Cryptology Polygraphic Substitution

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For a fixed l in each step an l-gram (block of l letters) is encrypted at once.

Bigraphic Substitution

As simplest example we consider bigraphic substitution. Here pairs of letters are encrypted together. The easiest description of the cipher is by a large square of sidelength = the number of letters. This is the key.

An example for the standard alphabet:

The earliest historical example was given by PORTA in 1563. His bigram table however contained strange symbols meeting the spirit of the time. For a picture look here.

The earliest use of letter pairs in ciphertext for letter pairs in plaintext seems to be by WHEATSTONE in the 1850s.

Properties of the Polygraphic Substitution

1. The key space is the set of all permutations of pairs of letters. It has a huge number of elements. (Of course one also could restrict the keys to a subspace.) The effective key length for a 26 letter alphabet is about 4500. Exhaustion surpasses all present or future computer capacity.
   
   
2. Compared with a monoalphabetic (and monographic) substitution the frequency distribution of single letters is flattened down. A statistical analysis therefore must resort to bigram frequencies and is a lot harder. Pattern recognition and search for probable words also is harder, but not so much. Also more general attacks with known plaintext are feasible.
   
   
3. We may interpret a polygraphic substitution of l-grams as a monographic substitution over the "alphabet" of l-grams, that is we interpret l-grams as letters of a superalphabet. The larger l, the more complicated is the cryptanalysis. However for the general polygraphic substitution also the complexity of specifying the key grows exponentially with l. Therefore this encryption method is useful only with a restricted keyspace.
   A bigraphic example from history is the [Wikipedia link] PLAYFAIR cipher, invented by WHEATSTONE.
   
   
4. Polygraphic substitutions are the predecessors of modern block ciphers.