Secrecy and Privacy in Multi-Access Combinatorial Topology

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.