Private Set Difference via Homomorphic Third-Party Computation
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Solution Overview
Problem
Existing technologies fail to efficiently compute the difference between two datasets while maintaining privacy, particularly in scenarios where a third party needs to determine the private set difference without revealing the underlying data sets.
Innovation Solution
A third-party private set difference (TP-PSD) protocol using homomorphic encryption schemes, specifically additively and fully homomorphic encryption, allows a third party to compute the difference between two datasets without learning the individual datasets by generating a key pair, performing homomorphic operations, and decrypting the results using the private key.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption is used to compute private set difference, then privacy is preserved, but computational complexity increases
Solution Approach 1:
The patent introduces an intermediate representation (encrypted polynomials) that mediates between the private datasets and the final set difference result. The homomorphic encryption scheme allows computations to be performed on encrypted data without decryption, using polynomial representations that can be manipulated through homomorphic operations. This intermediary structure enables privacy-preserving computation while managing complexity through algebraic transformations rather than brute-force cryptographic operations.
Solution Approach 2:
The patent transforms the set difference problem into a polynomial computation problem by representing sets as polynomial roots. This parameter change from set membership to polynomial coefficients enables the use of homomorphic encryption properties, where polynomial multiplication and evaluation can be performed on encrypted data. The transformation allows the third party to compute encrypted evaluations of polynomials that reveal only the set difference, not the underlying datasets.
2Productivity
If third party computes the difference, then the result is obtained, but the third party may learn additional information about the datasets
Solution Approach 1:
The encrypted polynomial evaluations serve as an intermediary that conveys only the necessary information (set difference) to the third party. The homomorphic encryption scheme ensures that the third party receives and processes only encrypted values that, when decrypted, reveal exclusively the set difference elements. The polynomial structure acts as a filter that eliminates information about individual dataset elements while preserving the difference computation.
Solution Approach 2:
The patent extracts only the set difference information from the encrypted polynomial computations. By designing the polynomial evaluations to evaluate to zero at dataset elements and using homomorphic operations to compute differences, the system extracts precisely the desired information (elements in one set but not the other) while leaving all other information encrypted and inaccessible to the third party.
3Reliability
If traditional encryption methods are used, then security is maintained, but communication complexity increases
Solution Approach 1:
The patent combines multiple cryptographic and computational operations into a unified homomorphic encryption framework. Instead of separate encryption, transmission, and computation steps that would increase communication overhead, the system merges these into a single flow where encrypted polynomials are computed and evaluated homomorphically. This consolidation reduces the quantity of data that needs to be communicated while maintaining security through the inherent properties of homomorphic encryption.
Data Source
AI summary
A third party cryptographically determines a private set difference between a data set of a first party and a data set of a second party. The third party cryptographically generates a key pair including a private key and a public key, provides the public key to the first party and the second party, receives an encrypted result from the second party, wherein the encrypted result is computed prior to receipt by the third party using homomorphic operations performed using the public key, the data set of the first party, and the data set of the second party, decrypts the encrypted result using the private key to yield an intermediate data set, and determines the private set difference between the first data set and the second data set based on the intermediate data set.