Authentication encryption $$\left( \text {AE}\right) $$ is a procedure that satisfies both privacy and authenticity on the data. It has many applications in the field of secure data communication such as digital signatures, ip-security, data-authentication, e-mail security, and security of pervasive computing. Additionally, the AE is a potential primitive of security solution for IoT-end device, RfID, and constrained device. Though there are many constructions of AE, but the most important argument is whether the AE is secure under nonce-reuse or nonce-respect. As far our understanding, the McOE is the pioneer construction of nonce-reuse AE. Following that, many schemes have been proposed such as APE, PoE, TC, COPA, ElmE, ElmD, COBRA, and Minalphar. However, Hoang et al. $$\left( \text {OAE}1\right) $$ claimed that the concept of nonce-reuse in the AE is not secure and proper. Hence, a door is re-opened for the nonce-respect AE. Moreover, the construction of AE should satisfies the properties of efficiency and upper security bound due to limitation of power and memory for the constrained device. Therefore, we propose a blockcipher based AE that satisfies upper privacy security bound $$\left( \text {Priv}=O\left( 2^{2n/3}\right) \right) $$ and it operates in parallel mode. It doesn’t need decryption oracle in the symmetric encryption module of the AE. The proposed construction satisfies padding free encryption. Furthermore, the efficiency-rate of the proposed scheme is 1.