Secret Sharing, Multi-Party Protocols, and Computational Differential Privacy
Stub. Statistical zero-knowledge with multiple (possibly colluding) verifiers and secret sharing as the tool that makes it work; PRIO's use of secret sharing for private, verifiable aggregate statistics across many clients with no trusted aggregator; and multi-party and computational differential privacy, which relax the central-curator and information-theoretic assumptions of standard DP respectively.
Corresponds to CS/ECE 598DA, Weeks 9–10. Extending zero-knowledge to multiple verifiers (who might pool information to learn more than any single verifier could) needs a way to split trust among them, which is exactly what secret sharing provides: split a secret into shares such that only a sufficiently large subset can reconstruct it, with smaller subsets learning nothing. PRIO applies this directly to privacy- preserving aggregate statistics: clients secret-share their individual data across a small set of non-colluding servers, each server performs computation on its own shares, and only the final aggregate is ever reconstructed. Multi-party differential privacy drops the trusted-curator assumption of central DP (replacing it with a multi-party protocol, echoing privacy-for-distributed-computing‘s local model but with parties cooperating cryptographically rather than randomizing in isolation), while computational differential privacy relaxes DP’s information-theoretic indistinguishability to indistinguishability against computationally bounded adversaries, the same relaxation public-key-encryption-schemes makes to classical perfect secrecy.
Outline (TODO — flesh out each)
- Secret sharing
- Statistical zero-knowledge with multiple verifiers
- PRIO — private, verifiable aggregate statistics
- Multi-party differential privacy
- Computational differential privacy