Private Set Intersection for Unbalanced Datasets
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional private set intersection (PSI) protocols are inefficient and costly when dealing with datasets of disparate sizes, as they require padding both sets to equal size, leading to quasi-linear computational and linear communication costs.
Innovation Solution
Implementing a server-side array, such as an inverted Bloom filter or cuckoo hash table, and using private information retrieval (PIR) protocols to enable a client to determine the intersection without learning additional information about the server's set, while the server learns nothing about the client's set.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional PSI algorithms pad both sets to equal size, then both sets need to be at least the size of the larger set, but computational cost scales quasi-linearly with the number of elements in the larger set and communication cost scales linearly with the number of elements in the larger set
Solution Approach 1:
The patent extracts only the necessary information (intersection elements) from the larger set without requiring the client to process or store the entire larger set. The server computes encrypted representations of only the intersection elements and transmits only those, extracting useful information while leaving the bulk of the larger set unprocessed and untransmitted.
Solution Approach 2:
The server performs preliminary computation by pre-computing encrypted representations of elements in the larger set and storing them in a database. This allows the client to query only for intersection elements without requiring the client to perform computationally intensive operations on the entire larger set.
2Reliability
If conventional PSI algorithms pad both sets to equal size, then both sets need to be at least the size of the larger set, but communication cost scales linearly with the number of elements in the larger set
Solution Approach 1:
The patent extracts only the necessary information (intersection elements) from the larger set without requiring the client to process or store the entire larger set. The server computes encrypted representations of only the intersection elements and transmits only those, extracting useful information while leaving the bulk of the larger set unprocessed and untransmitted.
3Productivity
If the client queries the server for each element of the client's set, then the client can learn the intersection, but the server learns which array locations had data retrieved
Solution Approach 1:
The patent introduces an intermediary mechanism using homomorphic encryption and zero-knowledge proofs. The client obtains encrypted representations of array elements without the server learning which elements were queried. The client decrypts only the necessary information locally, serving as an intermediary that prevents direct information flow from client queries to server knowledge.
Solution Approach 2:
The patent replaces direct mechanical querying (where the server would obviously see which indices are accessed) with cryptographic substitution using homomorphic encryption. The server operates on encrypted data without seeing the plaintext queries, substituting the mechanical query-response mechanism with a cryptographic one that obscures query patterns.
Data Source
AI summary
Private set intersection (PSI) protocols can be efficiently performed for sets of disparate sizes. A server can compute an array, such as an inverted Bloom filter or cuckoo hash table, that represents the content of the server set. A client can query the array, e.g., using a private information retrieval (PIR) protocol, to obtain information that enables the client to determine whether a particular element of the client's set is also in the server's set. By repeating the query for each element of the client's set, the client can learn the intersection.