[messaging] symmetric cyphers with independent key material

[Natanael]

Den 20 okt 2015 19:01 skrev "Jeff Burdges" <burdges at gnunet.org>:
> Are there any good symmetric-ish cyphers that involve three or more
> steps with independent key material for each step?
>
> Formally, there should be a function KG(s) that returns a tuple
> (k_1,..,k_n) and a function P(k,d) such that if d_i = P(k_i,d_{i-1})
> then d_n=d_0 but there are no known relationships between strictly
> fewer than n of the k_i.
>
> Stream cyphers provide this for n=2 of course, as the independence
> requirement becomes vacuous, but I'm unaware of anything with n>2
> that's both secure and efficient as a symmetric cypher.
>
> It's okay if we replace P by another operation P' for the i-th step for
> preferably at most one i but we do not want any relationship between
> k_i and k_j for j != i.
>
> One could use secret sharing algorithms, or simply XOR, to do this
> quite securely, but that'd require key material as big as the original
> file, making it inefficient.
>
> There are tricks for doing roughly this with asymmetric systems like
> elliptic curve scalar multiplication, but that's too slow for my
> purposes.

Secret Sharing on the symmetric key? Do you need it to be integrated into
the encryption algorithm itself? Your terminology is a bit unclear to me,
what exactly are you trying to achieve?

Seems like you want to use different subsets of keys for different
plaintexts, in some serial order, maybe? Or am I way off?
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