Checking the identity of students and authorship of their online submissions is a major concern in Higher Education due to the increasing amount of plagiarism and cheating using the Internet. The literature on the effects of e-authentication systems for teaching staff is very limited because it is a novel procedure for them. A considerable gap is to understand teaching staff' views regarding the use of e-authentication instruments and how they impact trust in e-assessment. This mixed-method study examines the concerns and practices of 108 teaching staff who used the TeSLA--Adaptive Trust-based e-Assessment System in six countries: the UK, Spain, the Netherlands, Bulgaria, Finland and Turkey. The findings revealed some technological, organisational and pedagogical issues related to accessibility, security, privacy and e-assessment design and feedback. Recommendations are to provide a FAQ and an audit report with results, to raise awareness about data security and privacy, to develop policies and guidelines about fraud detection and prevention, e-assessment best practices and course team support.