In this paper, the approach to providing a given level of information security for multipath routing of confidential messages in a network is considered. A method for providing secure routing over overlapping paths is developed and belongs to the class of proactive solutions for ensuring a given level of information security. The analysis has shown that using the proposed method within the presented calculated examples can improve the probability of compromising transmitted messages at average from 5–10% to 25–50% due to the possibility of using composite paths that are one of the subclasses of overlapping paths. A method of Secure Fast ReRouting (S-FRR) of messages in the network has been synthesized, the novelty of which lies in the fact that it focuses on the implementation of both proactive and reactive secure routing confidential messages. In this case, the proactive nature of the solutions is conditioned by the calculation of the set of primary composite paths forming the primary multipath, along which parts of the confidential message are transmitted. However, in the case of violation of the information security requirements in the network caused by the increased probability of compromising one or multiple composite paths constituent the primary multipath, the messages will be transmitted over the calculated set of the backup composite paths determining the backup multipath. Within the framework of the proposed S-FRR method, it is possible to protect both the primary multipath as a whole and one or several precomputed composite paths included in this primary multipath. The developed methods of secure routing can be used as the basis for new network protocols for routing and fast rerouting for multipath transmission of parts of a confidential message with specified requirements regarding the probability of its compromise in the network.