Q1. Designing Cryptographic Algorithm for Secure Nuclear Arsenal Control System (6 Marks) A nuclear arsenal is a weapon, such as atomic bomb or hydrogen bomb, is made of nuclear energy and has a tremendous destructive power comes from the release of nuclear energy. If the nuclear bomb is activated accidently, it can cause many deaths. Therefore, a secure control system should be designed for authorized activation and deactivation of the nuclear arsenal. 2365-01 F2 F726501 Figure-1.1: Nuclear Arsenal Key-1 0000 000 000D Key-2 Key-3 Master Key President Secretary Security of Advisor Defense Figure-1.2: Master Key generation at keypad from three keys If the secure nuclear arsenal control system is designed to work based on a single key, the security of the system would be less secure. Hence, a combination of multiple keys provided by multiple authorized participants for creating a single master key would increase the security of the system. Say, all three authorized participants (the President, Secretary of Defense, and Security Adviser) must provide the approval to confirm the activation and deactivation of the nuclear arsenal via a very sophisticated and specially designed secure control system. The secure control system has a digital keypad (see Figure-1.1) which is used to enter secret password for activating or deactivating the nuclear arsenal. The keypad accepts three secret keys one after another. Each secret key is an integer number of 5 digits. Page 3 of 9 When the keypad is initialized each participant enters individual secret key without anyone knowing that number. Once all three participants enter their secret numbers, the sophisticated logic in the keypad performs a mathematical operation and generates a master key by using the three numbers (see Figure-1.2). It then stores the master key in the memory and deletes the individual secret keys. Once the digital keypad is initialized, the three authorized participants must come all at the same time and enter the secret keys one after another. Similar to the initialization phase, keypad performs a mathematical operation and generates a new master key by using the three numbers. The new master key is then compared with old master key saved in the keypad. If they are same, the nuclear arsenal activates or deactivates. Explain the algorithm with an example to design the sophisticated keypad for the secured nuclear arsenal control system. You need to choose appropriate 5-digit numbers to show all the steps (i.e., initialization of master key and key verification process) of the algorithm