secure multi-party computation

**Secure Multi-Party Computation (SMPC or MPC)** is a cryptographic technique that enables multiple parties to **jointly compute a function** over their combined private inputs **without revealing** those inputs to each other. Each party learns only the final result, not any other party's data. **How MPC Works (Simplified)** - **Secret Sharing**: Each party's input is split into random "shares" distributed to other parties. No single party has enough shares to reconstruct any input. - **Computation on Shares**: Parties perform computations on their shares, exchanging intermediate results according to a predefined protocol. - **Result Reconstruction**: Only the final result can be reconstructed from the combined output shares — intermediate values and original inputs remain hidden. **MPC Protocols** - **Garbled Circuits (Yao's Protocol)**: One party "garbles" the computation into an encrypted circuit; the other evaluates it without learning intermediate values. Efficient for two-party computation. - **Secret Sharing (Shamir, BGW)**: Distribute data as polynomial shares among multiple parties. Supports addition natively; multiplication requires communication rounds. - **Oblivious Transfer (OT)**: A protocol where a sender transfers one of multiple items to a receiver without learning which item was selected. **Applications in AI/ML** - **Privacy-Preserving ML Training**: Multiple hospitals train a model on their combined patient data without any hospital sharing raw records. - **Federated Analytics**: Aggregate statistics across organizations without exposing individual data points. - **Private Inference**: A user sends an encrypted query to a model, receives the result, and the model operator never sees the query. - **Data Marketplaces**: Validate data quality or compute on purchased data without revealing it before payment. **Challenges** - **Performance**: MPC is **orders of magnitude slower** than plaintext computation due to communication and cryptographic overhead. - **Communication**: Parties must exchange messages proportional to the computation size, requiring reliable, high-bandwidth networks. - **Complexity**: Designing and implementing correct MPC protocols requires deep cryptographic expertise. MPC is gaining traction in **healthcare, finance, and cross-organizational AI** where data sharing is legally or competitively impossible but joint computation is valuable.