|Aspect|First‑principles view| |---|---| |**Goal**|Compute any agreed function on private inputs held by several players so that: • Output is correct. • Nobody learns anything beyond that output.| |**Actors**|_n_ parties, some may collude.| |**Game**|Protocol with message rounds. Parties finish with their share of the result or the whole result.| |**Security pillars**|1. **Correctness**: Output equals the true function value. 2. **Privacy**: Colluding subset learns nothing more than what the function value already reveals. 3. **Robustness / Fairness**: Optional guarantees against aborts or garbage outputs.| |**Building blocks**|Secret sharing, oblivious transfer, homomorphic encryption, garbled circuits.| |**Typical flow (secret‑sharing style)**|1. Split each input into random shares across players. 2. Run a share‑by‑share computation (addition is free, multiplication needs interaction). 3. Reconstruct the final value or keep it shared.| |**Variations**|Honest‑majority vs dishonest‑majority, semi‑honest vs malicious security, asynchronous vs synchronous networks.|