The problems studied in this thesis fall within two different topics in network information theory. The first part of this dissertation will be about information theoretic security and the second about distributed source coding. In the following a brief description of these problems will be given. In information theoretic security, we look at two different types of timing channels and we quantify the maximum rate at which a transmitter can communicate information reliably to a legitimate receiver while keeping an eavesdropper in the dark. The first timing channel that we study is the Poisson channel which is used to model certain direct detection optical communication systems. To transmit a message on this channel, the transmitter encodes information by modulating the intensity of an optical signal while the legitimate receiver and the eavesdropper use the arrival moments of the individual photons to decide which message was transmitted. The second timing channel studied is the exponential server queue. Here the transmitter encodes a message using a chosen sequence of packets inter-arrival times and both the legitimate receiver and the eavesdropper use the corresponding inter-departures from their respective exponential server queues to decode the transmitted message. In distributed source coding, we consider a rate-distortion problem in which a decoder is interested in estimating two correlated Gaussian random variables with mean-square error distortion constraints on each of the reproductions. The variables to be estimated are the roots of a given Gauss-Markov tree and each encoder observes one of the leaves of that tree. We show that a simple compression architecture that performs separate lossy quantization followed by SlepianWolf binning is sum-rate optimal for this problem.