Secure Multi-Access Coded Caching: A Lifting Approach

2026-10-04

AI Summary

This study addresses the challenge of simultaneously achieving file recovery and privacy preservation when users access shared caches in multi-access secure coded caching. A secure cyclic multi-access caching system is proposed, which recodes single-access cache placements and reuses multicast messages. By integrating deterministic Pascal windows with randomized complementary dual encoders, the scheme ensures that each user retrieves only the information of its requested file. Leveraging finite-field linear coding and combinatorial optimization techniques, it achieves minimum storage overhead under block divisibility conditions and establishes the exact trade-off for L=K−1. Furthermore, an achievable memory-rate region is derived for N,K≥2 and 1≤L<K, providing near-optimality guarantees alongside exact solutions in specific scenarios.

Abstract

We construct secure cyclic multi-access coded caching schemes by re-encoding the caches of a secure single-access scheme and reusing its multicast message unchanged. For a library of $N$ files, each of $K$ users reads $L<K$ consecutive shared caches and must recover its requested file while learning no information about the other files. Starting from a parent scheme with a cyclic representation of its cached symbols, the transformation lets each access window recover the corresponding parent-cache symbols and, conditioned on them, learn nothing about the remaining symbols. A deterministic Pascal-window encoder handles symbols whose consecutive appearances span at least $L$ users. A randomized complement-dual encoder handles shorter spans. Over a suitable finite field, these encoders attain the exact minimum per-block storage for every input length in the block-separable, parent-preserving class. Applying the transformation to two secure single-access schemes gives an achievable memory-rate family for $N,K\ge2$ and $1\le L<K$, including the exact rate-one cache size $(N-1)(K-1)/L$. Using converse bounds for arbitrary secure multi-access schemes, we prove approximation guarantees for the achievable family and give a proof of the exact $L=K-1$ tradeoff.

Problem

• Secure Coded Caching
• Multi-Access Caching
• Information-Theoretic Security
• Memory-Rate Tradeoff

Innovation

• Secure Multi-Access Coded Caching
• Lifting Approach
• Pascal-window Encoder
• Complement-dual Encoder
• Memory-Rate Tradeoff