ABSTRACT
In order to properly describe the DES cryptosystem, we need more mathematically oriented definitions of transposition and substitution ciphers than we have considered thus far.
Block ciphers, defined on page 91, are classically broken into two types, the first of which is described as follows. Note that, in the following, if S is a finite set, then a permutation on S is a bijection σ : S !→ S. Definition 3.1 Transposition/Permutation Ciphers
A simple transposition cipher, also known as a simple permutation cipher, is a symmetric-key block cryptosystem having blocklength r ∈ N, with keyspace K being the set of permutations on {1, 2, . . . , r}. The enciphering transformation is defined, for each m = (m1,m2 . . . ,mr) ∈M, and given e ∈ K, by
Ee(m) = (me(1),me(2), . . . ,me(r)),
and for each c = (c1, c2, . . . , cr) ∈ C, Dd(c) = De−1(c) = (cd(1), cd(2), . . . , cd(r)).
