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...

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.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-1.2) which is used to enter secret password for activating or deactivating the nuclear arsenal. The key pad accepts three secret keys one after another. Each secret key is an integer number of 5 digits.When the keypad is initialized eachparticipantenters individual secret key without anyone knowingthat number. Once all threeparticipantsenter their secret numbers, the sophisticated logic in thekeypad 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 participantsmust come all at the same timeand enter the secret keys one after another. Similartotheinitialization phase, keypad performs amathematical operation and generates a new master key by using the three numbers. The new masterkey is then compared with old master key saved in the keypad. If they are same, thenuclear arsenalactivates or deactivates.Explain the algorithm with an example to design the sophisticated keypad for thesecurednuclear arsenal control system. You need tochoose appropriate 5-digit numbers toshow allthe steps (i.e.,initializationof master key andkey verification process)of the algorithm.