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Secrecy and Privacy in Multi-Access Combinatorial Topology

Mallikharjuna Chinnapadamala, B. Sundar Rajan

TL;DR

This paper addresses secrecy and demand privacy in multi-access coded caching with combinatorial topology, where each of the $K$ users accesses a unique $r$-subset of $C$ caches. It develops a secretive and private caching scheme and a matching lower bound, showing optimality for $r\ge C-1$ (with $N\ge 2K$) and order-optimality when $r<C-1$ under a memory threshold; for the special case $r=1$, the scheme aligns with the rate of the dedicated-cache secretive scheme from Ravindrakumar et al. in most memory regions. The contribution hinges on a non-perfect secret-sharing construction, Cauchy-matrix based encoding, and carefully designed random keys to protect both file content and user demands during delivery. Overall, the work establishes fundamental rate-memory tradeoffs for secrecy and privacy in multi-access caching and provides practical schemes that outperform or match single-cache benchmarks in many regimes. The results have implications for secure content delivery in networks with shared caches and could inform privacy-preserving caching policies in distributed storage and edge networks.

Abstract

In this work, we consider the multi-access combinatorial topology with $C$ caches where each user accesses a unique set of $r$ caches. For this setup, we consider secrecy, where each user should not know anything about the files it did not request, and demand privacy, where each user's demand must be kept private from other non-colluding users. We propose a scheme satisfying both conditions and derive a lower bound based on cut-set arguments. Also, we prove that our scheme is optimal when $r\geq C-1$, and it is order-optimal when the cache memory size $M$ is greater than or equal to a certain threshold for $r<C-1$. When $r=1$, in most of the memory region, our scheme achieves the same rate as the one given by the secretive scheme for the dedicated cache setup by Ravindrakumar et al. ( 'Private Coded Caching,' in \textit{IEEE Transactions on Information Forensics and Security}, 2018), while satisfying both secrecy and demand privacy conditions.

Secrecy and Privacy in Multi-Access Combinatorial Topology

TL;DR

This paper addresses secrecy and demand privacy in multi-access coded caching with combinatorial topology, where each of the users accesses a unique -subset of caches. It develops a secretive and private caching scheme and a matching lower bound, showing optimality for (with ) and order-optimality when under a memory threshold; for the special case , the scheme aligns with the rate of the dedicated-cache secretive scheme from Ravindrakumar et al. in most memory regions. The contribution hinges on a non-perfect secret-sharing construction, Cauchy-matrix based encoding, and carefully designed random keys to protect both file content and user demands during delivery. Overall, the work establishes fundamental rate-memory tradeoffs for secrecy and privacy in multi-access caching and provides practical schemes that outperform or match single-cache benchmarks in many regimes. The results have implications for secure content delivery in networks with shared caches and could inform privacy-preserving caching policies in distributed storage and edge networks.

Abstract

In this work, we consider the multi-access combinatorial topology with caches where each user accesses a unique set of caches. For this setup, we consider secrecy, where each user should not know anything about the files it did not request, and demand privacy, where each user's demand must be kept private from other non-colluding users. We propose a scheme satisfying both conditions and derive a lower bound based on cut-set arguments. Also, we prove that our scheme is optimal when , and it is order-optimal when the cache memory size is greater than or equal to a certain threshold for . When , in most of the memory region, our scheme achieves the same rate as the one given by the secretive scheme for the dedicated cache setup by Ravindrakumar et al. ( 'Private Coded Caching,' in \textit{IEEE Transactions on Information Forensics and Security}, 2018), while satisfying both secrecy and demand privacy conditions.

Paper Structure

This paper contains 18 sections, 5 theorems, 60 equations, 7 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Our Contributions
  4. Paper Organisation
  5. Problem Setup and Preliminaries
  6. Secret Sharing schemes
  7. Cauchy matrix
  8. Secretive Coded Caching Scheme in RPKP
  9. Multi-access Coded CachingMKR
  10. Main Results
  11. Proof of Theorem \ref{['th1']}
  12. Proofs of Theorem \ref{['th2']} and Theorem \ref{['th3']}
  13. Proof of Theorem \ref{['th2']}
  14. Proof of Theorem \ref{['th3']}
  15. Numerical Evaluations
  16. ...and 3 more sections

Key Result

Theorem 1

For the multiaccess combinatorial topology described in Section sec2, when $M\geq \frac{K-1}{C-r}$, the optimal rate is lower bounded as where $z=(\min(l+r-1,C)$.

Figures (7)

  • Figure 1: Combinatorial topology.
  • Figure 2: Performance comparison of the proposed schemes with RPKP when C=5, r=1, N=7
  • Figure 3: Performance comparison of the proposed schemes when C=5, r=2, N=15.
  • Figure 4: Performance comparison with RPKP for different values of $r$ considering the same cache size and the same number of caches when C=5, N=10.
  • Figure 5: Performance comparison with RPKP for different values of $r$ considering the same cache size and the same number of caches when C=5, N=50.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Proposition 1
  • Example 1