[Paper Review] Secure Multi-Party Computation with a Helper

Johannes Schneider|arXiv (Cornell University)|Aug 31, 2015

Cryptography and Data Security26 references3 citations

TL;DR

This paper proposes a novel secure multi-party computation (MPC) framework using a dedicated helper party to drastically reduce communication complexity, achieving asymptotic optimality of one bit per AND gate under specific conditions. By leveraging pre-shared randomness and secret sharing with a helper, the scheme enables constant-round protocols for complex functions like exponentiation, outperforming prior work in communication efficiency while maintaining perfect security with a single corrupted party.

ABSTRACT

A client wishes to outsource computation on confidential data to a network of parties. He does not trust a single party but believes that multiple parties do not collude. To solve this problem, we use the idea of treating one of the parties as a helper. A helper assists computation only. Often using more parties ensures confidentiality despite more corrupted parties. This does not hold for adding a helper. But a helper can in some cases lower the amount of communication asymptotically to the theoretical minimum of one bit per AND gate, improving significantly on schemes without a helper. It can also allow for very efficient computations of certain functions, as we show for the exponential function with public base.

Motivation & Objective

• To investigate whether a dedicated helper party can improve communication and round complexity in secure multi-party computation without compromising security.
• To design a new MPC protocol for three-party computation that minimizes communication overhead while maintaining perfect security under the semi-honest model.
• To enable efficient computation of complex functions—especially the exponential function—using a helper to achieve constant-round protocols.
• To analyze the trade-off between communication and round complexity for large fan-in AND gates using the helper.
• To formalize a 'distrust attacker' model where only corrupted parties compromise security, allowing stronger security guarantees with fewer corruptions.

Proposed method

• The protocol uses a helper that does not hold secret shares but assists in computing AND and XOR gates via optimized communication patterns.
• Secrets are shared using linear encryption (e.g., additive sharing), and the helper is used to reduce redundant transmissions by reusing shared values across multiple operations.
• For exponential function computation, the method exploits mathematical identities involving two variables to compute the result in just two rounds using the helper.
• The scheme achieves one-bit communication per AND gate by reusing the helper’s role across multiple gate evaluations when variables are reused.
• A trade-off protocol is designed for large fan-in AND gates, allowing adjustment between communication and round complexity by varying the helper’s role.
• The approach assumes pre-shared randomness among parties and defines a 'distrust attacker' model where only corrupted parties can access secrets, not honest ones.

Experimental results

Research questions

• RQ1 Can a dedicated helper reduce communication complexity in MPC below the theoretical lower bound of two bits per AND gate?
• RQ2 Under what conditions can a helper achieve one-bit communication per AND gate with non-trivial security guarantees?
• RQ3 How can the helper be used to compute complex functions like the exponential function in constant rounds with minimal communication?
• RQ4 What is the impact of the helper on round complexity and communication trade-offs for large fan-in AND gates?
• RQ5 How does the 'distrust attacker' model affect security guarantees compared to traditional 'distrust all' models?

Key findings

• The protocol achieves one bit of communication per AND gate, matching the theoretical minimum, under the condition that variables are reused across multiple operations.
• For the exponential function with a public base, the protocol computes the result in just two rounds, significantly improving over prior schemes.
• The scheme reduces communication complexity by up to a factor of three compared to prior three-party MPC protocols for multiple AND gates.
• The helper enables a trade-off between communication and round complexity for large fan-in AND gates, allowing optimization based on system constraints.
• The security model allows only one corrupted party to compromise the system, improving on schemes that require two corruptions to break confidentiality.
• The protocol maintains local computation complexity at the same level as state-of-the-art schemes while drastically reducing communication and round counts.