An analysis of parallel mixing with attacker-controlled inputs

Abstract

Parallel mixing [7] is a technique for optimizing the latency of a synchronous re-encryption mix network. We analyze the anonymity of this technique when an adversary can learn the output positions of some of the inputs to the mix network. Using probabilistic modeling, we show that parallel mixing falls short of achieving optimal anonymity in this case. In particular, when the number of unknown inputs is small, there are significant anonymity losses in the expected case. This remains true even if all the mixes in the network are honest, and becomes worse as the number of mixes increases. We also consider repeatedly applying parallel mixing to the same set of inputs. We show that an attacker who knows some input-output relationships will learn new information with each mixing and can eventually link previously unknown inputs and outputs. © Springer-Verlag Berlin Heidelberg 2006.