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CHAPTER 30
Cryptography
Solutions to Odd-Numbered 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.
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 ร 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.
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.
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.
Exercises
9. If the two persons have two pairs of asymmetric keys, then they can send messages
using these keys to create a session symmetric key, a key which is valid for one
session and should not be used again. Another solution is to use a trusted center
that creates and send symmetric keys to both of them using the symmetric key or
asymmetric key that has been already established between each person and the
trusted center. We will discuss this mechanism in Chapter 31.
11.
a. We can show the encryption character by character. We encode characters A to
Z as 0 to 25. To wrap, we subtract 26.
T 1 9 + 2 0 = 3 9 โ 26 = 13 โ N
H 0 7 + 2 0 = 2 7 โ 26 = 01 โ B
I 08 + 2 0 = 2 8 โ 26 = 02 โ C
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