Re: A Question of Permutations of Vectors of Bits

From: Mok-Kong Shen (mok-kong.shen_at_t-online.de)
Date: 07/31/03 

Date: Thu, 31 Jul 2003 11:15:25 +0200

Simon G Best wrote:
>
> Mok-Kong Shen wrote:
> >
> > In the above, the first example is a 'substitution',
> > while the second is a 'permutation' (which is in fact
> > a special case of 'substitutions'), anyway as far as
> > the common terminology goes. So, if your problem says
> > 'P is a permutation', then one couldn't have the case
> > of the first example.
> >
> > M. K. Shen
>
> When we say, 'A block cipher's encryption function, with a particular
> key, is a permutation,' what do we mean? It's in that sort of sense
> that P is a permutation.

The problem arose with your saying a permutation of bits,
which one would commonly understand to be a shuffling
of bits. A block cipher maps 2^n blocks, each containing
n bits, to 2^n such blocks. That mapping is a permutation
of the elements (each a block) of a sequence of length
2^n to another such sequence (because a block cipher
does a bijecive mapping). So you should say P is
a block encryption function or P is a bijective mapping
of the space of n-bit entities to itself, in order
to avoid confusion. (You see I am not the single person
who got confused).

M. K. Shen

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