Explore a new cryptographic primitive called private resource allocators (PRAs) for allocating resources without revealing allocation information to clients. Learn about various PRA constructions offering guarantees from information-theoretic to differential privacy. Discover how PRAs prevent allocation-based side-channel attacks, which can compromise privacy in anonymous messaging systems. Examine the implementation of PRAs in Alpenhorn and its impact on network resources. Delve into allocation indistinguishability, avoiding trivial allocators, and the challenges of achieving privacy and liveness in allocators. Compare different PRA efficiencies and understand their applications in various settings, including those with unbounded active processes.