Exercises
Some exercises will require theory that will not be lectured. You should read the required theory on your own. If no references are given, you will find the material in Stinson. DH, SYM, PKE, SHOR, LAT and SIG refer to the lecture notes.
Some of the exercises will be in the Department of Mathematical Sciences' student computer lab.
The exercises are not obligatory, but they are essential for learning.
| Week | Date | Exercises | Notes |
|---|---|---|---|
| 35 | 30/8 | Routine: DH 1, SYM 1, 5, 10, 15, 16. Regular: DH 2,3, SYM 2, 3, 6, 7, 9, 11, 12, 17, 18, 20, 21. Problem 1 from the 2012 exam. For groups: SYM 4, 8, 14, 19. Computer helpful: SYM 13. | |
| 36 | 6/9 | Routine: SYM 22, 23, 24, 27, 30, 35, 37. DH 7, 15, 17, 18 Regular: Problem 1 from the 2013 exam. SYM 25, 26, 28, 29. DH 4-6, 8-14, 16. For groups: SYM 31, 33, 34, 36. Computer helpful: SYM 32 | |
| 37 | 13/9 | Routine: DH 23, 27, 33, 37. Regular: DH 19-22, 24-26, 28-32, 34-36, 38. | |
| 38 | 20/9 | Routine: DH 41, 47, 49. Regular: 39, 40, 42-46, 48, 50, 51. | |
| 39 | 27/9 | Regular: DH 52-55. Problem 2 from the 2001 exam. Problem 4 from the 2002 exam. Problem 2 from the 2003 exam. Problem 1a and 1b from the 2009 exam. | |
| 40 | 4/10 | Regular: DH 56, 58-64. Problem 2 from the 2012 exam. Problem 3 from the 2013 exam. Hard: DH 57. | |
| 41 | 11/10 | Routine: PKE 1, 2, 7, 10, 12, 19, 21. Regular: PKE 3, 4, 8, 9, 11, 13, 14, 18, 20. Problem 3 and 4 from the 2006 exam. | |
| 42 | 18/10 | Routine: PKE 22, 24, 26, 32. Regular: PKE 23, 25, 27-31, 33. Problem 6 and 7a from the 2014 exam. | |
| 43 | 25/10 | Routine: LAT 13. Minor: SHOR 1-4. LAT 3, 6, 8 Regular: LAT 1, 2, 4, 5, 7, 9-12. Problem 3 from the 2015 exam. | |
| 44 | 1/11 | Routine: LAT 20. Regular: LAT 15-19. Computer helpful: LAT 14, 21. | |
| 45 | 8/11 | Routine: SYM 38, 40, 41. SIG 7 Regular: SYM 39, 42. SIG 1, 2, 8-11. PKE 5-6, 15-17. Problem 1 from the 2010 exam. Problem 2 from the 2014 exam. | |
| 46 | 15/11 | Routine: SIG 19, 21. Regular: SIG 3-6, 12-18, 20, 22, 23. Problem 5 from the 2013 exam. | |
| 47 | 22/11 | Computer exercise: d.log., factoring and ec.d.log. Also: Make up your own factoring/d.log/ec.d.log problems and challenge your classmates. | Recap of previous exercises. |
Group exercises
SYM 33
The following ciphertext was encrypted using the Vigenère cipher with a key of length 5 \( (l = 5) \).
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
You could use this tool to decrypt.
SYM 34
The following ciphertext was encrypted using the Vigenère cipher.
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
Determine the length of the key.