We provide lower and upper bounds on the optimal rate for reliable and secret transmission of a message from one node to another in an arbitrary wireless network with deterministic signal interaction. Certain relay nodes are allowed to insert noise into the transmission, i.e., to use a source of independent, random noise in their encoding functions. The secrecy is with respect to an eavesdropper whose channel statistics are known. The upper bound is also valid for noisy signal interaction. Our construction for the achievability relies on an auxiliary result of independent interest: an inner and an outer bound on the achievable rates for reliable transmission of multiple sources to a single destination in arbitrary deterministic networks without secrecy constraints.