Edge networks connected to the Internet need effective monitoring techniques to drive routing decisions and detect violations of Service Level Agreements (SLAs). However, existing measurement tools, like ping, traceroute, and trajectory sampling, are vulnerable to attacks that can make a path look better than it really is. In this paper, we design and analyze path-quality monitoring protocols that reliably raise an alarm when the packet-loss rate and delay exceed a threshold, even when an adversary tries to bias monitoring results by selectively delaying, dropping, modifying, injecting, or preferentially treating packets. Despite the strong threat model we consider in this paper, our protocols are efficient enough to run at line rate on high-speed routers. We present a secure sketching protocol for identifying when packet loss and delay degrade beyond a threshold. This protocol is extremely lightweight, requiring only 250