Understanding Multi-Party Computation (MPC): What is it and how does it work?

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Multi-Party Computation (MPC) is a revolutionary technique that allows multiple parties to jointly compute a function without revealing their inputs to each other. This technology has been touted as a game-changer in the field of secure computation since it allows parties to conduct computations while keeping their data private and confidential. In this article, we will discuss what multi-party computation is, how it works, and its applications in various fields.

What is Multi-Party Computation (MPC)?

Multi-party computation (MPC) is a cryptographic technique that allows multiple parties to securely compute a function on their private inputs without revealing their inputs to each other. In other words, MPC enables several parties to jointly perform a computation without any of them knowing the values of each other's inputs. There are different techniques that can be used to construct an MPC, including secret sharing, homomorphic encryption, private set intersection, etc.

How Does Multi-Party Computation Work?

MPC involves several parties, each holding their own private input. These inputs can be numbers, messages, or any other data that needs to be computed jointly. 
To perform the computation, the parties first use secret sharing to divide their private inputs into multiple shares, and distribute these shares among the other parties. Each party only holds a share of each input, but no party knows the entire input of any other party. This secret sharing ensures that no party can reconstruct any other party's input without the cooperation of the other parties.
Once the inputs are shared, the parties use encryption to hide the shared inputs from each other. The encryption process ensures that no party can learn any other party's input, even if they manage to obtain all the encrypted shares of the input. The parties then jointly perform the computation on the encrypted inputs. The computation is done using a series of cryptographic protocols that enable the parties to compute the result without revealing any intermediate values or the final result to each other.
Finally, the parties use decryption and reconstruction to obtain the final result of the computation. The result is decrypted using a special decryption protocol that allows each party to obtain their share of the result without revealing their input or the result to the other parties. The parties can then reconstruct the final result by combining their shares of the result.

Example of Multi-Party Computation

mpc example
Image Source: https://bipartisanpolicy.org/blog/secure-multi-party-computation/
The illustration above explains the functioning of MPC using an example. Let's consider Alice, Bob, and Cynthia who want to determine the average of their hourly wages while keeping their individual wage amounts confidential. Each of them knows their hourly wage and splits it into four numbers that add up to the hourly wage (step 1). They keep one number for themselves and share one with each of the other two participants, while the third number is shared with a trusted third-party or an outside consultant. This sharing of individual data points reveals no information about their actual hourly wage.
Now, Alice, Bob, Cynthia, and the trusted third-party each have three pieces of information, and they all compute an average for their three numbers (steps 2 and 3). Then, Alice, Bob, and Cynthia share their averages with the trusted third-party who adds their own average calculation to the other three averages (step 4). The result is the average hourly wage of Alice, Bob, and Cynthia, without revealing their individual hourly wage amounts to each other. At the end of the process, the average hourly wage is known, but individual wage amounts remain confidential.

Applications of Multi-Party Computation

Multi-party computation has numerous applications in various fields. Some of the applications of MPC are:

Financial Transactions

MPC can be used in financial transactions to enable secure and private computation of financial transactions between multiple parties. Financial institutions can use MPC to compute financial transactions such as loan processing, credit scoring, and fraud detection without revealing their customer's financial data to each other.


MPC can be used in healthcare to enable secure and private computation of medical data between multiple parties. Medical institutions can use MPC to compute medical data such as disease diagnosis, patient treatment, and drug discovery without revealing their patient's medical data to each other.

Data Privacy

MPC can be used to protect the privacy of sensitive data such as personal information, credit card numbers, and social security numbers. MPC can be used to encrypt and securely compute this sensitive data without revealing it to any party involved in the computation.

Secure Multiparty Computation

MPC can be used to achieve secure multiparty computation, which enables secure and private computation of a function on private inputs. Secure multiparty computation has applications in various fields such as data mining, machine learning, and electronic voting.

Electronic Voting

MPC can be used in electronic voting to ensure secure and private computation of election results. MPC can enable a group of voters to compute the election results without revealing their individual votes to each other. This can provide a secure and transparent electronic voting system that preserves the privacy of individual voters.

Cloud Computing

MPC can be used in cloud computing to enable secure and private computation of data on cloud servers. Cloud computing providers can use MPC to compute data from multiple clients without revealing the data to other clients or the cloud provider. This can provide a secure and private cloud computing environment for sensitive data.

Challenges of Multi-Party Computation

While MPC offers numerous benefits, it also presents some challenges that need to be addressed. Some of the challenges of MPC are:

High Computational Overhead

MPC requires a significant amount of computation and communication between the parties, which can result in high computational overhead. This can make MPC impractical for some applications, especially those that require real-time processing.

Complexity of Implementation

MPC is a complex cryptographic protocol that requires expertise in cryptography, mathematics, and computer science. The implementation of MPC requires careful design and implementation to ensure that it is secure and efficient.

Communication and Coordination

MPC requires the parties to communicate and coordinate with each other during the computation process. This can be challenging, especially when the parties are located in different geographical locations or have different computing capabilities.


Multi-party computation (MPC) is a cryptographic technique that allows multiple parties to securely compute a function on their private inputs without revealing their inputs to each other. MPC has numerous applications in various fields, including finance, healthcare, data privacy, secure multiparty computation, electronic voting, and cloud computing. While MPC offers numerous benefits, it also presents some challenges that need to be addressed, including high computational overhead, complexity of implementation, and communication and coordination. With proper implementation and careful consideration of these challenges, MPC can provide a secure and private computation environment for sensitive data.

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