Approximate Calculation Verification via Finite Commutative Rings
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Solution Overview
Problem
Existing verifiable computing technologies face efficiency limitations in verifying approximate computations, particularly for complex operations like fixed point and floating point arithmetic, due to reduced verification efficiency.
Innovation Solution
A method involving arithmetic operations on a finite commutative ring and polynomial functions is used, where input values and output values are homomorphic ciphertexts, and polynomial functions are generated and transferred between devices for verification, enabling efficient computation and verification of approximate computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If verifiable computing is applied to approximate computation (fixed point, floating point arithmetic), then computation accuracy verification is enabled, but verification efficiency is significantly reduced
Solution Approach 1:
The patent segments the verification process by introducing intermediate verification points within the computation circuit. The circuit is divided into multiple stages, and verification is performed at each stage rather than only at the final output, enabling earlier detection of computation errors and reducing the overall verification burden.
Solution Approach 2:
The patent introduces an intermediary verification mechanism using polynomial functions that act as mediators between the computation circuit and the verification process. These polynomial functions enable efficient verification of intermediate computation results without requiring complete re-verification of the entire computation chain.
2Reliability
If direct computation is performed to confirm the correctness of computation results assigned to a third party, then accuracy verification is achieved, but computation resources are wasted
Solution Approach 1:
The patent creates a computational copy or representation of the verification process that operates independently from the original computation. The verification circuit processes the same input data through a parallel verification path, allowing accuracy confirmation without re-executing the entire original computation.
Solution Approach 2:
The patent changes the verification parameters by using polynomial representations and homomorphic encryption properties to verify computation results. Instead of performing complete recomputation, the verification process operates on transformed parameters that enable efficient accuracy checking with reduced computational overhead.
3Reliability
If polynomial functions are used for verification in approximate computation, then verification capability is enhanced, but system complexity increases
Solution Approach 1:
The patent implements a universal verification framework using polynomial functions that can handle multiple types of approximate computations (fixed point, floating point, and other numerical computations) through a single unified approach. This multi-functional verification system reduces the need for separate verification mechanisms for different computation types.
Solution Approach 2:
The patent replaces complex mechanical verification processes with algebraic polynomial-based verification. Instead of using traditional computational verification methods that require step-by-step checking, the system uses polynomial mathematical properties to enable more efficient and less complex verification operations.
Data Source
AI summary
Disclosed is a method of arithmetic operation. The arithmetic operation includes receiving an input value, generating an output value by reflecting the input value to a preset arithmetic circuit on a finite commutative ring and a first polynomial function to verify the output value, and transferring the generated output value and the first polynomial function to an external device.