Distributed Verification of Mixing - Local Forking Proofs Model
Jacek Cichon, Marek Klonowski, Miroslaw Kutylowski
Wroclaw University of Technology
One of generic techniques to achieve anonymity is to process messages through a batch
of cryptographic mixes. In order to guarantee proper execution verifiable mixes are
constructed: each mix provides a proof of correctness together with its output.
However, if a mix is working on a huge number of messages at a time, the proof itself
is huge since it concerns processing all messages. So in practice only a few verifiers
would download the proofs and in turn we would have to trust what they are saying.
We consider a different model in which there are many verifiers, but each of them
is going to download only a limited number of bits in order to check the mixes. Distributed
character of the process ensures effectiveness even if many verifiers are
dishonest and do not report irregularities found.
We concern a fully distributed and intuitive verification scheme which we call
local forking proofs. For each intermediate ciphertext a verifier may ask for a proof
that its re-encrypted version is in the output of the mix concerned.
The proof shows that the re-encrypted version is within some subset of k ciphertexts
from the output of the mix, and it can be performed with strong zero-knowledge or
algebraic methods. They should work efficiently concerning communication complexity,
if k is a relatively small constant.
There are many issues concerning stochastic properties of local forking proofs.
In this paper we examine just one: we estimate quite precisely
how many mixes are required so that if a local proof is provided for each message, then
a plaintext hidden in an input message can appear on any position of the final output set.
paper accepted for Australasian Conference on Information Security and Privacy (ACISP 2008)