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Suppose N people want to communicate with each of N – 1 other people using symmetric key encryption. All communication between any two peo- ple, i and j, is visible to all other people in this group of N, and no other per- son in this group should be able to decode their communication. How many keys are required in the system as a whole? Now suppose that public key encryption is used. How many keys are required in this case?

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