Multiplicity-Coded PIR Retrieval With Low Communication Overhead
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Solution Overview
Problem
Existing Private Information Retrieval (PIR) protocols face challenges in achieving practical, efficient, and information-theoretically secure solutions, particularly in cloud computing environments where data is outsourced and accessed by multiple users, with high communication overhead and vulnerability to collusion between servers.
Innovation Solution
A method using multiplicity codes with low communication complexity and robustness to collusion, allowing retrieval of information symbols from a matrix of multiplicity coded symbols, ensuring that each server remains unaware of the queried element, even in collusion scenarios, and optimizing storage and communication overhead through vectorial index calculations and decoding processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If information theoretical secure PIR algorithms are used, then security against unbounded computational adversaries is achieved, but communication overhead increases and practical efficiency decreases
Solution Approach 1:
The database is divided into multiple blocks, each encoded with a separate Locally Decodable Code. This segmentation allows the system to retrieve specific symbols without decoding entire blocks, reducing communication overhead while maintaining information-theoretic security through the distributed code structure
Solution Approach 2:
The patent transitions from traditional single-code PIR approaches to a multi-dimensional structure using multiple LDCs arranged in a specific configuration. This dimensional change enables efficient symbol retrieval by allowing queries to target specific positions across multiple code blocks without revealing the queried symbol to the server
2Reliability
If Locally Decodable Codes are used for PIR, then information theoretical security is achieved, but the constructions remain theoretical and lack practical efficiency
Solution Approach 1:
The database is pre-encoded into multiple LDC blocks before storage. This preliminary encoding action enables efficient retrieval operations later, as the structure is already optimized for local decoding. The pre-computation of code blocks makes the theoretical LDC construction practically implementable while maintaining security guarantees
Solution Approach 2:
The patent optimizes LDC parameters such as code length, dimension, and locality to achieve a practical balance between security, storage efficiency, and retrieval speed. By carefully selecting code parameters, the system transforms theoretical LDC constructions into practical implementations suitable for real-world PIR applications
3Loss of information
If traditional PIR protocols are used, then data privacy is protected, but communication complexity and storage overhead are high
Solution Approach 1:
The patent extracts and utilizes only the necessary portions of the encoded database for retrieval. By leveraging the local decodability property, the system extracts specific symbols from LDC blocks without requiring communication or access to entire blocks, significantly reducing communication complexity while maintaining data privacy through the information-theoretic security of LDCs
Data Source
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AI summary
Method system and computer-readable medium to retrieve an information symbol. This method uses a matrix of multiplicity coded symbols of size σ lines by n columns. The method comprises a step of determining a column j and a line i of the matrix of coded symbols where the information symbol is located and a step of calculated vectorial indexes lj(t) for t from 0 to L ≥ q - 1 by projecting a vectorial index pj of the column j of the matrix of coded symbols to a finite affine space GF(q)m and a step of determining for each vectorial indexes lj(t) with t from 0 to L ≥ q - 1a column of the matrix of coded symbols, associated to the vectorial indexes lj(t) and a step of requesting at least one of the elements of the matrix of coded symbols located at the line i of the information symbol and the columns determined during the step of determination and a step of decoding the information symbol using these requested elements.