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## 10.1 Types of operations

All block cipher operations are actually made up of conceptually simpler building blocks. Usually, the elements of V are represented as strings of a fixed length n out of an alphabet A, while elements of K are also represented as strings of some length k in the same alphabet (k < n).

There is one obvious way to obtain a permutation of V and that is to apply a permutation in Permn to permute the elements of the string. Such an operation is called a Transposition'' (which is confusing for group theorists familiar with the notion of transpositions as elements of the permutation group that interchange two elements!). Another obvious way to obtain a permutation on V is apply a permutation in Perm(A). Such an operation is called a Substitution'' since it substitutes one letter of the alphabet with another. It is clear that Substitutions and Transpositions commute with one another and form the subgroup Permn×Perm(A) of Perm(V). Thus, a cryptanalyst (or code cracker'') could try to solve the problem of finding the Substitution and Transposition independently, thus weakening the cryptosystem. Thus we need another operation that mixes'' the Substitutions with the Transpositions; appropriately this is known as Mixing''. One method used for mixing is Polyalphabetic'' Substitution; different substitutions rules are applied to different portions of the string; in addition a Transposition of these different portions can also be performed. A different procedure is break the string into words'' of m letters'' in the alphabet and directly find a nice permutation that performs Word substitution'' (using a code book'' for example).

Now only some of these operations need to depend on the key and the operations can be repeated in multiple rounds'' since the new collection is not commutative anymore (because of Mixing).

Next: 10.2 Modes of enciphering Up: 10 Symmetric Cryptosystems Previous: 10 Symmetric Cryptosystems
Kapil Hari Paranjape 2002-10-20