As the world evolves day by day with new technologies, there is a need to design a secure network in such a way that intruders and unauthorized persons should not have access to the network as well as information regarding the personnel in any firm. In this study, a new cryptographic technique for securing data transmission based on the LaplaceLaguerre polynomial (LLP) is developed and compared to an existing auto-associative neural network technique (AANNT).The performance of the LLPT and AANNT was tested with some selected files in a MATLAB environment and the results obtained provided comparative information (in respect of AANNT versus LLPT) as follows: encryption time (1.67 ms versus 3.9931s), decryption time (1.833 ms versus 2.1172s), throughput (26.2975 Kb/s versus 0.01098 Kb/s), memory consumption (3.349 KB versus 15.958 KB). From the compared results, it shows that AANNT offers a faster processing time, higher throughput, and takes up less memory space than the LLPT. However, cryptanalysis of the AANNT is possible if the network's weight and design are known; hence, the technique is unreliable for ensuring the data integrity and confidentiality of encrypted data. The proposed LLP cryptographic algorithm is designed to provide a higher security level by making the LLP algorithm computationally tedious to invert using the standard Laplace transform inversion method. When compared to the AANN-based cryptographic technique, cracking the algorithm to uncover the encryption key takes time. This shows the strength and robustness of the proposed LLP cryptographic algorithm against attacks, as well as its suitability for solving the problem of data privacy and security when compared to the AANN-based cryptographic algorithm.