# Sol30 - CHAPTER 30 Cryptography Solutions to Review...

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1 CHAPTER 30 Cryptography Solutions to Review Questions and Exercises Review Questions 1. Only one key (the shared secret key) is needed for two-way communication. How- ever, for more security, it is recommended that a different key be used for each direction. 2. A shared secret key can only be used between two entities. Alice needs a shared secret key to communicate with Bob and a different shared secret key to communi- cate with John. 3. Each person in the first group needs to have 10 keys to communicate with all peo- ple in the second group. This means we need at least 10 × 10 = 100 keys. Note that the same keys can be used for communication in the reverse direction. However, note that we are not considering the communication between the people in the same group. For this purpose, we would need more keys. 4. Each person needs 9 keys to communicate with the other people. At first glance, it looks like we need 10 × 9 keys. However, if the same key can be used in both directions (from A to B and from B to A), then we need only (10 × 9) / 2 = 45 keys . 5. For two-way communication, 4 keys are needed. Alice needs a private key and a public key; Bob needs a private key and a public key. 6. Alice can use the same pair of keys (private and public) to communicate with both Bob and John. However, if there is a need for two-way communication, Bob and John need to have their own pair of keys. In other words, for two-way communica- tion 6 keys are needed, two for each entity. 7. For two-way communication, the people in the first group need 10 pairs of keys, and the people in the second group need a separate 10 pairs of keys. In other words, for two-way communication 40 keys are needed. 8. Each person in the group needs only one pair of keys (private and public). In other words, 20 keys are needed for two-way communication.

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2 Exercises 9.
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