Optimizing Leaky Private Information Retrieval Codes to Achieve ${O}(log K)$ Leakage Ratio Exponent

2025-01-21

AI Summary

研究L-PIR问题，优化信息查找模式概率，使信息泄露程度从Θ(K)降至O(log K)，提高不完全保密信息查找的安全性。

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Privacy

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We study the problem of leaky private information retrieval (L-PIR), where the amount of privacy leakage is measured by the pure differential privacy parameter, referred to as the leakage ratio exponent. Unlike the previous L-PIR scheme proposed by Samy et al., which only adjusted the probability allocation to the clean (low-cost) retrieval pattern, we optimize the probabilities assigned to all the retrieval patterns jointly. It is demonstrated that the optimal retrieval pattern probability distribution is quite sophisticated and has a layered structure: the retrieval patterns associated with the random key values of lower Hamming weights should be assigned higher probabilities. This new scheme provides a significant improvement, leading to an ${O}(log K)$ leakage ratio exponent with fixed download cost $D$ and number of servers $N$, in contrast to the previous art that only achieves a $Theta(K)$ exponent, where $K$ is the number of messages.

Problem

• Information Leakage
• Probability Distribution
• Logarithmic Reduction

Innovation

• Optimized Probability
• Reduced Information Leakage
• Enhanced L-PIR Solution