This paper demonstrates why security issues related to the continually increasing bandwidth of High Speed Networks (HSN) cannot be addressed with conventional firewall mechanisms. A single packet screen running on a fast computer is not capable of filtering all packets traversing a Fast/Gigabit Ethernet. This problem can be addressed by using parallel processing methods to implement a fast, scalable packet screen for Ethernets. The paper shows how hardware may be utilized to distribute the network load among such parallel packet screens. Empirical results using `off-the-shelf' equipment indicate that this approach is usable.