Multi-Party Computation (MPC)

Multi-Party Computation (MPC) is a cryptographic protocol that allows multiple parties to jointly compute a function over their private inputs without revealing those inputs to each other. This is achieved through a series of mathematical operations that distribute the computation across the participants, ensuring that no single party ever has access to the complete, unencrypted data. The final result of the computation is revealed, but the individual inputs remain confidential, a property known as input privacy.

The core security model of MPC is based on the concept of a trusted dealer being replaced by a distributed protocol. In traditional schemes, a single trusted entity holds all secrets. MPC eliminates this single point of failure by distributing the secret—such as a private key or sensitive dataset—into secret shares. Each party holds only a meaningless fragment, and the secret can only be reconstructed or used in a computation when a pre-defined threshold of parties (e.g., 2-of-3) collaborate. This makes MPC resilient to compromise.

In blockchain and digital asset custody, MPC is a leading technology for threshold signatures. Instead of a single private key that can be stolen, a signing key is split into shares held by multiple devices or entities. To authorize a transaction, these parties run an MPC protocol to collaboratively generate a valid signature without any single device ever reconstructing the full key. This provides a superior security model compared to traditional multi-signature (multisig) schemes, as the signature itself is standard and does not reveal the multi-party nature on-chain, improving privacy and interoperability.

MPC protocols are broadly categorized by their adversarial model and communication structure. Key models include honest-majority (where most participants follow the protocol) and dishonest-majority settings. They can also be interactive, requiring multiple rounds of communication between parties during computation, or non-interactive. Common underlying techniques include Garbled Circuits, Secret Sharing (like Shamir's Secret Sharing), and Oblivious Transfer, which are combined to construct efficient MPC schemes for specific functions like private auctions, secure data analysis, or key generation.

At its core, MPC works by distributing a secret—such as a private key or sensitive data—into multiple secret shares. Each party holds one share, and no single share reveals any information about the original secret. To perform a computation (e.g., generating a digital signature or calculating an average), the parties engage in a secure, interactive protocol where they perform calculations on their individual shares and exchange intermediate results. The final output of the computation is reconstructed, but the private inputs remain concealed throughout the process. This is often achieved through cryptographic primitives like Shamir's Secret Sharing or Garbled Circuits.

The security model of MPC is defined by a threshold scheme, typically denoted as (t, n). In such a scheme, n parties hold shares, and the protocol is designed so that the computation can proceed correctly as long as at least t (the threshold) parties participate honestly. For example, in a (2,3)-threshold scheme, three parties hold shares, and any two of them can collaborate to sign a transaction, while any single party—or a malicious actor compromising one node—learns nothing and cannot forge a signature. This structure eliminates single points of failure and enhances security against insider threats and external attacks.

A practical implementation involves distinct protocol phases: setup (where secret shares are initially distributed), computation (the interactive, share-based processing), and output (where the final result is revealed). During computation, parties must communicate over secure channels, and the protocol must ensure correctness (the output is accurate if parties follow the protocol) and privacy (inputs remain hidden). Advanced MPC techniques provide robustness, guaranteeing output even if some parties deviate, and fairness, ensuring all parties receive the output or none do. This makes MPC suitable for high-stakes applications like decentralized custody and private data analytics.

In blockchain and digital asset custody, MPC's workflow is often applied to threshold signatures. Instead of a single private key, signing power is split among multiple servers or devices. To authorize a transaction, a quorum of devices (meeting the threshold) collaborates using their shares to produce a standard, valid signature on the blockchain (e.g., an ECDSA signature). From the network's perspective, it appears as a signature from a single key, maintaining compatibility, while the actual signing key never exists in one place. This elegantly bridges the security of distributed control with the simplicity of existing blockchain infrastructure.