This paper proposes a hybrid technique for data security. The computational model of the technique is grounded on both the non-linearity of neural network manipulations and the effective distortion operations. To accomplish this, a two-layer feedforward neural network is trained for each plaintext block. The first layer encodes the symbols of the input block, making the resulting ciphertext highly uncorrelated with the input block. The second layer reverses the impact of the first layer by generating weights that are used to restore the original plaintext block from the ciphered one. The distortion stage imposes further confusion on the ciphertext by applying a set of distortion and substitution operations whose functionality is fully controlled by random numbers generated by a key-based random number generator. This hybridization between these two stages (neural network stage and distortion stage) yields a very elusive technique that produces ciphertext with the maximum confusion. Furthermore, the proposed technique goes a step further by embedding a recurrent neural network that works in parallel with the first layer of the neural network to generate a digital signature for each input block. This signature is used to maintain the integrity of the block. The proposed method, therefore, not only ensures the confidentiality of the information but also equally maintains its integrity. The effectiveness of the proposed technique is proven through a set of rigorous randomness testing.