In this paper, we propose, implement and analyze an Authenticated Encryption with Associated Data Scheme (AEADS) based on the Modified Duplex Construction (MDC) that contains a chaotic compression function (CCF) based on our chaotic neural network revised (CNNR). Unlike the standard duplex construction (SDC), in the MDC there are two phases: the initialization phase and the duplexing phase, each contain a CNNR formed by a neural network with single layer, and followed by a set of non-linear functions. The MDC is implemented with two variants of width, i.e., 512 and 1024 bits. We tested our proposed scheme against the different cryptanalytic attacks. In fact, we evaluated the key and the message sensitivity, the collision resistance analysis and the diffusion effect. Additionally, we tested our proposed AEADS using the different statistical tests such as NIST, Histogram, chi-square, entropy, and correlation analysis. The experimental results obtained on the security performance of the proposed AEADS system are notable and the proposed system can then be used to protect data and authenticate their sources.