We consider a coded caching problem with multiple demands under a privacy constraint. In this problem, a server with access to \(N\) files serves \(K\) users over a shared link, and each user requests \(L\) distinct files. The privacy constraint requires that each user obtain no information about the demands of the other users. We propose a new achievable scheme for arbitrary numbers of files and users. The scheme is obtained via a transformation from a non-private coded caching scheme under uncoded placement for \(N\) files and \(K \cdot \min\{N,KL\}\) users, where each user requests one file and the demands are restricted to a subset of all possible demands. We then derive a converse bound, and the proposed scheme is shown to be order optimal within a factor of 6 of this bound.

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