Verifiable Computation Using Matrix Group Mapping and Polynomial Encoding
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Solution Overview
Problem
Conventional verifiable computation methods face challenges in reducing the computational costs for verifiers, especially when dealing with complex functions and large input sizes, and lack flexibility in verifying various functions across different fields.
Innovation Solution
The method involves generating an evaluation key and a verification key based on a security parameter and a function defined as a mapping between matrix groups over a finite field, encoded into a polynomial, allowing for efficient verification by computing a proof and checking its validity, which reduces computational complexity and enhances flexibility in verifying polynomial-size functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional verifiable computation methods are used, then verification correctness is ensured, but computational costs for verifiers increase significantly
Solution Approach 1:
The verification process is segmented into two distinct phases: an expensive key generation phase performed once offline, and a lightweight verification phase performed online. The verification key encapsulates the computational complexity, allowing verifiers to perform only simple checks during the actual verification process rather than repeating expensive computations.
Solution Approach 2:
The verification key is generated in advance through a computationally intensive setup process that pre-computes all necessary parameters. This preliminary action transfers the computational burden from the verification phase to the key generation phase, enabling efficient online verification with minimal computational resources.
2Reliability
If conventional verifiable computation methods are used, then function verification is achieved, but flexibility in verifying various functions is limited
Solution Approach 1:
The verification key generation process is designed to be universal and adaptable to different functions. The system can generate verification keys for various computational tasks including machine learning model evaluations, statistical computations, and other complex functions, making the verification framework versatile across multiple application domains.
3Measurement precision
If detailed function encoding is used, then verification precision is improved, but encoding complexity increases from O(q^2) to O(q^3)
Solution Approach 1:
The system changes the parameter representation by working with polynomial evaluations at specific points rather than full polynomial coefficients. This parameter transformation reduces the encoding complexity from cubic to quadratic while maintaining the ability to verify function computations with high precision through the verification key structure.
Data Source
AI summary
A method for verifying information includes receiving a proof for a function to be evaluated from a proofer which has computed an output of the function. The proof is based on an evaluation key generated based on the function and a security parameter. Validity of the proof is verified based on a verification key generated based on the function and the security parameter. The function is defined as a mapping between matrix groups over a finite field and encoded into a polynomial that is described and implemented as an arithmetic circuit. The function to be evaluated is encoded such that the polynomial is a trace of a difference between the product of left and right input matrix polynomials of all gates of the arithmetic circuit and the output matrix polynomial of all gates of the arithmetic circuit.