The Exact Memory-Rate Tradeoff for Three-User Secure Coded Caching
Abstract
We determine the exact zero-error memory-rate tradeoff for secure coded caching with three users and any number N≥2 of independent files. Each user recovers its requested file, while its cache and the broadcast jointly reveal no information about the complete tuple of unrequested files. For N≥4, two converse inequalities establish the optimality of the known achievable points and the memory-sharing segments between them. For N=3, two additional bounds identify a new corner at (M,R)=(3/2,2), where memory and rate are measured in file units. An explicit linear code over 𝔽3 attains this corner and reduces the rate by one quarter of a file relative to memory sharing between the known points. The converse links the information held by cache pairs and triples to delivery under repeated and distinct requests. Its equality conditions guide the construction: users cancel the keys to recover their requested files, while uniform masking protects the complete tuple of unrequested files.
Related
- Secure Multi-Access Coded Caching: A Lifting Approach
- Secure D2D Coded Caching under Radius-Limited Connectivity via Lifting
- Heterogeneous Demand-Private Coded Caching: Exact Characterization for Two Users and Two Files
- Exact Rate Exponent Tradeoff for New Classes of Distributed Hypothesis Testing Problems
- Rate-Distortion-Perception Tradeoff for Vector Gaussian Sources with Limited Common Randomness: Exact Characterization and Approximate Universality
BibTeX
@misc{fang2026exact,
title = {{The Exact Memory-Rate Tradeoff for Three-User Secure Coded Caching}},
author = {Han Fang and Nan Liu and Wei Kang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06311},
eprint = {2611.06311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06311},
}
RIS
TY - UNPB
TI - The Exact Memory-Rate Tradeoff for Three-User Secure Coded Caching
AU - Han Fang
AU - Nan Liu
AU - Wei Kang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06311
UR - https://arxiv.org/abs/2611.06311
AB - We determine the exact zero-error memory-rate tradeoff for secure coded caching with three users and any number N≥2 of independent files. Each user recovers its requested file, while its cache and the broadcast jointly reveal no information about the complete tuple of unrequested files. For N≥4, two converse inequalities establish the optimality of the known achievable points and the memory-sharing segments between them. For N=3, two additional bounds identify a new corner at (M,R)=(3/2,2), where memory and rate are measured in file units. An explicit linear code over 𝔽_3 attains this corner and reduces the rate by one quarter of a file relative to memory sharing between the known points. The converse links the information held by cache pairs and triples to delivery under repeated and distinct requests. Its equality conditions guide the construction: users cancel the keys to recover their requested files, while uniform masking protects the complete tuple of unrequested files.
ER -