A method of securely accessing a database with sensitive data, such as the clinical information of patients, by a client in a privacy-preserving manner, including: communicating with the server to obtain tags for specific attribute-value pairs when the client is authorized to make a query; imposing a tag quota per client and restricting tag generation to authorized query terms with valid digital signatures from a third-party authority; storing the tags and their associated query terms in confidence for future queries; sending a combination of tags that define the terms of a conjunctive query over a secure channel to a proxy; receiving from the proxy encrypted coefficients of a polynomial whose roots are indices to the query results; decrypting the encrypted coefficients in a first protocol with the server; calculating the roots of the polynomial based upon the decrypted coefficients and discarding any superfluous roots; obtaining the encrypted records associated with the calculated roots from the proxy; and decrypting the encrypted records in a second protocol with the server.

This document describes systems and techniques for using cryptography, secret sharing, secure MPC, garbled circuits, and oblivious transfer to select digital components in ways that preserve user privacy and protects the security of data of each party that is involved in the selection process. A method includes obtaining, by a first computer of a secure multi-party computation (MPC) system, at least a first share of user data related to a user of a client device. For each digital component in a set, a first secret share of a condition bit for the condition is obtained for each of one or more conditions that condition eligibility of the digital component for distribution. A garbled circuit is executed to select a given digital component for which each of the one or more conditions of the digital component is satisfied using the first secret share and the second secret share for each condition.

Background-share a one-time pad key from a first location to a second location over a secure background channel. Send a message, encrypted with the one-time pad key, from the first location to the second location, over an unsecure channel.

The present disclosure involves methods, apparatus, and systems for processing equality testing in secure multi-party computation (MPC). In one aspect, a method includes, generating, by a first party of the secure MPC, a difference between a secret share of a first value and a secret share of a second value. During a first iteration, the difference is partitioned into N sections each including M bits. For each section, a random bit is generated, a group of 2.sup.M bits are generated based on the random bit, and a selected bit from the group of 2.sup.M bits is sent to a second party of the secure MPC based on oblivious transfer (OT) protocol. The random bits of the N sections are concatenated as an input of a second iteration. The method further includes determining whether the first value equals the second value based on performing a plurality of iterations.