Re: commuting?/non-group cipher?

From: Peter Fairbrother (zenadsl6186_at_zen.co.uk)
Date: 10/29/04 

Date: Fri, 29 Oct 2004 08:22:50 +0100

bmm wrote:
 
> I don't see it. But first things first. You originally talked about:
>> E(k3)[P] = E(k1)[E(k2)[P]]
> Just to be explicit, you mean this for all P, right? If so, I would just
> write it as something like E(k3) = E(k1)[E(k2)] to make it clearer that we
> are saying the permutations are equal.
>
> The set S are all of the permutations described by E(k), where the operation
> is composition. Let a = E(k1) and b = E(k2). Then a*b = E(k1) * E(k2), ie
> the permutation defined by P -> E(k1)[E(k2)[P]]. The question is about
> whether this is E(k3) for some k3. This is closure.

Could you explain what you mean by "the operation is composition" please? I
think I am beginning to understand, but that's confusing me.

Thanks, 

-- 
Peter Fairbrother