Digital public services have revolutionised citizen and private sector interactions with governments. Certain communities are strongly dependent on such digital services for ensuring the availability of public services due to geographical isolation or the presence of adverse geophysical and weather phenomena. However, strong and effective security is key to maintaining the integrity of public records and services yet also for ensuring trust in them. Trust is essential for user uptake, particularly given a global increase in data-protection concerns and a turbulent geopolitical security environment. In this paper, we examine the case of public trust in various forms of authentication for electronic identification in Iceland, which has high availability requirements for digital public services due to its unique and dynamic geophysical characteristics. Additionally, Iceland has historically low levels of institutional trust which may conflict with the requirement for an increased need for digital public services. Through surveying the Icelandic general public, we find that there is a high-level of trust in digital identification services across all demographics. We conclude with a discussion and future research challenges towards improving the effectiveness of authentication considering the diverse groups within Icelandic society, such as the rapidly increasing population of migrants and the large and dynamic population of tourists.