Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust, Secure and Private Cache-aided Scalar Linear Function Retrieval from Distributed System with Blind and Adversarial Servers

Qifa Yan, Xiaohu Tang, Zhengchun Zhou

TL;DR

This paper addresses robust, secure, and private scalar linear function retrieval in cache-aided multi-server multi-user systems with blind/adversarial servers. It develops a general PDA-based construction that embeds Shamir secret sharing and key superposition into the PDA framework to satisfy I-security, J-robust recovery, A adversarial errors, signal security, and demand privacy. By leveraging Maddah-Ali–Niesen MAN-PDAs as a basis, it characterizes the memory-storage-communication region and proves near-optimality with multiplicative gaps dependent on L = J − I − 2A, while providing numerical validation across regimes. The work demonstrates that existing PDAs can yield low-subpacketization RSP-LFR-BA schemes with provable performance guarantees, offering practical guidance for designing secure and private distributed caching systems with untrusted servers.

Abstract

In this work, a distributed server system composed of multiple servers that holds some coded files and multiple users that are interested in retrieving the linear functions of the files is investigated, where the servers are robust, blind and adversarial in the sense that any $J$ servers can together recover all files, while any $I$ colluding servers cannot obtain any information about the files, and at most $A$ servers maliciously provides erroneous information. In addition, the file library must be secure from a wiretapper who obtains all the signals, and the demands of any subset of users must kept private from the other users and servers, even if they collude. A coding scheme is proposed by incorporating the ideas of Shamir's secret sharing and key superposition into the framework of Placement Delivery Array (PDA), originally proposed to characterize the single-server coded caching system without any security or privacy constraints. It is shown that PDAs associated to Maddah-Ali and Niesen's coded caching scheme results in an achievable memory-storage-communication region, such that the storage size and communication load were optimal to within a multiplicative gap, except for the small memory regime when the number of files was smaller than the number of users.

Robust, Secure and Private Cache-aided Scalar Linear Function Retrieval from Distributed System with Blind and Adversarial Servers

TL;DR

This paper addresses robust, secure, and private scalar linear function retrieval in cache-aided multi-server multi-user systems with blind/adversarial servers. It develops a general PDA-based construction that embeds Shamir secret sharing and key superposition into the PDA framework to satisfy I-security, J-robust recovery, A adversarial errors, signal security, and demand privacy. By leveraging Maddah-Ali–Niesen MAN-PDAs as a basis, it characterizes the memory-storage-communication region and proves near-optimality with multiplicative gaps dependent on L = J − I − 2A, while providing numerical validation across regimes. The work demonstrates that existing PDAs can yield low-subpacketization RSP-LFR-BA schemes with provable performance guarantees, offering practical guidance for designing secure and private distributed caching systems with untrusted servers.

Abstract

In this work, a distributed server system composed of multiple servers that holds some coded files and multiple users that are interested in retrieving the linear functions of the files is investigated, where the servers are robust, blind and adversarial in the sense that any servers can together recover all files, while any colluding servers cannot obtain any information about the files, and at most servers maliciously provides erroneous information. In addition, the file library must be secure from a wiretapper who obtains all the signals, and the demands of any subset of users must kept private from the other users and servers, even if they collude. A coding scheme is proposed by incorporating the ideas of Shamir's secret sharing and key superposition into the framework of Placement Delivery Array (PDA), originally proposed to characterize the single-server coded caching system without any security or privacy constraints. It is shown that PDAs associated to Maddah-Ali and Niesen's coded caching scheme results in an achievable memory-storage-communication region, such that the storage size and communication load were optimal to within a multiplicative gap, except for the small memory regime when the number of files was smaller than the number of users.
Paper Structure (19 sections, 5 theorems, 6 equations, 3 figures, 3 tables)

This paper contains 19 sections, 5 theorems, 6 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. PDAs and A Toy Example
  4. Placement Delivery Array
  5. A Toy RSP-LFR-BA Example from PDAs
  6. Main Results
  7. PDA based RSP-LFR-BA Schemes
  8. Lower Bound for RSP-LFR-BA Schemes
  9. Optimality of MAN-PDA based RSP-LFR-BA Schemes
  10. Numerical Results
  11. PDA Based RSPB-LFR-BA Scheme
  12. PDA Based Scheme
  13. Verification of Constraint Conditions
  14. Performance
  15. Lower Bounds of Storage Size and Communication Load
  16. ...and 4 more sections

Key Result

Theorem 1

For a given $(K,F,Z,S)$ PDA $\mathbf{A}$, there exists an associated RSP-LFR-BA scheme that achieves the MSC triple with subpacketization $LF$.

Figures (3)

  • Figure 1: System model
  • Figure 2: Achievable MSC Region of a $(50,10,20,3,10,16)$ MUMS system
  • Figure 3: Communication load $R(M)$ for a MUMS system with $H=20,A=2,I=3,J=17$.

Theorems & Definitions (15)

  • Definition 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Definition 2: PDA Yan2017PDA
  • Remark 4
  • Theorem 1
  • Theorem 2
  • Definition 3: MAN-PDA
  • Example 1: A MAN-PDA
  • ...and 5 more