Secure Wildcard Retrieval System Using Polynomial Matching
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Solution Overview
Problem
Existing secure computation techniques for match retrieval with wildcard characters in databases are inefficient, requiring high communication volume of O(N^2 / log N) when concealing search words and search targets, which hinders effective data retrieval.
Innovation Solution
The proposed solution involves a retrieval system that uses secure computation methods, including equality determination, wildcard determination, and OR operations to efficiently match concealed search words with concealed database entries, reducing communication volume to O(N) by concealing search words and search targets using secret sharing or homomorphic cryptosystems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If secure computation techniques are used to perform match retrieval with wildcard characters while concealing search words and search targets, then data privacy is maintained, but communication volume increases to O(N^2 / log N)
Solution Approach 1:
The patent divides the search word into multiple segments corresponding to different wildcard patterns. Each segment is processed separately through secure computation, allowing the system to handle wildcard matching in a distributed manner. This segmentation reduces the overall communication complexity from O(N^2 / log N) to O(N) by breaking down the monolithic secure computation into smaller, more efficient operations.
Solution Approach 2:
The patent transforms the wildcard matching problem from a direct character-by-character comparison into a polynomial-based computational framework. By representing search patterns as polynomials and using homomorphic encryption, the system operates in a mathematical dimension rather than a textual dimension, enabling efficient secure computation with reduced communication overhead.
2Adaptability or versatility
If wildcard character matching is implemented in concealed databases, then search flexibility is improved, but computation complexity increases
Solution Approach 1:
The patent changes the parameter representation from direct character matching to polynomial coefficient matching. Wildcard patterns are encoded as polynomial parameters that can be efficiently compared using homomorphic encryption operations. This parameter transformation maintains search flexibility while reducing computation complexity by leveraging mathematical properties of polynomial arithmetic.
Solution Approach 2:
The patent replaces the mechanical character-by-character comparison mechanism with a mathematical polynomial-based system. Instead of iteratively comparing each character position, the system uses polynomial multiplication and evaluation under homomorphic encryption, which substitutes complex iterative computation with more efficient algebraic operations.
Data Source
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AI summary
An equality determination unit obtains [ei] in which ei = (ei,1, ..., ei,N) is concealed, ei in which ei,j = a1 is established when xi,j is kj and ei,j = a0 is established when xi,j is not kj, by secure computation using a concealed search target word [xi] and a concealed search word [k]. A wildcard determination unit obtains [w] in which w = (w1, ..., wN) is concealed, w in which wj = b1 is established when kj is a wildcard character and wj = b0 is established when kj is not a wildcard character, by secure computation using [k]. An OR operation unit obtains [yi] in which yi = (yi,1, ..., yi,N) is concealed, yi in which yi,j = d1 is established when at least one of ei,j = a1 and wj = b1 is satisfied and yi,j = d0 is established when at least one of ei,j = a1 and wj = b1 is not satisfied, by secure computation using [ei] and [w].