Secure multi-party computation

As explained in Real-World Cryptography

Secure multi-party computation is a cryptographic protocol in which multiple participants jointly execute a computation while keeping their respective inputs private.

Suppose two millionaires want to learn who is richer without revealing their fortunes. Secure multi-party computation (MPC) lets participants jointly execute a program while keeping their inputs private. It replaces a trusted third party with a cryptographic protocol that participants run themselves. section 15.1

Figure 15.1 A secure multi-party computation (MPC) protocol turns a distributed computation that can be calculated via a trusted third party (image on the left) into a computation that doesn’t need the help of a trusted third party (image on the right).

Use the diagram to compare ordinary distributed computation through a trusted third party with MPC, which removes that intermediary. section 15.1

General-purpose MPC can represent arbitrary programs by translating them into arithmetic circuits made from addition and multiplication gates. Protocols differ in efficiency, tolerated dishonesty, participant behavior, and fairness when someone stops early. section 15.1.2

A simplified honest-majority construction using Shamir’s secret sharing proceeds in three stages:

• Share inputs: publish public inputs and split private inputs into secret shares distributed among participants. section 15.1.2
• Evaluate the circuit: compute addition gates locally and exchange messages for multiplication gates, producing shares of intermediate results. section 15.1.2
• Reconstruct the output: exchange the necessary shares to reveal the result, or keep them separate for continued computation. section 15.1.2

Existing MPC-shaped systems

Threshold signatures and distributed key generation are examples of MPC; both belong more specifically to threshold cryptography. section 15.1

MPC has become more practical, but implementations remain difficult to use and lack a general standardization effort. Secret sharing is only one construction; garbled circuits and fully homomorphic encryption provide alternatives. section 15.1.3

How Real-World Cryptography covers it

How deep it goes

Works through circuit translation, secret sharing, gate evaluation, and output reconstruction, while omitting technical reasons behind multiplication interaction.

Examples

Uses the Millionaires’ problem, arithmetic circuits, Shamir shares, threshold signatures, and distributed key generation.

What it assumes

Assumes familiarity with secret sharing and distributed computation while motivating MPC through a plain-language privacy problem.

What you can do after

Evaluate and understand the phases, privacy goal, tradeoffs, and construction choices behind general-purpose MPC.

How it connects

Connects arithmetic circuits, secret sharing, threshold cryptography, garbled circuits, and fully homomorphic encryption.

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Also explained in

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  liveBookmanning.com
  First-Party Data ActivationA cryptographic technique that lets multiple parties compute jointly over their inputs without revealing those inputs to one another.

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Related concepts

• Shamir's Secret Sharingused by · Shamir’s secret sharing is a threshold secret-sharing scheme that distributes a secret as polynomial-derived shares reconstructible by a qualified subset of participants.
• arithmetic circuituses · An arithmetic circuit is a directed acyclic computation structure whose gates perform arithmetic operations over a specified field or ring.
• secret sharinguses · Secret sharing is a cryptographic technique that divides a secret into shares so authorized combinations of participants can reconstruct or use it.
• cryptographykind of · Cryptography is the study and application of mathematical techniques for protecting information and communications through confidentiality, integrity, authentication, and related security properties.

This explainer was generated by Manning's knowledge graph from the text of Real-World Cryptography. The section links point to the parts of the book it draws on.