In this article, we established an innovative application of number theory in the field of cryptography. We introduce the concept of ‘Duo-triples’ from the motivation of Diophantine triples and establish the necessary and sufficient conditions for their existence, supported by numerical illustrations validated through MATLAB algorithms. We delve into their cryptographic applications, enhancing data security via multiple encryption and decryption protocols, such as the Caesar Cipher and AES-128 algorithms. The input keys for these schemes are generated using Duo-triples in which the cipher key for the AES encryption process is inherited from the cipher key for the Caesar cipher encryption. The entire process is implemented and evaluated using Python (Version 3.11.9). The elapsed times for the encryption and decryption processes are graphically represented. Finally, we assess the time and space complexity to evaluate the efficiency of the algorithms.
