Secure Aggregate Median Computation via Bit Decomposition
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Solution Overview
Problem
Conventional secure computation techniques require inefficient communication to obtain a group-by median, with a high number of communication instances (log(n)) needed to compute this statistic.
Innovation Solution
A secure aggregate median system is developed, comprising secure computation apparatuses that sort and process shares of value and key attributes to efficiently compute the median within groups, using bit decomposition, flag generation, and permutation to minimize communication to O(1) instances while maintaining confidentiality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional secure computation techniques are used to compute group-by median, then confidentiality is maintained, but communication efficiency deteriorates due to requiring log(n) communication instances
Solution Approach 1:
The patent segments the computation by introducing separate shares for ascending order ([a]) and descending order ( [d]) within groups. This segmentation allows independent processing of order information without requiring full data revelation, enabling confidentiality while reducing communication to O(1) instances through localized bit decomposition and flag generation.
Solution Approach 2:
The patent transforms the computation from a single-dimensional sorting approach to a multi-dimensional approach by adding order indicator dimensions ([a] and [d] shares). This dimensional expansion enables the system to determine medians through bit decomposition and flag operations rather than full sorting, reducing communication complexity while maintaining security.
2Reliability
If conventional secure computation techniques are used to compute group-by median, then confidentiality is maintained, but computational complexity increases due to multiple sorting operations
Solution Approach 1:
The patent extracts only the necessary order information into separate shares [a] and [d], removing the need for complete sorting operations. By taking out only the essential ordering flags rather than full sorted data, the system maintains confidentiality while significantly reducing computational complexity through bit decomposition and flag-based median determination.
Solution Approach 2:
Instead of performing complex sorting operations to find medians, the patent inverts the approach by using bit decomposition and flag generation to directly determine median positions. This inversion transforms the computational task from sorting-based to flag-based, reducing complexity while preserving confidentiality through the share mechanism.
Data Source
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AI summary
An aggregate median is efficiently obtained while confidentiality is kept. An order computing part (11) generates ascending order a and descending order d within a group when a table which has been stably sorted based on a desired value attribute and a key attribute is grouped based on the key attribute. A subtracting part (12) generates shares {a-d}, {d-a} of a-d, d-a. A bit deleting part (13) generates shares {a'}, {d'} of a', d' obtained by excluding least significant bits from {a-d}, {d-a}. An equality determining part (14) generates shares {a"}, {d"} of {a"}: = {|a'=0|}, {d"}: = {|d'=0|}. A format converting part (15) converts {a"}, {d"} into [a"], [d"]. A flag applying part (16) generates shares [va], [vd] of [va]: = [v1a"], [vd]: = [v1d"]. A permutation generating part (17) generates shares {{σa}}, {{σd}} of permutations σa, σd which sort ¬a", ¬d". A median computing part (18) generates a share [x] of a vector x which represents a median of each group by computing [x]: = [σa(va)+σd(σd)].