Re: [NEWBIE]vigenere

Kristian Gjøsteen wrote:
> Sebastian Gottschalk <seppi@seppig.de> wrote:
>> Kristian Gjøsteen wrote:
>>> Sebastian Gottschalk <seppi@seppig.de> wrote:
>>>> A perfect cipher is isomorph to addition within a group,
>>> What exactly does this sentence mean? I cannot at first reading
>>> distinguish it from nonsense.
>> Any cipher that is perfectly secure in terms of Shannon information
>> theory can be expressed / is strictly isomorph to the operation of
>> adding a randomly chosen key to the plaintext, assuming that the base
>> mathematical structure is a group and all values are uniformly
>> distributed. Hence One Time Pad.
>
> Let the alphabet be a group with more than two elements. The set
> of keys is the set of sequences of permutations of the alphabet.
> Encrypt by applying the permutations in sequence. Decrypt by applying
> the inverse permutations.
>
> This is clearly a perfect cipher, yet it is not "isomorphic" (for
> any reasonable value of "isomorphic" that I can think of) to the
> cipher that adds a random sequence to the plaintext.

As permutations are an (even associative) group with their sequential
application as operation, this is exactly an isomorphism.
Received on Tue Jan 17 16:50:38 2006