# Classical ciphers and historical development

The term classical ciphers refers to encryption techniques which have become well-known over time, and generally created prior to the second half of the twentieth century' (in some cases, many hundreds of years earlier). Many classical techniques are variations of simple substitution and simple transposition. Some techniques that are not technically block ciphers are also included here for convenience and context.

Classical ciphers and techniques are presented under §7.3 for historical and pedagogical reasons only. They illustrate important basic principles and common pitfalls. However, since these techniques are neither sophisticated nor secure against current cryptanalytic capabilities, they are not generally suitable for practical use.

## Transposition ciphers (background)

For a simple transposition cipher with fixed period t, encryption involves grouping the plaintext into blocks of t characters, and applying to each block a single permutation e on the numbers 1 through t. More precisely, the ciphertext corresponding to plaintext block m = mi... mt is c = Ee(m) = me(X)... me(ty The encryption key is e, which implicitly defines t the key space К has cardinality f! for a given value t. Decryption involves use of the permutation d which inverts e. The above corresponds to Definition 1.32.

The mathematical notation obscures the simplicity of the encryption procedure, as is evident from Example 7.43.

7.43 Example (simple transposition) Consider a simple transposition cipher with t = 6 and

e = (6 4 1 3 5 2). The message m = CAESAR is encrypted to c = RSCEAA. Decryption uses the inverse permutation d = (3 64251). The transposition may be represented by a two-row matrix with the second indicating the position to which the element indexed by the corresponding number of the first is mapped to: (3 g 4 11) - Encryption may be done by writing a block of plaintext under headings “3 6 4 2 5 1”, and then reading off the characters under the headings hr numerical order. □

7.44 Note (terminology: transposition vs. permutation) While the term “transposition” is traditionally used to describe a transposition cipher, the mapping of Example 7.43 may alternately be called a permutation on the set {1,2,... ,6}. The latter terminology is used, for example, in substitution-permutation networks, and in DES (§7.4).

A mnemonic keyword may be used hr place of a key, although this may seriously decrease the key space entropy. For example, for n = 6, the keyword “CIPHER” could be used to specify the column ordering 1, 5,4, 2, 3, 6 (by alphabetic priority).

• 7.45 Definition Sequential composition of two or more simple transpositions with respective periods ti,t2, ■ ■ ■ ■ t, is called a compound transposition.
• 7.46 Fact The compound transposition of Definition 7.45 is equivalent to a simple transposition of period t = lcm(ti,... , fj).
• 7.47 Note (recognizing simple transposition) Although simple transposition ciphers alter dependencies between consecutive characters, they are easily recognized because they preserve the frequency distribution of each character.