Private Information Retrieval Query Arithmetic Function
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Solution Overview
Problem
Current private information retrieval methods face challenges in achieving efficient communication complexity, with existing schemes either being impractical for large databases or falling short of the theoretical lower bound of O(log m) communication complexity, while maintaining database privacy and user query secrecy.
Innovation Solution
The method involves generating a query as an arithmetic function of an index and a secret value, using a modulus with a prime power order, where the secret value is factorized into prime numbers, allowing for logarithmic communication complexity by ensuring the database owner cannot determine the index queried and the user does not learn excessive information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the database owner sends the entire database to the user, then the user can make any query privately, but the total communication complexity becomes O(m) which is impractical for large databases
Solution Approach 1:
The database is segmented into multiple blocks, and the query process is divided into two phases: a setup phase where cryptographic parameters are pre-computed, and a query phase where only logarithmic communication is required. This segmentation allows the system to achieve both privacy and efficiency.
Solution Approach 2:
Cryptographic parameters including moduli, generators, and trapdoors are pre-computed and stored in the database during a setup phase before any queries are executed. This preliminary action enables efficient query processing with O(log m) communication complexity while maintaining security.
2Quantity of substance
If multiple replicas of databases are used to reduce communication complexity, then communication can be reduced to O(m1/k) for k databases, but the databases cannot communicate with each other which increases system complexity
Solution Approach 1:
A trusted setup authority acts as an intermediary to generate cryptographic parameters and distribute them to the database owner and user. This intermediary enables the single-database scheme to achieve O(log m) communication complexity without requiring multiple non-communicating replicas.
3Quantity of substance
If computational intractability assumptions are used to achieve single database private information retrieval, then communication complexity can be reduced below O(m), but the security relies on unproven cryptographic assumptions
Solution Approach 1:
The invention changes the cryptographic parameters used in previous schemes by employing a specific mathematical structure based on quadratic residues and Jacobi symbols. This parameter change maintains computational security while achieving the desired O(log m) communication complexity.
Data Source
AI summary
A method, article of manufacture and apparatus for performing private retrieval of information from a database is disclosed. In one embodiment, the method comprising obtaining an index corresponding to information to be retrieved from the database and generating a query that does not reveal the index to the database. The query is an arithmetic function of the index and a secret value, wherein the arithmetic function includes a multiplication group specified by a modulus of a random value whose order is divisible by a prime power, such that the prime power is an order of the random value. The secret value is an arithmetic function of the index that comprises a factorization into prime numbers of the modulus. The method further comprises communicating the query to the database for execution of the arithmetic function against the entirety of the database.