Polynomial Function Secret Sharing With Verifiable Function Shares
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Solution Overview
Problem
Existing function secret sharing methods lack verifiability, allowing corrupted or hacked servers to potentially influence proprietary algorithm computations, compromising data privacy and security.
Innovation Solution
Implementing a verifiable polynomial function secret sharing model that allows servers to compute functions on input data without learning the function itself, ensuring validity through cryptographic validation parameters and verification mechanisms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If function secret sharing is implemented without verification mechanisms, then computational efficiency is improved, but security and reliability deteriorate as corrupted servers can influence computations
Solution Approach 1:
The patent applies preliminary action by having the function client generate validation parameters (including cryptographic signatures) for the polynomial function coefficients before distributing the function to servers. These pre-computed validation parameters enable servers to verify the authenticity of function shares they receive, preventing corrupted servers from introducing malicious computations without requiring complex real-time verification mechanisms during the actual computation process.
Solution Approach 2:
The patent introduces validation parameters as an intermediary element that mediates between the function client and servers. These validation parameters (including digital signatures and polynomial commitments) serve as a trusted intermediary that allows servers to verify the integrity of function shares without needing to directly trust the function client or perform complex cryptographic proofs during computation, thus maintaining efficiency while ensuring security.
2Measurement precision
If validation parameters are generated for each coefficient, then verification accuracy is improved, but device complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the validation parameters into distinct components corresponding to each polynomial coefficient. Each coefficient has its own validation parameter (including digital signature and polynomial commitment), allowing independent verification of each coefficient's authenticity. This segmented approach enables precise verification of individual coefficients without requiring verification of the entire function at once, reducing the complexity of the verification process while maintaining high verification accuracy.
3Reliability
If cryptographic validation parameters are transmitted to all servers, then security is improved, but communication overhead increases
Solution Approach 1:
The patent applies merging by combining multiple validation parameters (digital signatures, polynomial commitments, and coefficient validations) into a single integrated validation package that is transmitted to each server. This consolidated validation package reduces communication overhead compared to transmitting separate validation parameters for each polynomial coefficient, while still providing comprehensive security verification. The merged validation structure allows servers to verify all function shares using a unified set of validation parameters.
Data Source
AI summary
A dealer receives a first addend function and a second addend function. A function client provides first validation parameters, each first validation parameter corresponding to a coefficient of the first addend function and a corresponding coefficient of the second addend function. The sum of the first addend function and the second addend function equals the polynomial function. The dealer generates a function share for each share party based on a sampling of first random polynomials and second random polynomials and generates second validation parameters for each share party based on the function shares. The dealer transmits the second validation parameters to the share parties and transmits each function share to a corresponding share party. Each function share is verifiable by the corresponding share party based on the second validation parameters and a signed concatenation of the first validation parameters.