Re: Note on general application of Feistel's technique

On 2010-07-22, Mok-Kong Shen <mok-kong.shen@xxxxxxxxxxx> wrote:

In DES, in which Feistel's technique was first commonly known,
a block is divided to two fields B_1 and B_2 and one of the basic
operations in the algorithm is e.g.:

B_2 = F1(B_1) ^ B_2

where F1 is a key-dependent non-linear function which is
different for different rounds (via the different round keys).

This means that in the general case, where there are, say, three

No this does not mean that at all. There is no reason to have say three
fields. It is liable to require more work for worse security.

fields B_1, B_2 and B_3, the 'natural' operations corresponding
to the above will be:

B_2 = F1(B_1) ^ B_2 B_3 = F1(B_1) ^ B_3

Below we'll say that in the above B_1 is the pivot field in the
operation. After the above F2(B_2) will be computed to xor B_1
and B_3, i.e. B_2 will be the pivot field, etc.

There is a tiny possibility of variation of the scheme for a block
having m fields B_i with i in [1,m], namely the sequence of pivot
fields for a block of m fields need not be in the natural order
1, 2, ... m but may be a key-dependent permutation of that and, if
the algorithm has h such permutations being used in succession in
the procesing of a block, these h permutations may be all different.

Why? Operations in cryptography need to be justified.

Eg, in the limit we do single bit operations. And have a weak cypher.




M. K. Shen

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