We introduce a secure data-independent priority queue which supports polylogarithmic-time insertion operations and constant-time deletions and read-front (aka peek) operations as opposed to the originally introduced queue by Toft (PODC '11). Moreover, we minimize the number of comparisons required to perform different operations on Toft's priority queue. Data-independent data structures—first identified explicitly by Toft, and further elaborated by Mitchell and Zimmerman (STACS '14)—serve the purpose of computing on encrypted data without executing branching code which can be used to avoid prohibitively expensive operations in secure computation applications. Focusing on the costly sorting operations, we show significant asymptotic improvements over prior privacy preserving dark pool applications. Dark pools are securities-trading venues which attain ad-hoc order privacy, by matching orders outside of publicly visible exchanges via the so-called dark pool operators. In this paper, we describe an efficient and secure dark pool (implementing a full continuous double auction) based on our new priority queue. Our construction's security guarantees are cryptographic based on secure multiparty computation (MPC), and do not require that the dark pool operators are trusted. Our construction improves upon the asymptotic 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 MPC protocol with malicious security in the honest majority setting. We also report benchmarks of our implementation and compare them to prior works. Our protocol reduces the total running time by several orders of magnitude over prior secure dark pool solutions.

Anonymous Zether, proposed by Bünz, Agrawal, Zamani, and Boneh (FC’20), is a private payment design whose wallets demand little bandwidth and need not remain online; this unique property makes it a compelling choice for resource-constrained devices. In this work, we describe an efficient construction of Anonymous Zether. Our protocol features proofs which grow only logarithmically in the size of the "anonymity sets" used, improving upon the linear growth attained by prior efforts. It also features competitive transaction sizes in practice (on the order of 3 kilobytes).Our central tool is a new family of extensions to Groth and Kohlweiss’s one-out-of-many proofs (Eurocrypt 2015), which efficiently prove statements about many messages among a list of commitments. These extensions prove knowledge of a secret subset of a public list, and assert that the commitments in the subset satisfy certain properties (expressed as linear equations). Remarkably, our communication remains logarithmic; our computation increases only by a logarithmic multiplicative factor. This technique is likely to be of independent interest.We present an open-source, Ethereum-based implementation of our Anonymous Zether construction.