Cryptology Autokey Ciphers

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The first one to propose autokey ciphers was BELLASO in 1564. Also this cipher is often attributed to VIGENÈRE.

Encryption and Decryption

The key is a string of a certain length l. To the key the plaintext is appended, the last l letters chopped. In this way we get a keytext of the same length as the plaintext.

This keytext is used for a running-text encryption.

Example: (l = 2, key = XY)

    P L A I N T E X T
    X Y P L A I N T E
    -----------------
    M J P T N B R Q X

A Perl program is here.

Remark: Instead of the standard alphabet (or the TRITHEMIUS table) one could also use a permuted primary alphabet.

Approaches to Cryptanalysis

The four most promising approaches are:

1. Exhaustion for small key length
   
   
2. Interpretation as running-key cipher from position l, in case of a key word or phrase from the plaintext language, even from the beginning of the ciphertext:
   1. Probable word and zigzag exhaustion
   2. Frequent word fragments
   3. Frequency analysis
   4. Frequent letter combinations
   The repetition of the plaintext in the key makes the task considerably easier compared with a proper running-key cipher.
   
   
3. Similarity with the TRITHEMIUS-BELLASO cipher, see Section 8 below
   
   
4. Algebraic cryptanalysis (for known plaintext): Solving equations, see the mathematical complement

Ciphertext Autokey

Using ciphertext instead of plaintext as extension of the l-letter key is a useless variant, but also proposed by VIGENÈRE. We only describe it by an example:

    P L A I N T E X T
    X Y M J M R Z K D
    -----------------
    M J M R Z K D H W

Exercise. Give a formal description of this cipher. Why is cryptanalysis almost trivial? Work out an algorithm for cryptanalysis.

Exercise. Apply this algorithm to the cryptogram

   IHTYE VNQEW KOGIV MZVPM WRIXD OSDIX FKJRM HZBVR TLKMS FEUKE
   VSIVK GZNUX KMWEP OQEDV RARBX NUJJX BTMQB ZT

Remark. Using a nonstandard alphabet makes this cipher a bit stronger.