Implementing Secure Multi-Party Computation

Overview

Secure Multi-Party Computation (SMPC) enables multiple parties to jointly compute a function over their combined inputs while keeping each party's individual input private. No party learns anything beyond the output of the computation and what can be inferred from their own input and the output.

SMPC supports GDPR Article 5(1)(c) data minimization by eliminating the need to centralize data, Article 25(1) data protection by design by building privacy into the computation architecture, and Article 26 joint controller arrangements by enabling collaborative analytics without data sharing.

Core SMPC Techniques

Shamir Secret Sharing

Shamir's Secret Sharing (1979) splits a secret value into n shares such that any t shares can reconstruct the secret (threshold t-out-of-n), but fewer than t shares reveal no information.

Properties:

• Information-theoretic security (unbreakable regardless of computational power)
• Supports addition of shared values without communication
• Multiplication requires an interactive protocol (Beaver triples or resharing)