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New Bounds and a Generalization for Share Conversion for 3-Server PIR
Anat Paskin-Cherniavsky1, Olga Nissenbaum1
1Computer Science Department, Ariel University, Ariel 40700, Israel.
Entropy (Basel, Switzerland)
|April 23, 2022
Summary
This study advances Private Information Retrieval (PIR) by proving share conversion existence for even m with p=2, and absence for p>2. New PIR constructions may offer shorter server responses and improved efficiency.
Area of Science:
- Cryptography and Information Security
- Theoretical Computer Science
Background:
- Multi-server Private Information Retrieval (PIR) protocols enhance efficiency using replicated databases.
- Existing paradigms for PIR construction rely on share conversion schemes from secret sharing.
Purpose of the Study:
- To investigate the existence of share conversion for specific parameters in multi-server PIR construction.
- To explore new avenues for constructing efficient PIR protocols with improved parameters.
Main Methods:
- Utilized algebraic techniques to analyze the solvability of linear systems related to share conversion.
- Employed computer search within the Beimel et al. (BIKO) framework to identify new sets for share conversion.
Main Results:
- Proved the existence of share conversion for even m when p=2, and its absence for even m when p>2.
- Discovered extended relations (CSm') that enable share conversion with reduced parameters (β' < β).
- Identified potential for shorter server responses and enhanced PIR efficiency through these new constructions.
Conclusions:
- The findings expand the understanding of PIR construction possibilities, particularly for composite moduli m.
- The identified extended relations offer a promising direction for optimizing 3-server PIR efficiency.
- Further research into matching vector families with higher Vapnik-Chervonenkis dimensions could yield more efficient PIR protocols.
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