E-Assessment is an innovative form for the evaluation of learners' knowledge and skills in online education, as well as in blended-learning environments, where part of the assessment activities is carried out online. As e-assessment involves online communication channel between learners and educators, as well as data transfer and storage, security measures are required to protect the environment against system and network attacks. The issue concerning security is challenging from both educational and technical point of views. Such issues are discussed under the scope of the TeSLA project. Educational challenging problems at e-assessment are analyzed and technical architectural recommendations for securing the e-assessment system according to the General Data Protection Regulation are provided