Optimal Memory-Rate Tradeoff for Secure Multi-Access Coded Caching: The Case of Largest Access Number

This work addresses the secure multi-access coded caching (SMACC) problem involving <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> files, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> users, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> caches, where each user can access <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> consecutive caches in a cyclic wrap-around manner. It is required that no user can obtain any information about the files other than the requested one. The optimal memory-rate tradeoff for the largest access number, i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L=K-1$</tex>, is found for the case of an arbitrary number of users and files. This is done by proposing two new optimal achievability schemes and providing tight converse results. As a special case, the optimal memory-rate tradeoff for the secure coded caching (SCC) problem [1] in the two-user case has been found.