Paper 2023/1014

An Efficient Data-Independent Priority Queue and its Application to Dark Pools

Abstract

We introduce a new data-independent priority queue which supports amortized polylogarithmic-time insertions and constant-time deletions, and crucially, (non-amortized) constant-time \textit{read-front} operations, in contrast with a prior construction of Toft (PODC'11). Moreover, we reduce the number of required comparisons. Data-independent data structures - first identified explicitly by Toft, and further elaborated by Mitchell and Zimmerman (STACS'14) - facilitate computation on encrypted data without branching, which is prohibitively expensive in secure computation. Using our efficient data-independent priority queue, we introduce a new privacy-preserving dark pool application, which significantly improves upon prior constructions which were based on costly sorting operations. Dark pools are securities-trading venues which attain ad-hoc order privacy, by matching orders outside of publicly visible exchanges. In this paper, we describe an efficient and secure dark pool (implementing a full continuous double auction), building upon our priority queue construction. Our dark pool's security guarantees are cryptographic - based on secure multiparty computation (MPC) - and do not require that the dark pool operators be trusted. Our approach improves upon the asymptotic and concrete efficiency attained by previous efforts. Existing cryptographic dark pools process new orders in time which grows linearly in the size of the standing order book; ours does so in polylogarithmic time. We describe a concrete implementation of our protocol, with malicious security in the honest majority setting. We also report benchmarks of our implementation, and compare these to prior works. Our protocol reduces the total running time by several orders of magnitude, compared to prior secure dark pool solutions.