Proxy Calculation System for Unreliable Devices
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Solution Overview
Problem
Existing calculation techniques face challenges in ensuring correct calculations by unreliable calculating apparatuses, particularly when the probability of correct calculation is low.
Innovation Solution
A proxy calculation system is introduced, utilizing integer calculation, randomizable samplers, and exponentiation parts to determine and correct calculation results, ensuring accurate computation even with low-probability correct calculations by unreliable apparatuses.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a self-corrector uses majority decision to calculate a function, then the calculation reliability is improved, but the calculating apparatus must make correct calculations with a probability equal to or higher than a certain level, which limits the applicability to unreliable calculators
Solution Approach 1:
The patent introduces a proxy calculator as an intermediary between the unreliable calculator and the requester. The proxy calculator receives calculation requests, performs verification by requesting the unreliable calculator to compute the same function multiple times with different inputs, and determines whether to accept the results based on consistency checks. This intermediary mechanism enables the system to work with calculators that have arbitrarily low correct calculation probabilities, resolving the contradiction between reliability improvement and adaptability to unreliable devices.
2Adaptability or versatility
If the calculating apparatus makes correct calculations with low probability, then the system can use unreliable calculators, but the calculation correctness cannot be ensured
Solution Approach 1:
The proxy calculator implements a feedback mechanism where it requests the unreliable calculator to perform the same function computation multiple times with different input values. By comparing the results across multiple trials, the proxy calculator can detect inconsistencies and determine when the unreliable calculator produces incorrect results. This feedback loop ensures calculation correctness is maintained even when using calculators with low correct calculation probabilities.
Solution Approach 2:
The system employs periodic verification by requesting the unreliable calculator to compute the function repeatedly at different intervals with varied inputs. This periodic action allows the proxy calculator to statistically assess the reliability of the unreliable calculator's outputs and ensure correctness through multiple sampling points, thereby maintaining calculation accuracy despite the calculator's low inherent correctness probability.
Data Source
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AI summary
A function f(x) is calculated with a calculating apparatus that makes a correct calculation with a low probability. Provided that G and H are cyclic groups, f is a function that maps an element x of the group H into the group G, X1 and X2 are random variables whose values are elements of the group G, x1 is a realized value of the random variable X1, and x2 is a realized value of the random variable X2, an integer calculation part calculates integers a' and b' that satisfy a relation a'a + b'b = 1 using two natural numbers a and b that are relatively prime. A first randomizable sampler is capable of calculating f(x)bx1 and designates the calculation result as u. A first exponentiation part calculates u' = ua. A second randomizable sampler is capable of calculating f(x)ax2 and designates the calculation result as v. A second exponentiation part calculates v' = vb. A determining part determines whether u' = v' or not. A final calculation part calculates ub'va' in a case where it is determined that u' = v'.