Abstract: 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.

Abstract: Methods and systems for implementing secure aggregation with one-shot clients are described herein. A server receives, from each client, (i) an encrypted client input represented by a client input encrypted by a Key-Additive Homomorphic Encryption (KAHE) scheme using a client key, and (ii) an encrypted client key represented by the client key encrypted by an Additive Homomorphic Encryption (AHE) scheme using a public key received by the client from a decryptor. The server adds the encrypted client input to a combination (e.g., a running sum) of encrypted client inputs received from at least some of the clients. The server further adds the encrypted client key to a combination (e.g., a running sum) of encrypted client keys received from the clients which supplied their client inputs to the server. The server then transmits, to the decryptor, the running sum of encrypted client keys.

Abstract: 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.

Abstract: A method for outsourcing exponentiation in a private group includes executing a query instruction to retrieve a query element stored on an untrusted server by selecting a prime factorization of two or more prime numbers of a modulus associated with the query element stored on the server, obtaining a group element configured to generate a respective one of the prime numbers, generating a series of base values using the prime factorization and the group element, and transmitting the series of base values from the client device to the server. The server is configured to determine an exponentiation of the group element with an exponent stored on the server using the series of base values. The method also includes receiving a result from the server based on the exponentiation of the group element with the exponent.

Abstract: Provided are systems and methods for the computation of sparse, (?, ?)-differentially private (DP) histograms in the two-server model of secure multi-party computation (MPC). Example protocols enable two semi-honest non-colluding servers to compute histograms over the data held by multiple users, while only learning a private view of the data.

Abstract: A method for outsourcing exponentiation in a private group includes executing a query instruction to retrieve a query element stored on an untrusted server by selecting a prime factorization of two or more prime numbers of a modulus associated with the query element stored on the server, obtaining a group element configured to generate a respective one of the prime numbers, generating a series of base values using the prime factorization and the group element, and transmitting the series of base values from the client device to the server. The server is configured to determine an exponentiation of the group element with an exponent stored on the server using the series of base values. The method also includes receiving a result from the server based on the exponentiation of the group element with the exponent.

Abstract: A method for outsourcing exponentiation in a private group includes executing a query instruction to retrieve a query element stored on an untrusted server by selecting a prime factorization of two or more prime numbers of a modulus associated with the query element stored on the server, obtaining a group element configured to generate a respective one of the prime numbers, generating a series of base values using the prime factorization and the group element, and transmitting the series of base values from the client device to the server. The server is configured to determine an exponentiation of the group element with an exponent stored on the server using the series of base values. The method also includes receiving a result from the server based on the exponentiation of the group element with the exponent.

Abstract: A method for outsourcing exponentiation in a private group includes executing a query instruction to retrieve a query element stored on an untrusted server by selecting a prime factorization of two or more prime numbers of a modulus associated with the query element stored on the server, obtaining a group element configured to generate a respective one of the prime numbers, generating a series of base values using the prime factorization and the group element, and transmitting the series of base values from the client device to the server. The server is configured to determine an exponentiation of the group element with an exponent stored on the server using the series of base values. The method also includes receiving a result from the server based on the exponentiation of the group element with the exponent.