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Single-Server Pliable Private Information Retrieval with Identifiable Side Information

Megha Rayer, Charul Rajput, B. Sundar Rajan

TL;DR

This work introduces PPIR-ISI, a single-server PPIR setting where the user knows the identities of side information for a subset of classes (η identifiable classes). It develops an MDS-code–based scheme achieving $R_{PPIR-ISI}=\dfrac{1}{(k_{un}+1)(Γ-η+1)}$ under explicit side-information constraints, showing that identifiability can improve rate relative to PPIR-USI in some cases. The paper further extends to a multi-user scenario with cooperative querying, achieving $R_{PPIR-ISI}=\dfrac{1}{(k_{un}+1)(Γ-η')}$ where $η'=\lceil(η-1)/U\rceil$, and provides constructions (Algorithm 2) that preserve privacy via non-repetition and MDS decodability. The results highlight how structured side-information identifiability can reduce download cost while maintaining privacy, with potential impact on private content delivery and coded PIR schemes in practical networks.

Abstract

In Pliable Private Information Retrieval (PPIR) with a single server, messages are partitioned into $Γ$ non-overlapping classes. The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. In S. A. Obead, H. Y. Lin and E. Rosnes, Single-Server Pliable Private Information Retrieval With Side Information, arXiv:2305.06857, authors consider the problem of PPIR with Side Information (PPIR-SI), where the user now has side information. The user wants to retrieve any new message (not included in the side information) from its desired class without revealing the identity of the desired class and its side information. A scheme for the PPIR-SI is given by Obead et al. for the case when the users side information is unidentified, and this case is referred to as PPIR with Unidentifiable SI (PPIR-USI). In this paper, we study the problem of PPIR for the single server case when the side information is partially identifiable, and we term this case as PPIR with Identifiable Side Information (PPIR-ISI). The user is well aware of the identity of the side information belonging to $η$ number of classes, where $1\leq η\leq Γ$. In this problem, The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. We give a scheme for PPIR-ISI, and we prove that having identifiable side information is advantageous by comparing the rate of the proposed scheme to the rate of the PPIR-USI scheme given by Obead et al. for some cases. Further, we extend the problem of PPIR-ISI for multi-user case, where users can collaborately generate the query sets, and we give a scheme for this problem.

Single-Server Pliable Private Information Retrieval with Identifiable Side Information

TL;DR

This work introduces PPIR-ISI, a single-server PPIR setting where the user knows the identities of side information for a subset of classes (η identifiable classes). It develops an MDS-code–based scheme achieving under explicit side-information constraints, showing that identifiability can improve rate relative to PPIR-USI in some cases. The paper further extends to a multi-user scenario with cooperative querying, achieving where , and provides constructions (Algorithm 2) that preserve privacy via non-repetition and MDS decodability. The results highlight how structured side-information identifiability can reduce download cost while maintaining privacy, with potential impact on private content delivery and coded PIR schemes in practical networks.

Abstract

In Pliable Private Information Retrieval (PPIR) with a single server, messages are partitioned into non-overlapping classes. The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. In S. A. Obead, H. Y. Lin and E. Rosnes, Single-Server Pliable Private Information Retrieval With Side Information, arXiv:2305.06857, authors consider the problem of PPIR with Side Information (PPIR-SI), where the user now has side information. The user wants to retrieve any new message (not included in the side information) from its desired class without revealing the identity of the desired class and its side information. A scheme for the PPIR-SI is given by Obead et al. for the case when the users side information is unidentified, and this case is referred to as PPIR with Unidentifiable SI (PPIR-USI). In this paper, we study the problem of PPIR for the single server case when the side information is partially identifiable, and we term this case as PPIR with Identifiable Side Information (PPIR-ISI). The user is well aware of the identity of the side information belonging to number of classes, where . In this problem, The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. We give a scheme for PPIR-ISI, and we prove that having identifiable side information is advantageous by comparing the rate of the proposed scheme to the rate of the PPIR-USI scheme given by Obead et al. for some cases. Further, we extend the problem of PPIR-ISI for multi-user case, where users can collaborately generate the query sets, and we give a scheme for this problem.
Paper Structure (12 sections, 5 theorems, 37 equations, 3 figures, 2 algorithms)

This paper contains 12 sections, 5 theorems, 37 equations, 3 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Prior Work
  3. Contributions and organization
  4. System Model and Problem Setting
  5. System Model
  6. Problem Setting
  7. MAIN RESULTS
  8. Achievability of Theorem 1
  9. Single-Server PPIR-ISI for Multi-User Scenario
  10. Multi-user PPIR-ISI scheme
  11. Achievability of Theorem 5
  12. Conclusion

Key Result

Theorem 1

Consider a single server with F messages divided among $\Gamma$ classes out of which $\eta$ classes are identifiable and Class $i$ contains $\mu_i$ messages, $i \in [\Gamma]$. The number of messages from Class $i$ present in the side information of user is $k_i, i \in [\Gamma]$, such that $k_1, k_2,

Figures (3)

  • Figure 1: Single-Server PPIR problem containing $F$ messages divided into $\Gamma$ classes with a single user having side information set, $S$.
  • Figure 2: Index mapping of $F$ messages classified into $\Gamma$ classes using class-subclass indices.
  • Figure 3: The Single-Server PPIR problem containing F files divided into $\Gamma$ classes with U, each having side information set $S^u, \ \forall \ u \in [U]$.

Theorems & Definitions (22)

  • Example 1
  • Remark 1
  • Theorem 1
  • proof : Proof of correctness
  • Remark 2
  • proof : Proof of privacy
  • Remark 3
  • Remark 4
  • Example 2
  • Remark 5
  • ...and 12 more