A nuclear arsenal is a weapon, such as atomic bomb or hydrogen bomb, is made of nuclear energyandhas a tremendous destructive power comes from the release ofnuclearenergy.If the nuclearbomb is...

A nuclear arsenal is a weapon, such as atomic bomb or hydrogen bomb, is made of nuclear energyandhas a tremendous destructive power comes from the release ofnuclearenergy.If the nuclearbomb is activatedaccidently, it can cause many deaths.Therefore, a secure control system should bedesigned 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 securityof the system would be less secure. Hence, a combination of multiple keys provided by multipleauthorized participants for creating a singlemaster keywould increase the security of the system. Say,allthreeauthorized participants(the President, Secretary of Defense, and Security Adviser)mustprovide the approval to confirmthe activation and deactivation of the nuclear arsenal via averysophisticated and specially designedsecure control system. The secure control systemhas a digitalkeypad(see Figure-1.2)whichis usedtoenter secret passwordforactivatingor deactivating thenuclear arsenal.Thekeypad acceptsthree secret keys one after another. Each secret key is an integernumber of5digits.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 amaster keyby 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.