Privacy in form of anonymous communication could be comparably both faster and harder to break in optical routers than in today's anonymous IP networks based on The Onion Routing (Tor). Implementing the practical privacy alloptically,however, is not straightforward, as it requires key generation in each anonymization node to avoid distribution of long keys, and layered encryption, both at the optical line rate. Due to the unavailability of cryptographically strong optical key generation and encryption components, not only a layered encryption is a challenge, but an optical encryption in general. In this paper, we address the challenges of optical anonymous networking for the first time from the system's perspective, and discuss options for practical implementation of all-optical layered encryption. To this end, we propose an optical anonymization component realized with the state-of-the-art optical XOR logic and optical Linear Feedback Shift Registers (oLFSRs). Given that LFSR alone is known for its weak cryptographic security due to its linear properties, we propose an implementation with parallel oLFSRs and analyze the resulting computational security. The results show that proposed optical anonymization component is promising as it can be practically realized to provide a high computational security against deanonymization (privacy) attack.