Hassan Mohammed Alsibyani
Dar Alfikr Schools, Jeddah, SAUDI ARABIA
Encryption methods have been consistently improving with the goal of making it harder to break the codes. This research studies the Frobenius problem and how it can be applied to computer science encryption aspects to create a stronger methodology. The key points during the procedure of this investigation have been; One; numbers have been selected for corresponding letters, then its Frobenius numbers were identified using Rodseth Algorithm with some random multiplication done over the public key. Two; the finite solutions of the Frobenius equation were identified and one of them was selected and its Frobenius number has been similarly identified thereby creating the private key and an additional Frobenious equation. Three; the recipient solves the equation and a finite set of solutions will appear. Then by using the private key, it can be determined the lower and upper equations and the right solution. The results from the math experiments proved this methodology efficient at a certain level. These efficiency of these results may be affected by the partities of the numbers and its relative primarily. The conclusion of this project is that the Frobenius problem can positively affect the encryption methods due to the nature of its complexity in polynomial time calculations. Based on future studies, this methodology may be applied to more complex systems and becomes even more effective on a wider scale.