Breaking and (Partially) Fixing Provably Secure Onion Routing

After several years of research on onion routing, Camenisch and Lysyanskaya, in an attempt at rigorous analysis, defined an ideal functionality in the universal composability model, together with properties that protocols have to meet to achieve provable security. A whole family of systems based their security proofs on this work. However, analyzing HORNET and Sphinx, two instances from this family, we show that this proof strategy is broken. We discover a previously unknown vulnerability that breaks anonymity completely, and explain a known one. Both should not exist if privacy is proven correctly. In this work, we analyze and fix the proof strategy used for this family of systems. After proving the efficacy of the ideal functionality, we show how the original properties are flawed and suggest improved, effective properties in their place. Finally, we discover another common mistake in the proofs. We demonstrate how to avoid it by showing our improved properties for one protocol, thus partially fixing the family of provably secure onion routing protocols. ‡ This work in parts was carried out while affiliated with TU Dresden. 1 according to https://metrics.torproject.org/userstats-relay-country.html 2 Understanding of OR varied in the field. To be compliant with the terms of [8], we understand OR in this work as a free-route Chaumian MixNet [10] without requiring that messages are delayed. This conforms with the understanding of [21] and [16] except that circuits are excluded.