Secure Computation Intersection Using Stable Sorting of Multisets
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Solution Overview
Problem
Conventional secure computation methods cannot handle overlapping elements in multisets, leading to high computation costs when obtaining concealed information of the Intersect operation result.
Innovation Solution
A secure computation device processes the concealed information of two multisets X and Y, removes element duplicates to obtain sets X' and Y', and then applies conventional methods to these sets, using input flag addition, stable sorting, equality checks, and output flag generation to achieve the Intersect operation at reduced computational cost.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional secure computation methods are used to obtain concealed information of the Intersect operation result from multisets with overlapping elements, then the computation cost becomes excessively large, but if the conventional methods are applied directly without preprocessing, then the element overlap handling is not possible
Solution Approach 1:
The patent applies preliminary action by performing stable sorting on the multisets X and Y before executing the Intersect operation. The sorting is performed in advance to arrange elements in a deterministic order, which enables efficient duplicate detection and removal during the subsequent Intersect computation. This preliminary organization of data reduces the computational complexity of handling overlapping elements during the actual secure computation phase.
Solution Approach 2:
The patent segments the Intersect operation into distinct phases: first performing stable sorting on input multisets to organize elements, then executing the Intersect operation on the sorted data. This segmentation allows the system to handle element overlaps systematically by processing sorted sequences rather than raw multisets, thereby reducing computation cost while maintaining correctness.
2Productivity
If stable sorting is performed on concealed information to enable Intersect operation on multisets, then the computation cost is reduced, but the device complexity increases due to additional processing steps
Solution Approach 1:
The stable sorting unit performs a universal function that serves multiple purposes: it organizes elements for efficient Intersect computation, maintains the concealed information property, and enables subsequent duplicate detection. By making the sorting operation universal and integrating it into the secure computation framework, the patent reduces overall computation efficiency without proportionally increasing device complexity.
Solution Approach 2:
The patent introduces stable sorting as an intermediary step between the input multisets and the Intersect operation. This intermediary process transforms the input data into a sorted form that facilitates efficient computation of the Intersect operation on concealed information, thereby improving productivity while managing device complexity through a well-defined intermediate transformation.
3Adaptability or versatility
If the concealed information of sets X' and Y' (obtained by removing duplicates) is used as input to conventional secure computation methods, then the Intersect operation can be performed, but the computation cost for obtaining concealed information of X' and Y' is large
Solution Approach 1:
The patent performs preliminary stable sorting on the concealed information of multisets X and Y before executing the Intersect operation. This preliminary action organizes the concealed data in advance, enabling the subsequent Intersect computation to efficiently handle element overlaps without incurring excessive computation cost. The sorting is performed on the concealed information itself, maintaining security while improving efficiency.
Solution Approach 2:
The patent replaces the conventional approach of first removing duplicates and then computing Intersect with a substituted mechanism that performs stable sorting on concealed information followed by a single Intersect operation. This substitution eliminates the need for separate duplicate removal steps on concealed data, thereby reducing computation cost while maintaining the ability to handle element overlaps correctly.
Data Source
AI summary
A concealed operation result indicating concealed information of an Intersect operation result of X and Y is obtained while X={{x0, . . . , xn−1}} and Y={{y0, . . . , ym−1}} are concealed. A secure computation device obtains a sequence ([s], [M]) including [s] including n [B0] and m [B1] and [M] including [x0], . . . , [xn−1] and [y0], . . . , [ym−1], performs stable sorting on the sequence ([s], [M]) according to an order relationship of content represented by each of the elements M0, . . . , Mn+m−1 to obtain a sequence ([s′], [M′]), obtain [eqq] where eqq=T when M′q=M′q+1 and eqq=F otherwise and [seqq] where seqq=T when s′q=s′q+1 and seqq=F otherwise, obtain [fq] where fq=D1 when eqq=T and seqq=F and fq=D0 otherwise, and outputs [fq] and [M′q]. Where, [α] is concealed information of α.