Current computing device authentication often presents accessibility barriers for people with upper extremity impairments (UEI). In this paper, we present a framework called Accessible image-Association-based Authentication for Computing-devices (A3C) , a novel recognition-based graphical authentication framework specifically designed for people with UEI to authenticate to their computing devices. A3C requires users to provide a set of primary images that the user knows that are recognizable to them and subsequently associate each primary image with a secondary image. To evaluate the efficacy of the A3C framework, we instantiated the framework by implementing a version of A3C called A3C-FA , which uses images of faces of people the user knows as the primary image and animal images as the secondary image. We then performed three studies to evaluate A3C-FA: a shoulder-surfing attack study ( N=319 ), a close-adversary attack study ( N=268 ), and a usability study with people with UEI ( N=14 ). We found that A3C was robust against both shoulder-surfing and close-adversary attacks. We also performed a detailed study to evaluate the accessibility of A3C-FA. Our participants reported that A3C-FA was more usable and more secure than the authentication approaches with which they were familiar. Based on these findings, we suggest four areas of future research to further improve the design of A3C framework.