Proxy Calculation System Reducing Black Box Operations
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Solution Overview
Problem
Existing techniques require at least 2M calculations using a black box function to compute f(x) for M input values, leading to inefficient processing.
Innovation Solution
A proxy calculation system that generates random numbers and calculates f(x)r for each input, then combines results to determine f(xa1 × xa2 × ... × xMaM), minimizing the number of black box operations to M + 1 times by leveraging homomorphic properties and random variables in cyclic groups.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the randomizable sampler and the sampler calculate at least twice using the black box function for each input, then the calculation accuracy is ensured, but the calculation efficiency deteriorates with 2M calculations required for M inputs
Solution Approach 1:
The patent combines multiple separate calculations into a single unified calculation by computing f(x1a1 × x2a2 × ... × xMaM) once to obtain z0, which then serves to verify all M individual results simultaneously. This merging approach reduces the total number of black box calculations from 2M to M+1 while maintaining accuracy through the verification mechanism.
Solution Approach 2:
The patent introduces an intermediary verification value z0 = f(x1a1 × x2a2 × ... × xMaM)r0 that acts as a mediator to check the correctness of all M calculated values. By computing this single intermediary value and comparing it with the product of individual results, the system ensures accuracy without requiring separate verification calculations for each input.
2Reliability
If separate calculations are performed for each of the M input values, then individual result accuracy is maintained, but the overall processing time increases proportionally with M
Solution Approach 1:
The patent merges the verification process for all M individual results into a single combined verification calculation. By computing the product (z1)a1 × (z2)a2 × ... × (zM)aM and comparing it with z0 in one operation, the system maintains reliability for all results while reducing total processing time from 2M separate operations to M+1 operations.
3Reliability
If the black box function is called 2M times for M inputs, then comprehensive verification is achieved, but the computational resource consumption increases
Solution Approach 1:
The patent combines multiple verification operations into a single resource-efficient process. Instead of calling the black box function 2M times, the system calls it M+1 times: M times to obtain individual results and once to obtain the verification value z0. This merging significantly reduces computational resource consumption while maintaining comprehensive verification through the mathematical relationship validation.
Data Source
AI summary
Where G and H are cyclic groups, M is an integer of two or more, i = 1, ..., M, f is a homomorphic function of mapping a member xi of group H to group G, Ri and R0 are random variables with a value in group G, ri is a realized value of the random variable Ri,, r0 is a realized value of the random variable R0, and ai is a random number of an integer of 0 or more, a random number generation unit 11 generates random numbers a1, a2, ..., aM. A sampler 21 is capable of calculating f(x1)r1, f(x2)r2, ..., f(xM)rM to obtain a calculation result thereof as z1, z2, ..., zM, respectively. A power calculation unit 12 calculates (z1)a1, (z2)a2, ..., (zM)aM. An extended randomizable sampler 22 is capable of calculating f(x1a1 × x2a2 × ... × xMaM)r0 to obtain a calculation result z0 thereof. A determination unit 16 determines whether or not (z1)a1 × (z2)2 × ... × (zM)aM = Z0.