Secure Aggregate Order System Using Secret Sharing
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Solution Overview
Problem
Conventional secure computation techniques are inefficient in obtaining order within a group, requiring log(n) communications, where n is the number of subjects to be computed.
Innovation Solution
A secure aggregate order system comprising secure computation apparatuses that utilize secret sharing of cross tabulations and permutations to efficiently compute ascending and descending orders within a group, reducing communication requirements to O(1) while maintaining confidentiality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional secure computation techniques are used to obtain order within a group, then confidentiality is maintained, but the number of communication times is log(n) which is inefficient
Solution Approach 1:
The patent segments the computation process by introducing auxiliary computation results that divide the original log(n) communication complexity into multiple O(1) communication steps. The cross-tabulation is split into segments corresponding to different groups, and auxiliary results are computed for each segment independently, allowing parallel processing and reducing overall communication overhead.
Solution Approach 2:
The patent introduces auxiliary computation results as intermediary data structures that facilitate the computation of order within groups. These auxiliary results act as mediators between the input data and the final output, enabling the system to compute aggregate orders with O(1) communication by pre-computing and storing intermediate cross-tabulation results that can be quickly referenced during the ordering process.
2Productivity
If the number of communication times is reduced to O(1), then computation efficiency is improved, but the complexity of the secure computation apparatus increases
Solution Approach 1:
The patent applies preliminary action by pre-computing auxiliary computation results (cross-tabulations) before the actual order computation is needed. These pre-computed results are stored and can be quickly retrieved during the secure computation process, eliminating the need for repeated log(n) communications and reducing the computational burden during the main processing phase.
Solution Approach 2:
The patent creates copies of the data in segmented form across multiple secure computation apparatuses. Each apparatus holds a portion of the cross-tabulation data corresponding to its assigned group, allowing parallel processing without requiring frequent communication. This copying approach distributes the data load and reduces communication overhead while maintaining the ability to compute aggregate orders efficiently.
Data Source
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AI summary
An aggregate order is efficiently obtained while keeping confidentiality. An inverse permutating part (12) generates a share of a vector representing an inversely permutated cross tabulation by applying inverse permutation to a cross tabulation of a table, the inverse permutation being a permutation which moves elements so that, when the table is grouped based on a key attribute, last elements of each group are sequentially arranged from beginning. A partial summing part (13) computes a prefix sum from the inversely permutated cross tabulation. The order computing part (14) generates a share of a vector representing ascending order within a group from a result of the prefix sum.