Secure Multiset Intersection Using Stable Sorting and Concealed Flags
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Solution Overview
Problem
Conventional secure computation methods do not allow for the overlapping of elements in sets, making it impossible to obtain concealed information of Intersect (X, Y) using the concealed information of two multisets X and Y as input, and the computation cost for removing element duplication is high.
Innovation Solution
A secure computation device and method that first eliminates element duplication from multisets X and Y, then applies stable sorting and equality checks to obtain the concealed information of Intersect (X, Y) at a reduced computation cost, using input flags and sorting units to maintain correspondence and perform equality checks by secure computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional secure computation method is used to eliminate element duplication from multisets, then the concealed information of Intersect (X, Y) can be obtained, but the computation cost becomes large
Solution Approach 1:
The patent segments the multiset elements into two distinct groups by assigning unique flags: the first flag value for elements from the first multiset X and the second flag value for elements from the second multiset Y. This segmentation allows the secure computation to process elements from different multisets separately while maintaining their identities, enabling efficient duplicate removal without requiring complex conventional secure computation protocols.
Solution Approach 2:
The patent performs preliminary actions by adding flags to elements before the main secure computation process. Each element is pre-marked with information about its origin multiset, which enables the subsequent secure sorting and duplicate removal to proceed more efficiently. This preliminary flagging avoids the need for expensive conventional secure computation steps during the main processing phase.
2Reliability
If conventional secure computation method is used, then security of concealed information is maintained, but overlapping elements cannot be processed in multisets
Solution Approach 1:
The patent introduces flags as intermediary markers that carry information about element origins without revealing the actual element values. These flags act as mediators that enable the secure computation system to distinguish between elements from different multisets and identify duplicates, thereby extending the capability to handle multisets with overlapping elements while maintaining security through the concealed nature of the flag comparison process.
Data Source
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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.