Introduction to Cryptography with Coding Theory, 3rd Edition

Appendix E Answers and Hints for Selected Odd-Numbered Exercises

Chapter 2

1. 1. Among the shifts of EVIRE, there are two words: arena and river. Therefore, Anthony cannot determine where to meet Caesar.

2. 3. The decrypted message is ’cat’.

3. 5. The ciphertext is QZNHOBXZD. The decryption function is $21x+9$.

4. 7. The encryption function is therefore $11x+14$.

5. 9. The plaintext is happy.

6. 11. Successively encrypting with two affine functions is the same as encrypting with a single affine function. There is therefore no advantage of doing double encryption in this case.

7. 13. Mod 27, there are 486 keys. Mod 29, there are 812 keys.

8. 15.

   1. The possible values for $\alpha$ are 1,7,11,13,17,19,23,29.

   2. There are many such possible answers, for example $x=1$ and $x=4$ will work. ...