Solving the Byzantine Postman Problem

Over the last several decades, there have been numerous systems proposed which aim to preserve the anonymity of the recipient of some data. Some have involved trusted third-parties or trusted hardware; others have been constructed on top of link-layer anonymity systems or mix networks. In this paper, we examine the Pynchon Gate [34], a pseudonymous message system which takes an alternate approach to this problem by using Private Information Retrieval (PIR) as the basis for its pseudonymity properties. We restrict our examination to a flaw in the Pynchon Gate system first described in our technical report [35]; as it was originally presented, the Pynchon Gate detects the presence of (and protects against certain attacks by) Byzantine servers operating in the system, but it fails to identify which server or set of servers is Byzantine, thus opening the door for denial of service attacks as well as other potential anonymity compromises by Byzantine servers. We show a trivial modification to the original PynGP which allows for detection and identification of Byzantine nodes, with no weakening of the security model necessary, at the relatively affordable cost of greater bandwidth requirements during certain communication operations. We demonstrate that this adequately solves the problems raised by [35], and argue that it is the most suitable method of addressing the attack in question yet proposed. We then evaluate an alternate approach to solving to the problem described in [35], proposed by Goldberg in his recent paper [21]. We compare the security and performance trade-offs made in that proposal, and find it less secure against anonymity attacks as compared to the original (but flawed) Pynchon Gate Protocol (PynGP) [24] presented in the first Pynchon Gate paper. We show that this proposal is significantly weaker than the solution offered in this paper, which retains the security properties of the original Pynchon Gate Protocol.