfi eqw lrd iku vvw

In each case, the resulting plaintext appears almost random because the key is not aligned for most of the ciphertext. However, examining the results can suggest locations of the key being properly aligned. In those cases, the resulting decrypted text is potentially part of a word. In this example, it is highly unlikely that <code>dfl</code> is the start of the original plaintext and so it is highly unlikely either that the first three letters of the key are <code>THE</code>. Examining the results, a number of fragments that are possibly words can be seen and others can be eliminated. Then, the plaintext fragments can be sorted in their order of likelihood:

 unlikely ←—————————→ promising
 eqw dfl tqt ... ... eta oun fax

A correct plaintext fragment is also going to appear in the key, shifted right by the length of the keyword. Similarly, the guessed key fragment (<code>THE</code>) also appears in the plaintext shifted left. Thus, by guessing keyword lengths (probably between 3 and 12), more plaintext and key can be revealed.

Trying that with <code>oun</code>, possibly after wasting some time with the others, results in the following:

 shift by 4:
 ciphertext: WMPMMXXAEYHBRYOCA
 key:        K.LTM.ETA.THE.OUN
 plaintext:  m.eta.the.oun.ain

 shift by 5:
 ciphertext: WMPMMXXAEYHBRYOCA
 key:        SWT..EQW..THE..OU
 plaintext:  eqw..the..oun..og

 shift by 6:
 ciphertext: WMPMMXXAEYHBRYOCA
 key:        D...TQT...THE...O
 plaintext:  t...the...oun...m

A shift of 4 can be seen to look good (both of the others have unlikely Qs either in the plaintext or in the keyword).

A lot can be worked with now. The keyword is probably 4 characters long (<code>K.LT</code>), and some of the message is visible:

 m.eta.the.oun.ain

Because the plaintext guesses have an effect on the key 4 characters to the left, feedback on correct and incorrect guesses is given. The gaps can quickly be filled in, giving both the plaintext and the keyword:

 meetatthefountain
 KILT

The ease of [[cryptanalysis]] is caused by the feedback from the relationship between plaintext and key. A three-character guess reveals six more characters (three on each side), which then reveal further characters, creating a cascade effect. That allows incorrect guesses to be ruled out quickly.