Private Set Intersection with Branching Programs and Homomorphic Encryption
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Solution Overview
Problem
In computing environments where multiple parties with private data need to compute a common function without revealing their data, existing methods struggle with scalability and efficiency, especially when one party has a significantly larger dataset and limited computational resources.
Innovation Solution
A protocol using a branching program and fully homomorphic encryption allows two parties to securely compute the intersection of their private sets, with the server evaluating encrypted inputs and the client decrypting the result, minimizing communication overhead and enabling easy scalability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If traditional private set intersection methods are used, then security is maintained, but communication overhead increases significantly with larger server datasets
Solution Approach 1:
The server dataset is organized into a branching program structure with internal nodes and leaf nodes, segmenting the large dataset into a hierarchical format that enables efficient traversal and comparison without requiring the client to process the entire dataset at once
Solution Approach 2:
A branching program acts as an intermediary structure between the server's large dataset and the client's smaller dataset, enabling secure comparison through encrypted traversals without requiring direct exchange of the complete datasets
2Power
If the server has larger computational power, then computation speed improves, but the ability to protect client privacy deteriorates
Solution Approach 1:
The patent replaces traditional mechanical data exchange with fully homomorphic encryption, allowing the server to perform computations on encrypted client data without ever accessing the plaintext, thus maintaining client privacy while utilizing server computational power
Solution Approach 2:
Encrypted data serves as an intermediary that allows the server to process information without seeing the actual client data, maintaining privacy while enabling computation
3Reliability
If the client processes the entire server dataset, then intersection accuracy is ensured, but client computational resources are exhausted
Solution Approach 1:
The branching program segments the server dataset into a hierarchical structure where the client only needs to traverse paths relevant to its own data, avoiding the need to process the entire server dataset
Solution Approach 2:
The client performs only the necessary partial traversal of the branching program corresponding to its data, rather than processing the entire server dataset, thus conserving computational resources while maintaining accuracy
Data Source
AI summary
In an example embodiment, a protocol for private set intersection is introduced that provides for two-party computation. Each party has a private data set and both parties want to securely compute the intersection of their sets, such that only the result is revealed and nothing else. Construction rules are provided that rely on the evaluation of a branching program (BP) using a fully homomorphic encryption (FHE) scheme. Using the properties of an FHR scheme, a non-interactive protocol is built with extendable functionalities. Thus, not only can the intersection be securely computed but the result can be used for further secure computations. Furthermore, the communication overhead for practical applications is independent of the server's set size, allowing for easy scalability.