Paper 2022/1395

Non-Interactive Anonymous Router with Quasi-Linear Router Computation

Abstract

Anonymous routing is an important cryptographic primitive that allows users to communicate privately on the Internet, without revealing their message contents or their contacts. Until the very recent work of Shi and Wu (Eurocrypt’21), all classical anonymous routing schemes are interactive protocols, and their security rely on a threshold number of the routers being honest. The recent work of Shi and Wu suggested a new abstraction called Non-Interactive Anonymous Router (NIAR), and showed how to achieve anonymous routing non-interactively for the first time. In particular, a single untrusted router receives a token which allows it to obliviously apply a permutation to a set of encrypted messages from the senders. Shi and Wu’s construction suffers from two drawbacks: 1) the router takes time quadratic in the number of senders to obliviously route their messages; and 2) the scheme is proven secure only in the presence of static corruptions. In this work, we show how to construct a non-interactive anonymous router scheme with sub-quadratic router computation, and achieving security in the presence of adaptive corruptions. To get this result, we assume the existence of indistinguishability obfuscation and one-way functions. Our final result is obtained through a sequence of stepping stones. First, we show how to achieve the desired efficiency, but with security under static corruption and in a selective, single-challenge setting. Then, we go through a sequence of upgrades which eventually get us the final result. We devise various new techniques along the way which lead to some additional results. In particular, our techniques for reasoning about a network of obfuscated programs may be of independent interest.

Note: The revised version includes all the appendices that contain some of the main results and all of additional results.