Batch-wise Distributed Preprocessing Verification for Multi-Party Computation
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Solution Overview
Problem
Existing multi-party computation (MPC) protocols face challenges in efficiently preprocessing data without requiring full trust in a dealer device, as current methods either rely on a fully trusted dealer for efficiency or require computationally expensive MPC protocols to ensure correctness.
Innovation Solution
A dealer device generates and distributes secret-shares of random values and message authentication codes to evaluator devices, enabling batch-wise provisioning and verification using a checking polynomial, allowing evaluators to check the correctness of preprocessing information without fully trusting the dealer.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If an external trusted dealer device is used to perform preprocessing, then efficiency is improved, but the need for full trust in the dealer device increases
Solution Approach 1:
The preprocessing information is segmented into secret-shares that are distributed to multiple evaluator devices. The dealer device generates secret-shares of random values and proof values, distributing them in a way that no single evaluator device can reconstruct the full preprocessing information without collaboration, thereby reducing trust requirements while maintaining efficiency.
Solution Approach 2:
A checking polynomial is introduced as an intermediary mechanism between the dealer device and evaluator devices. The checking polynomial serves as a verification tool that allows evaluator devices to check the correctness of preprocessing information without needing to fully trust the dealer device, thus resolving the trust-efficiency contradiction.
2Reliability
If the preprocessing phase is executed as an MPC protocol by protocol participants, then trust in external dealer device is reduced, but computational cost and time increase
Solution Approach 1:
The dealer device performs the computationally intensive preprocessing operations in advance, generating secret-shares and proof values before the actual MPC protocol execution. This preliminary action shifts the computational burden from the online MPC phase to the offline preprocessing phase, significantly reducing the time required during the actual computation while maintaining correctness guarantees through the checking polynomial mechanism.
Solution Approach 2:
Instead of having evaluator devices perform expensive MPC computations to verify preprocessing correctness, the system uses a checking polynomial that provides a simplified verification mechanism. The checking polynomial acts as a copy or representation of the preprocessing correctness, allowing fast verification without repeating the full MPC computation.
3Measurement precision
If multiple polynomial checking equations are verified separately, then correctness is ensured, but verification complexity and computational overhead increase
Solution Approach 1:
Multiple polynomial checking equations are merged into a single checking polynomial. Instead of verifying each polynomial equation separately, the system combines them into one unified checking polynomial that encapsulates all verification requirements. This merging reduces verification complexity while maintaining the same level of correctness assurance, as the single checking polynomial can be evaluated more efficiently than multiple separate equations.
Data Source
AI summary
Some embodiments are directed to a dealer device for batch-wise provisioning of preprocessing information for a multiparty computation and an evaluator device for batch-wise distributed verification with one or more other evaluator devices of the preprocessing information. The preprocessing information comprises multiple random values and multiple message authentication codes for blinding and integrity checking respectively in the multi-party computation. The multiple random values and a set of proof values together define a checking polynomial. The dealer device computes proof values wherein the checking polynomial is identical to zero. The evaluator device obtains secret-shares of the random values, proof values, and message authentication codes. The evaluator device checks by a distributed computation with the one or more other evaluator devices that an evaluation of the checking polynomial in a random evaluation point is zero, thus verifying that multiple polynomial checking equations are satisfied on the multiple random values.