Zeyu Liu
Yale University

Katerina Sotiraki
Yale University

Eran Tromer
Boston University

Yunhao Wang
Yale University

Keywords:

Abstract

Oblivious message retrieval (OMR) allows resource-limited recipients to outsource the message retrieval process without revealing which messages are pertinent to which recipient. Its realizations in recent works leave an open problem: can an OMR scheme be both practical and provably secure against spamming attacks by malicious senders (i.e., DoS-resistant) under standard assumptions?

In this paper, we present DoS-PerfOMR: a provably DoS-resistant OMR construction that is 12x faster than OMRp2 (a conjectured DoS-resistant OMR construction in prior works), and (almost) matches the performance of the state-of-the-art OMR scheme that is not DoS-resistant (proven by the attacks we show).

To achieve this, we analyze the snake-eye resistance property for general PKE schemes, i.e., whether it is hard to encrypt an identical message under two public keys. We construct a new lattice-based PKE scheme: LWEmongrass, that is provably snake-eye resistant and has better efficiency than the PVW scheme underlying OMRp2. We also show that natural candidates (e.g., RingLWE PKE) are not snake-eye resistant.

Furthermore, we show that a snake-eye resistant PKE scheme implies a robust PKE scheme, thus introducing the first robust lattice-based PKE scheme without relying on the KEM-DEM paradigm, avoiding its inherent inefficiencies.

Of independent interest, we introduce two variants of LWE with side information, as components towards proving the properties of LWEmongrass, and reduce standard LWE to them for the parameters of interest.