[messaging] symmetric cyphers with independent key material

Jeff Burdges burdges at gnunet.org
Tue Oct 20 10:02:02 PDT 2015

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

Anything like this exist? 

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