Modern programmable network switches let developers write complex packet processing pipelines that can run at speeds of 6.5Tbps, and the programming language P4 provides high-level constructs that make programming such switches fairly simple. The increase in speed and programmability has started a new era of network programming where many complex functionalities, e.g., key-value stores and load balancers, are being moved to these fast switches. We show that this increased programmability enables a new family of security bugs, that is, information leaks that can lead to broken confidentiality, integrity, and isolation in the network. We then present a new information-flow control type system for dataplane programming in P4 that can detect this family of security bugs. Our type system contains rules that are completely specific to the P4 language and can therefore handle complex constructs such as P4 tables. We implement our type system in a tool, P4bid, which extends the type checker in the p4c compiler, the reference compiler for P4_16, the latest version of P4. We present a number of case studies and show that P4bid can successfully detect information flow violations in all of them, while correctly type-checking corrected versions of these programs where the information leaks are removed.