Secure Multi-Party Computation (SMPC)

The fundamental guarantee that no party learns anything about another party's private input beyond what can be inferred from the designated output. This is achieved through secret sharing, where data is split into mathematically random shares that reveal no information in isolation. Even if an attacker compromises a subset of parties, the original input remains information-theoretically secure.

The protocol ensures the computed output is mathematically correct, as if a trusted third party performed the calculation on the plaintext inputs. This holds even if a minority of participants are malicious adversaries actively trying to deviate from the protocol. Robust implementations use verifiable secret sharing and zero-knowledge proofs to detect and prevent cheating.

A security property ensuring that if any party receives the output, all honest parties receive it. This prevents a malicious participant from aborting the protocol after learning the result while leaving others with nothing. In practice, fairness often requires an honest majority assumption; without it, protocols like Cleve's impossibility result show fairness cannot be achieved unconditionally.

A stronger property than fairness, Guaranteed Output Delivery (GOD) ensures that honest parties always receive the correct output regardless of malicious behavior. This requires a super-majority of honest parties (typically $t < n/3$ for malicious security) and relies on consensus mechanisms within the MPC protocol to reconstruct the result even when some parties refuse to participate.

SMPC protocols are proven secure under specific adversarial models:

• Semi-honest (Honest-but-Curious): Parties follow the protocol correctly but try to learn private information from received messages.
• Malicious: Parties can arbitrarily deviate from the protocol to steal data or corrupt the output.
• Covert: Malicious behavior is detectable with a defined probability, offering a practical middle ground between efficiency and strong security guarantees.

The primary bottleneck in practical SMPC is the volume of data exchanged between parties. For complex functions like neural network inference, the communication overhead can be orders of magnitude larger than local computation. Modern protocols optimize this using techniques like function-dependent preprocessing and batching to make privacy-preserving machine learning feasible on real-world networks.

The process of partitioning a neural network's computational graph and parameters across multiple isolated devices or secure enclaves. Unlike SMPC, which distributes computation on secret-shared data, model sharding distributes the model itself so no single node possesses the complete architecture. The two techniques can be combined: each shard holder participates in an SMPC protocol, ensuring neither the model nor the input is ever reconstructed in one location.