secure multi-party computation

Secure multi-party computation (MPC) lets several parties jointly compute a function of their private inputs while each learns only the result — never anyone else's input. The classic picture: a group of employees compute their average salary without any of them revealing their own.

Foundational theory shows any function can be computed securely: Yao's garbled circuits for two parties, and GMW or BGW for many, built from primitives like secret sharing, oblivious transfer, and homomorphic operations. Security is defined against an adversary corrupting up to some threshold of parties, in either the semi-honest model (follows the protocol but tries to learn extra) or the malicious model (deviates arbitrarily). The dominant cost is communication — rounds and bandwidth — which is usually the practical bottleneck rather than raw computation.

In blockchain, MPC underpins institutional key custody (the private key exists only as shares and signing is an MPC that yields a threshold signature), distributed key generation, sealed-bid auctions, and dark-pool order matching. It is the engine beneath MPC wallets and threshold signing, delivering 'no single point of failure' custody without relying on a single hardware enclave.