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# Conclusions

This chapter deals with ancilliary functions, rather than encryption itself.

However, the idea of converting text from binary form to letters of the alphabet does suggest a way to complicate any attempt to analyze a cipher system. Since such a conversion unavoidably adds a small degree of redundancy to the message being encrypted, as a safety precaution the key used for encryption before conversion and the key used for encryption after conversion should be unrelated.

The various forms of encryption we have seen here can be organized into groups based on common properties: I once essayed to classify the ciphers of the first four chapters, ciphers other than public-key systems, by the following scheme, based on the kind of operations performed on the plaintext:

• Transposition: pure transposition ciphers, such as double columnar
• Substitution
• Single-character ciphers
• Displacement: the Caesar cipher
• Substitution: monalphabetic substitution
• Polygraphic ciphers
• Convolution and Substitution
• (includes transposition - exchange of column coordinates, or displacement - two characters in same row or column): Playfair
• (variation of displacement and trivial convolution - the XOR with the f-function output, with embedded variation of substitution within the f-function itself): DES in ECB mode
• Convolution and Transposition and Substitution
• Fractionation
• Stream ciphers: plain
• Variation of Displacement: Vigenere, Porta, Beaufort, DES in OFB mode, Hagelin lug and pin machines
• (with trivial convolution): Vernam two-tape system, Lorenz Schlusselzusatz, additive superenciphered code
• Stream ciphers: fancy
• Substitution and Variation of Displacement: most rotor machines, DES in CBC or PCBC mode
• (with trivial convolution): Hagelin B-21, B-211
• Variation of Substitution: Cypher SA, PURPLE, HC-9
• (with embedded transposition): Dynamic Substitution
• (by means of transposition, trivial convolution, and variation of displacement): Siemens and Halske T52
• Variation of Substitution and Variation of Displacement: Bazeries Cylinder

This form of classification only, however, addresses one dimension in which ciphers vary. Another classification has been mentioned in a previous section in the current chapter, which does include public-key systems:

• The one-time pad requires the previous exchange of an amount of key that corresponds exactly to the quantity of messages to be transmitted.
• A conventional, or symmetric-key, cipher can protect a large volume of messages with one small key, without a clear boundary beyond which further messages become insecure.
• A public-key cipher can allow two parties to communicate securely without any previous contact for the exchange of key material.

Also, the first classification is based on what happens to the plaintext. But when stream ciphers are classified, while the classification takes into account what changes as successive letters or bits or blocks are enciphered, how the changes are determined was ignored. A classification of stream ciphers based on this dimension might look like this:

• Repeating key: Vigenere
• Multiple repeating keys: Vernam two-tape system, Hagelin lug and pin machines
• Chained repeating keys: most rotor machines, PURPLE
• (with other elements): SIGABA, Converter M-228
• Cyclically encrypted key: DES in OFB mode
• Reservoir system: Alleged RC4, MacLaren-Marsaglia PRNG, Dynamic Substitution
• Autokey: Vigenere autokey, Cypher SA
• Random key: Bazeries cylinder, one-time-pad

however, this classification is little more than a listing of methods commonly in use.

Another way of looking at the deficiency in the first classification that this one attempts to remedy is that the first classification is based on the operation performed directly on the plaintext to produce ciphertext.

But that operation may not be the principal difficulty in cracking a cipher.

For example, let us compare these two ciphers:

• A standard rotor machine cipher
• A Vigenère autokey, in which each letter is enciphered by means of the Vigenère tableau with the key letter being the encipherment of the previous letter of the message...by the exact same rotor machine as used to encipher the message itself in the previous example cipher.

Thus, all the workings of a cipher need to be considered in classifying it.

I originally composed the classification of ciphers which appears first on this page to illustrate my own view of how cipher systems should be categorized, as a response to the classification entitled "A Cipher Taxonomy", by Terry Ritter. That illustrates another approach to the classification of different types of cipher.

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