Secure Multi-Party Computation (SMPC)

The foundational guarantee that no party learns anything about another party's private input beyond what can be logically inferred from the agreed-upon function's output. This is achieved through secret sharing, where data is split into mathematically random fragments that are individually useless. Even if an attacker compromises a subset of parties, they cannot reconstruct the original secret. This property is critical for privacy-preserving machine learning and financial benchmarking.

The protocol ensures that the computed output is mathematically identical to what would have been produced if a trusted third party had performed the calculation on the plaintext inputs. This is enforced through verifiable secret sharing and message authentication codes (MACs) embedded in the computation. Malicious adversaries who deviate from the protocol are detected and ejected. This property is essential for high-stakes applications like supply chain auctions and credit scoring.

A property ensuring that if the protocol terminates, either all parties receive the output or none do. This prevents a malicious party from aborting the computation after learning the result while denying it to honest participants. In practice, fairness is often achieved through commitment schemes and output delivery guarantees. For example, in a sealed-bid auction, fairness prevents the auctioneer from dropping the connection after seeing the winning bid.

Parties must commit to their inputs before seeing any other participant's data. This prevents adaptive corruption, where an adversary modifies their input based on information leaked during the protocol. Cryptographic commit-and-prove schemes ensure that a party's input is fixed at the start of the computation. This property is vital for preventing manipulation in collaborative data analysis and secure voting.

A stronger form of fairness where the protocol is guaranteed to produce an output to all honest parties regardless of adversarial behavior. This is typically achieved using a broadcast channel and a consensus mechanism among a majority of honest parties. If a minority attempts to abort, the honest majority can reconstruct the output from their shares. This property is essential for blockchain threshold signatures and decentralized key generation.

A realistic security model that deters cheating by guaranteeing a high probability of detection. Unlike the strict malicious model, which assumes an adversary will always try to break the protocol, the covert model acknowledges that rational actors fear reputational damage. The protocol is designed so that any cheating attempt is detected with a tunable probability (e.g., 99%). This offers a practical balance between performance and security for enterprise data sharing consortiums.

A mathematical definition of privacy that guarantees the output of a computation reveals virtually nothing about any single individual's data. It is often combined with SMPC to prevent information leakage from the final result itself. By injecting calibrated statistical noise, differential privacy ensures an adversary cannot infer whether a specific record was included in the input, addressing the output-privacy gap that SMPC alone does not solve.

A privacy attack where an adversary reconstructs sensitive training data by repeatedly querying a model and analyzing its confidence scores. SMPC directly mitigates this threat by ensuring that during collaborative inference or training, no party sees the raw model outputs of another party's query. The computation is split, preventing the gradient leakage or confidence-score analysis required for successful inversion.

A lightweight cryptographic protocol designed specifically for Federated Learning. It allows a central server to compute the sum of model updates from multiple clients without inspecting any individual contribution. Secure Aggregation is a specialized, single-purpose instance of SMPC optimized for high-dimensional vector summation, trading off general computation for extreme efficiency in bandwidth and latency.

A hardware-based isolation mechanism, such as Intel SGX or AMD SEV, that protects code and data in use. Unlike SMPC, which relies on cryptographic mathematics, a TEE relies on a hardware root of trust. While TEEs offer higher performance, they require trust in the silicon vendor. SMPC provides a purely algorithmic trust model, eliminating hardware supply-chain risks.

A method by which a prover convinces a verifier of a statement's truth without revealing any information beyond validity. ZKPs are often paired with SMPC to ensure computational integrity. While SMPC hides inputs, ZKPs prove that the computation was executed correctly without revealing the inputs, preventing malicious parties from submitting falsified results during the multi-party protocol.