A wide variety of authentication mechanisms have been designed to ensure information security. Individuals with cognitive disabilities depend on computers and the Internet for a variety of tasks and, therefore, use authentication applications on an everyday basis. However, although there have been numerous studies investigating password usage by neurotypical users, there have been no research studies conducted to examine the use of authentication methods by individuals with cognitive disabilities. In this article, we systematically investigate how individuals with cognitive disabilities, specifically Down syndrome (DS), interact with various user authentication mechanisms. This research provides the first benchmark data on the performance of individuals with DS when using multiple authentication methods. It confirms that individuals with DS are capable of using the traditional alphanumeric passwords with reasonable efficiency. The passwords created by individuals with DS are of similar strength to those created by neurotypical people. Graphic passwords are not as effective as traditional alphanumeric and mnemonic passwords regarding efficiency, and are less preferred by the participants. Based on the findings of the study, we propose design guidelines that aim to assist both practitioners and researchers in designing and developing effective authentication applications that fit the specific needs of individuals with DS.