With the current continuous increase in the usage of communication technologies and data transmission amount, the available web services and mobile applications are used to access and complete several online activities such as online education, e-commerce, and online financial transactions. The needs for a strong and secure access control authentication solution for users' data and the available online resources are crucial. Authentication can play a major role in protection by implementing a solution, which allows users to prove their identities and provide access permission to all legitimate users only. This paper proposes two-factor authentication scheme based on the usage of a modified copy of the Schnorr Signcryption algorithm. The proposed scheme achieves the target goal of this paper, which provides the users with an efficient solution that can be implemented in any authentication solution as the second factor, with no special requirement and can be used to authenticate the users and control recourses access permission. Moreover, a Java-based application is developed to examine the proposed scheme in a client-server architecture where it is found that the solution can successfully authenticate authorized users and reject any unauthorized access request with an adequate security protection level and acceptable performance.Povzetek: V članku je predlagana rešitev z dvofaktorsko avtentikacijo na osnovi modificiranega algoritma Schnorr Signcryption, ki omogoča učinkovito avtentikacijo uporabnikov in nadzor dostopa do virov. Rezultati preizkusa kažejo zadostno varnost in sprejemljivo zmogljivost.