Secure Multi-Party Computation (SMPC)

The foundational guarantee that no party learns anything about another party's private inputs beyond what can be inferred from the agreed-upon function's output. This is achieved through secret sharing, where data is split into mathematically randomized fragments that are individually meaningless.

• A malicious adversary controlling n-1 parties cannot reconstruct the nth party's input.
• This property holds even if participants deviate from the protocol.
• Distinct from Trusted Execution Environments, which rely on hardware isolation rather than mathematical guarantees.

The protocol ensures that the final computed output is mathematically identical to what would have been produced if a trusted third party had performed the computation on the plaintext inputs. This prevents any coalition of dishonest parties from forcing an incorrect result.

• Validated through zero-knowledge proofs in malicious security models.
• Prevents output manipulation in auction clearing, financial netting, and collaborative analytics.
• The guarantee is probabilistic or deterministic depending on the underlying cryptographic scheme.

The property ensuring that if any party receives the computation output, all parties entitled to the output receive it. No participant can abort the protocol prematurely after learning the result while denying it to others.

• Critical for sealed-bid auctions and contract signing.
• Achieved through commitment schemes and output delivery protocols.
• In practice, fairness is often relaxed to fairness with abort where honest parties are compensated or notified of a breach.

Each party must select its input independently of the inputs chosen by other parties. The protocol prevents a corrupt party from tailoring its input based on an honest party's input to manipulate the function's outcome.

• Enforced through non-malleable commitment schemes.
• Prevents strategic manipulation in collaborative machine learning and benchmarking.
• A critical defense against input substitution attacks in multi-round protocols.

The strongest termination guarantee where the protocol ensures that all honest parties always receive the correct output, regardless of adversarial behavior by a minority of participants. This requires a majority of honest parties.

• Achieved through verifiable secret sharing and robust reconstruction.
• Contrasts with security with abort, where the protocol halts upon detecting malicious activity.
• Essential for mission-critical financial infrastructure and regulatory reporting.

A cryptographic scheme enabling computation directly on ciphertext. Unlike SMPC, which distributes trust across parties, Fully Homomorphic Encryption (FHE) allows a single untrusted server to process encrypted data without ever decrypting it. This is ideal for outsourcing AI inference to the cloud while keeping inputs private. Partially Homomorphic Encryption (PHE) supports only limited operations (addition or multiplication), offering better performance for specific use cases like encrypted aggregation.

A mathematical definition of privacy that guarantees an adversary cannot determine whether any single individual's data was included in a computation. It works by injecting calibrated statistical noise into query results or model gradients. While SMPC protects data during computation, differential privacy protects the output from revealing individual contributions. The privacy loss is quantified by the parameter epsilon (ε), with lower values providing stronger guarantees.

A decentralized machine learning paradigm where a shared global model is trained across multiple edge devices or servers holding local data. Only model weight updates are transmitted to a central aggregation server, never raw data. SMPC can be integrated into the aggregation step to prevent the central server from inspecting individual updates, creating a Secure Aggregation protocol. This combination is critical for training on sensitive silos like hospital records or mobile keyboard data.

A hardware-enforced isolated area within a main processor (e.g., Intel SGX, AMD SEV) that protects code and data loaded inside it from the host operating system and hypervisor. TEEs provide confidential computing by performing computation in an encrypted memory enclave. Unlike SMPC, which distributes trust mathematically, TEEs concentrate trust in the hardware manufacturer. They offer significantly higher performance than cryptographic MPC but introduce a hardware root of trust.

A cryptographic method allowing a prover to convince a verifier that a statement is true without revealing any information beyond the statement's validity. In the context of SMPC and AI governance, ZKPs enable verifiable computation: a party can prove they executed a model correctly on private data without revealing the data or the model weights. This provides cryptographic auditability for purpose limitation compliance.

A secure, governed environment where multiple parties can bring sensitive datasets for collaborative analysis or model training under strict, mutually agreed-upon rules. Clean rooms enforce purpose limitation by allowing only pre-approved queries and preventing raw data extraction. SMPC can serve as the underlying cryptographic enforcement layer within a clean room, replacing legal contracts with mathematical guarantees that no party's raw data is exposed during joint computation.