Secure Partial Character String Detection Using Matrix Operations
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Solution Overview
Problem
Existing secure computation methods for pattern matching require O(1) rounds and a communication amount of Ω(m^3 < n) to locate partial character strings in a text while concealing the contents, which is inefficient.
Innovation Solution
A partial-character-string position detecting device and method that generates matrices to efficiently detect the positions of partial character strings in a text by using secret sharing and logical operations, reducing the rounds to O(log m) and communication to O(mn) through matrix operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If secure computation is used to locate positions of partial character strings while concealing text and pattern contents, then security is improved, but communication amount increases to Ω(m³) and rounds increase to O(1)
Solution Approach 1:
The pattern matching process is segmented into three independent matrix operations: generating matrix E from character-by-character matching results, generating matrix F by shifting and permuting E, and generating matrix H by combining F with vector c. Each operation processes independent data structures, allowing parallel execution and reducing total communication overhead while maintaining security through secret sharing.
Solution Approach 2:
The invention transforms the one-dimensional pattern matching problem into a two-dimensional matrix problem. By representing matching results as matrix E (m rows × n columns) and applying linear transformations to generate matrices F and H, the system achieves O(mn) communication complexity instead of Ω(m³), as the matrix structure enables efficient batch processing of multiple character comparisons simultaneously.
2Reliability
If secure computation is used to locate positions of partial character strings while concealing text and pattern contents, then security is improved, but processing rounds increase to O(1)
Solution Approach 1:
The character-by-character matching between pattern and text is performed in advance to generate matrix E before the secure computation protocol begins. This preliminary action allows the subsequent matrix operations (generating F and H) to proceed with pre-computed data, reducing the number of interactive rounds required during the secure computation phase from O(1) to O(log m).
Solution Approach 2:
The invention introduces dynamic matrix transformations where matrix F is generated by shifting and permuting matrix E based on the vector c, and matrix H is dynamically computed by combining F with logical operations. These dynamic operations adapt to the specific pattern and text being matched, optimizing the computation path and reducing iterative rounds compared to static secure computation approaches.
3Measurement precision
If character-by-character matching results are used to generate matching matrices, then detection precision is improved, but device complexity increases due to multiple matrix operations
Solution Approach 1:
The matrix generation device performs multiple functions through a unified matrix operation framework: it generates matrix E from character matching, transforms E to F through shifting and permutation, and computes H by combining F with vector c. This universal matrix-based approach replaces multiple specialized algorithms, reducing overall system complexity while maintaining high detection precision through systematic processing.
Solution Approach 2:
Matrix F serves as an intermediary structure between the character-by-character matching results (matrix E) and the final position detection (matrix H). The intermediary matrix F encapsulates the transformed matching data in a form that facilitates efficient computation of H, breaking down the complex detection process into manageable stages and reducing the cognitive and computational burden on the system.
Data Source
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AI summary
The positions in a text in which partial character strings in a pattern appear are efficiently detected. A partial-character-string position detecting device 1 takes inputs of a secret text [t] of a text t, a secrete text of a pattern p, a secret text <c> of a vector c, and a secret text <E> of a matrix E and outputs a secret text <H> of a matrix H. A first matrix generating part 20 generates a secret text <F> of a matrix F, in which F[i][j] = E[i][j + i mod n + 1] (where it is assumed that E[i][n] = ¬c[i]). A second matrix generating part 30 generates a secret text <F'> of a matrix F', in which F[i][j] = 1 is set if c[i] = 0 or if c[i] = 1 and F[k][j] = 1 for every k that is successively c[k] = 1, otherwise F[i][j] = 0 is set, where k = i, ..., n - 1. A third matrix generating part 40 computes <H[i][j]> = <F[i][j - i mod n + 1]> ∧ <c[i]> ∧ ¬c[i - 1]> to generate the secrete text <H>.