Secure Multi-Party Computation (MPC)

Secure multi-party computation (MPC) is a cryptographic protocol that enables multiple parties to jointly compute a function over their combined inputs while keeping each party's input private from all other parties.

Definition

Secure multi-party computation (MPC, also written as SMPC) is a subfield of cryptography that enables a group of parties to jointly evaluate a function over their private inputs in such a way that no party learns anything about the other parties’ inputs beyond what can be inferred from the function’s output. Each participant provides input, all participants receive the output, and the protocol guarantees that no coalition of fewer than a threshold number of participants can reconstruct any individual input.

The theoretical foundations were established by Andrew Yao in 1982 with his “Millionaires’ Problem”—two millionaires want to determine who is wealthier without revealing their actual net worth. Yao’s garbled circuits protocol provided the first general solution. Subsequent work by Goldreich, Micali, and Wigderson extended MPC to arbitrary functions with arbitrary numbers of participants.

Why It Matters

MPC has moved from theoretical curiosity to production deployment. The Boston Women’s Workforce Council has used MPC since 2015 to compute aggregate gender pay gaps across over 200 Boston-area employers without any employer revealing individual salary data. In 2023, the Danish sugar beet industry completed its second decade of using MPC for auction pricing among 1,200 farmers—the longest-running production MPC system in the world.

In the financial sector, Fireblocks processes over $4 trillion in cumulative digital asset transfers using MPC-based key management, where no single party (and no single server) ever holds a complete private key. This eliminates the catastrophic risk of single-point key compromise that has plagued centralized cryptocurrency exchanges—an industry that lost over $1.7 billion to hacks in 2023 alone, according to Chainalysis.

The broader significance: MPC proves that collaboration does not require trust, and joint computation does not require data exposure. Two parties can compute together without either party seeing the other’s cards.

How It Works

Two dominant MPC paradigms have emerged:

Garbled circuits (Yao’s protocol): One party “garbles” a boolean circuit representing the function to compute—encrypting each gate’s truth table so that the evaluator can compute the output without learning intermediate values. The other party evaluates the garbled circuit using oblivious transfer to obtain their input labels. Efficient for two-party computation; scales poorly to many parties.
Secret sharing (BGW/SPDZ protocols): Each party splits their private input into random shares distributed among all participants using Shamir’s Secret Sharing or additive sharing. Computation proceeds on shares: parties exchange messages to perform additions and multiplications on their shares without ever reconstructing the original values. The final result is reconstructed by combining output shares.

Both approaches can be combined with zero-knowledge proofs to ensure parties follow the protocol honestly, and with differential privacy to protect the output against inference attacks.

Key performance metrics: modern MPC protocols achieve sub-second computation for functions like private set intersection on datasets of millions of records. The communication overhead—the volume of data parties must exchange—remains the primary bottleneck, typically requiring bandwidth proportional to the circuit size.

Stealth Cloud Relevance

Stealth Cloud’s current architecture does not require multi-party computation for its core Ghost Chat flow, because the architecture is designed so that computation occurs either entirely client-side or within a single ephemeral isolate that self-destructs. There is no “other party” to compute with—the server is architecturally blind.

MPC becomes relevant in two areas of Stealth Cloud’s roadmap. First, key management: splitting user recovery keys across multiple independent nodes using threshold MPC, so that no single node (including Stealth Cloud itself) can reconstruct a user’s key. This is the same model that Fireblocks uses for digital asset custody, applied to communication privacy.

Second, confidential analytics: if Stealth Cloud ever enables enterprise teams to compute aggregate statistics across their collective usage—average response times, model preference distributions, cost analysis—MPC would allow each team member’s individual data to remain private while contributing to the group computation. The zero-persistence principle demands that even the analytics layer cannot see individual sessions.

The Stealth Cloud Perspective

Secure multi-party computation is proof that you can compute together without trusting together. Stealth Cloud internalizes this principle at the single-user level: even the relationship between user and server should require no trust beyond mathematics.