Privacy-preserving computing with third-party service

A computer-implemented method, comprising:

• at a third computing entity:
• obtaining, from a first computing entity, a first cryptographically protected data set comprising a first set generated based on cryptographic material shared between the first computing entity and a second computing entity;
• obtaining, from the second computing entity, a second cryptographically protected data set comprising:
• a second set generated based on the cryptographic material;
• and
• a plurality of encrypted data elements generated according to a homomorphic encryption scheme that correspond to the second set;
• performing a join, based on the first cryptographically protected data set and the second cryptographically protected data set, to identify a collection of one or more encrypted data elements;
• performing, according to the homomorphic encryption scheme, one or more privacy-preserving computations using the collection of one or more encrypted data elements;
• and
• providing an encrypted result of the one or more computations to the second computing entity.

A non-transitory computer-readable storage medium storing executable instructions that, as a result of being executed by one or more processors of a computer system, cause the computer system to at least:

• establish a first cryptographic secret with a second computer system;
• obtain a first data set comprising a plurality of rows of data elements;
• determine a cryptographically protected first data set by at least:
• cryptographically protecting a first portion of the first data set using the first cryptographic secret;
• and
• homomorphically encrypting a second portion of the first data set using a second cryptographic secret and according to a homomorphic encryption scheme;
• shuffling the plurality of rows;
• provide, to a third computer system and according to a multiparty computation (MPC) protocol, the cryptographically protected first data set to cause the third computer system to perform one or more privacy-preserving computations based on the first cryptographically protected data set and a second cryptographically protected data set generated by the second computer system, wherein:
• the second cryptographically protected data set is also generated based on the first cryptographic secret;
• and
• the third computer system lacks access to the first cryptographic secret;
• obtain an encrypted result of the one or more privacy-preserving computations performed based on the first cryptographically protected data set and the second cryptographically protected data set;
• and
• decrypt the encrypted result to obtain a plaintext result.