Secure Multi-Party Computation (SMPC)

A primary technique for two-party SMPC. The function is represented as a Boolean circuit. One party (the garbler) encrypts the circuit by assigning two random cryptographic labels to each wire (representing 0 and 1) and encrypting the truth tables of each gate. The second party (the evaluator) receives the garbled circuit and uses Oblivious Transfer (OT) to retrieve the labels corresponding to its private input without revealing which labels it chose. The evaluator decrypts the circuit gate-by-gate, learning only the final output labels.

A cryptographic scheme enabling computation directly on ciphertexts without requiring decryption. Unlike SMPC, which distributes computation across parties, homomorphic encryption allows a single untrusted server to process encrypted data. Fully Homomorphic Encryption (FHE) supports arbitrary computations but incurs significant computational overhead. Partially Homomorphic Encryption (PHE) supports only addition or multiplication, while Somewhat Homomorphic Encryption (SHE) supports limited circuits. In model inversion protection, homomorphic encryption enables inference on encrypted inputs without exposing the query to the model host.

A foundational building block of many SMPC protocols where a secret value is split into mathematically randomized shares distributed among parties. No single share reveals any information about the original secret. Common schemes include:

• Shamir's Secret Sharing: Uses polynomial interpolation over a finite field; requires t+1 of n shares to reconstruct
• Additive Secret Sharing: Splits a value into random shares that sum to the original; trivial to implement but requires all shares for reconstruction
• XOR-based Sharing: Used for binary circuits; each bit is masked with random bits In SMPC, parties compute functions directly on their shares without ever reconstructing the original secrets.

A two-party SMPC protocol introduced by Andrew Yao where one party encrypts a Boolean circuit representing the function to be computed. The circuit's truth table is garbled—each wire value is replaced with encrypted labels—and the second party evaluates the circuit obliviously using oblivious transfer to obtain input labels. Key properties:

• Constant-round complexity: evaluation requires a fixed number of communication rounds
• Efficient for small circuits but scales poorly with circuit size
• Provides security against semi-honest adversaries; extensions exist for malicious security Garbled circuits excel in scenarios with asymmetric computation where one party holds the function and the other holds the data.

A cryptographic primitive where a sender transmits one of potentially many pieces of information to a receiver, but remains oblivious to which piece was selected. The receiver learns only their chosen value and nothing about the others. Variants include:

• 1-out-of-2 OT: The foundational variant; receiver chooses one of two messages
• k-out-of-n OT: Receiver selects k messages from n options
• Random OT: Both parties receive random outputs correlated by the receiver's choice Oblivious transfer is a complete primitive for secure computation—any SMPC functionality can be constructed from OT alone, making it the theoretical bedrock of the field.

A hardware-enforced secure enclave that isolates code and data from the host operating system, hypervisor, and other processes. Unlike SMPC's cryptographic approach, TEEs rely on hardware trust assumptions. Major implementations:

• Intel SGX: Enclaves within Intel CPUs with remote attestation capabilities
• AMD SEV: Encrypted virtual machine memory with Secure Encrypted Virtualization
• ARM TrustZone: Split-world architecture separating secure and normal execution TEEs offer orders of magnitude better performance than pure cryptographic SMPC but require trusting the silicon vendor. Confidential computing combines TEEs with SMPC for defense-in-depth against both software and hardware adversaries.

A mathematical framework providing provable privacy guarantees by injecting calibrated noise into computation outputs. While SMPC protects inputs during computation, differential privacy protects against inference from outputs. The privacy budget (ε) quantifies the maximum information leakage permitted. Key mechanisms:

• Laplace Mechanism: Adds noise calibrated to L1 sensitivity
• Gaussian Mechanism: Uses L2 sensitivity with Gaussian noise
• Exponential Mechanism: Privately selects from discrete options In practice, SMPC and differential privacy are complementary technologies: SMPC secures the computation process, while differential privacy ensures the final output does not reveal individual contributions.