The rapid advancement in neurotechnology in recent years has created an emerging critical intersection between neurotechnology and security. Implantable devices, non-invasive monitoring, and non-invasive therapies all carry with them the prospect of violating the privacy and autonomy of individuals' cognition. A growing number of scientists and physicians have made calls to address this issue, but applied efforts have been relatively limited. A major barrier hampering scientific and engineering efforts to address these security issues is the lack of a clear means of describing and analyzing relevant problems. In this paper we develop Cognitive Neurosecurity, a mathematical framework which enables such description and analysis by drawing on methods and results from multiple fields. We demonstrate certain statistical properties which have significant implications for Cognitive Neurosecurity, and then present descriptions of the algorithmic problems faced by attackers attempting to violate privacy and autonomy, and defenders attempting to obstruct such attempts.