MPC

n-Party MPC

$$\mathsf{MPC}_n(f, w_1, \dots, w_n, x) \rightarrow f(w_1, \dots, w_n, x)$$

n-Party MPC (Multi-Party Computation) is a cryptographic protocol that allows $n$ parties to jointly compute a function $f(w_1, \dots, w_n, x)$ over their respective private inputs without revealing them to each other.

In other words:

• For $1 \le i \le n$, each party $p_i$ holds a secret input $w_i$

• A shared input $x$ is known to every party

• They compute $f(w_1, \dots, w_n, x)$ without disclosing their inputs

This approach is designed for privacy-preserving computation in security-sensitive environments, enabling collaboration without compromising data confidentiality.

Notation for $f$ without a shared input is as follows:

$$\mathsf{MPC}_n(f, w_1, \dots, w_n) \rightarrow f(w_1, \dots, w_n)$$