Re: [NEWBIE]vigenere

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.

-- 
Kristian Gjøsteen