Secure Multi-Set Product Computation Using Count and Equality Flags
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Solution Overview
Problem
Conventional secret product set computation methods are limited to handling two sets as inputs and require repetitive computations for three or more sets, leading to increased computation cost due to redundancy.
Innovation Solution
A secure computation device and method that directly handles concealed information of three or more sets by using a counting unit to obtain count results, an equality check unit to verify equality, and an output flag adding unit to associate key information with equality check results, enabling direct computation of a product set operation result.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If secret product set computation is repeated for three or more sets using two-set computation as base, then concealed information of product set operation result can be obtained, but the number of rounds increases and computation cost increases due to redundant processing
Solution Approach 1:
The computation process is segmented into distinct functional units: a counting unit that obtains count results through secure computation, an equality check unit that verifies equality of count results, and an output flag adding unit that adds flags to elements satisfying the product set condition. This segmentation allows each unit to perform its specific function efficiently without redundant processing across multiple rounds.
Solution Approach 2:
The counting unit performs preliminary secure computation to obtain count results indicating the number of elements representing each key information before the equality check unit verifies equality. This preliminary action eliminates the need for repeated rounds of computation, as all necessary counting is done in advance of the equality verification stage.
2Reliability
If conventional two-set computation method is used for three or more sets, then concealed information can be obtained, but processing becomes redundant between rounds increasing computation cost
Solution Approach 1:
The secure computation process continues continuously through the counting unit, equality check unit, and output flag adding unit without interruption or repetition. The counting unit performs secure computation to obtain count results, which are then immediately verified by the equality check unit and processed by the output flag adding unit in a continuous workflow, eliminating redundant computation rounds while maintaining the security of concealed information throughout the entire process.
3Adaptability or versatility
If repetitive secret product set computation is performed for multiple sets, then product set operation result can be obtained, but the number of rounds increases affecting processing speed
Solution Approach 1:
The secure computation device is designed with universal functionality to handle any number of sets (three or more) simultaneously through a single integrated process. The counting unit can process multiple sets in parallel to obtain count results for all sets, the equality check unit can verify equality across all sets in one operation, and the output flag adding unit can add flags to elements satisfying the product set condition for all sets. This multi-functional design eliminates the need for repeated rounds and achieves high-speed parallel computation for multi-set operations.
Data Source
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AI summary
By using [x0,0], ..., [x0,r(0)-1], ..., [xL-1,0], ..., [xL-1,r(L-1)-1] obtained by concealing L sets X0 = {x0,0, ..., X0,r(0)-1}, ..., XL-1 = {xL-1,0, ..., xL-1,r(L-1)-1}, [c0], ..., [cm-1] obtained by concealing the number cp of elements representing kp among x0,0, ..., x0,r(0)-1, ..., xL-1,0, ..., xL-1,r(L-1)-1 for p = 0, ..., m-1 are obtained, [eq0], ..., [eqm-1] obtained by concealing eqp = T when cp is L and eqp = F when cp is not L for p = 0, ..., m-1 are obtained, and a data structure including [kp] and [eqp] associated with each other is output as a concealed operation result of a product set of X0, ..., XL-1.