Is it permissible for me to falsely swear that I did not speak about the information, knowing that it concerns serious military matters, and that I am indeed the one who spoke about it?

The basic ruling for swearing a false oath is prohibition. However, it is permissible if refraining from it would lead to severe harm, such as dismissal from an essential job, imprisonment, or unbearable beating, provided there is no other way to escape it, and that it does not result in harm to an innocent person. According to the majority of scholars, no expiation (kaffarah) is required for it, though it is preferable to offer it as a precautionary measure.