Classical Systems

Abstract

In this chapter we shall discuss a number of classical systems. For further reading we refer the interested reader to [Bek82], [Den82], [Kah67], [Kon81] or [Mey82]. One of the oldest cryptosystems is due to Julius Caesar. It shifts each letter in the text cyclicly over k places in the alphabet. In our terminology the Caesar cipher is defined by:

$$ {E_k}\left( i \right) = \left( {i + k} \right)\underline {\bmod } {\text{ }}q,0 \leqslant i < q $$

(2.1)

$$ E = \left\{ {{E_k}|0 \leqslant k < q} \right\} $$

(2.2)

, where i mod n denotes the unique integer j, satisfying j = i mod n and 0 ≤ j < n. In this case the keyspace K is the set {0,1,…,q-1} and D _k = E _q-k . For most practical alphabet sizes the cryp-tanalist can break this system easily by trying all q possible keys. This is called exhaustive key search. For instance, when q = 26 and we use {a,b,..., z} as alphabet, one only has to check 26 possibilities. In Table 2.1 one can find the cryptanalysis of the ciphertext IYBABZ.