Multi-party computation and Multi-signature

Multi-party computation (MPC) is a cryptographic protocol that enables multiple parties to jointly compute a function over their private inputs without revealing those inputs to each other. In other words, it allows a group of participants to collaboratively perform a computation on their individual private data without any party gaining access to the sensitive information of others. MPC ensures privacy and security in scenarios where the participants do not fully trust each other or a third-party intermediary.

MPC involves a series of cryptographic techniques, such as secret sharing and secure function evaluation, to distribute the computation and ensure privacy. The process typically involves the following steps:

1. Key Generation: Each participant generates their own private and public key pair.
2. Input Preparation: Each participant privately prepares their input data.
3. Secret Sharing: The input data of each participant is divided into shares using cryptographic techniques like Shamir's secret sharing. The shares are distributed among the participants.
4. Computation: Participants perform computations on their individual shares without revealing them. They exchange messages and collaborate to compute the desired result.
5. Result Reconstruction: The final result is obtained by combining the computed shares without exposing any private information.

Multi-signature (multisig), on the other hand, is a mechanism used to enhance security and control over transactions in blockchain networks. It involves requiring multiple signatures to authorize and execute a transaction, usually involving multiple parties. In the context of blockchain, multisig refers to the requirement of multiple private keys (belonging to different participants) to validate and authorize a transaction.

With multisig, a certain number of authorized participants need to provide their signatures (using their private keys) to approve a transaction before it is considered valid and added to the blockchain. This approach provides added security by reducing the risk of a single point of failure or compromise. For example, in a 2-of-3 multisig setup, at least two out of three participants must sign off on a transaction for it to be considered valid.

The key difference between MPC and multisig lies in their objectives and use cases. MPC focuses on secure computation, enabling multiple parties to jointly compute a function without revealing their private inputs. It ensures privacy and security in scenarios where participants do not fully trust each other. On the other hand, multisig is primarily concerned with transaction authorization and control, requiring multiple signatures to validate a transaction. It enhances security by distributing control among multiple parties and reducing reliance on a single entity.

In summary, MPC enables secure computation while preserving privacy, whereas multisig enhances security and control over transactions by requiring multiple signatures for validation. Both concepts have their unique applications and play important roles in the blockchain ecosystem.