## Hons 195N: A Social and Mathematical History of Cryptography

### Fall 2009

**Course Info:**

**Course:**A Social and Mathematical History of Cryptography**Lectures:**Monday, Wednesday, Friday, 12:50 - 1:40 p.m.**Dates:**31 August 2009 - 9 December 2009**Room:**University Heights North Complex 016**Instructor:**John Voight**Office:**16 Colchester Ave, Room 207C**Phone:**(802) 656-2271**E-mail:**jvoight@gmail.com**Office hours:**Mondays, 10:00 - 11:30 a.m. and 2:00 - 3:30 p.m.; or please make an appointment!**Course Web Page:**http://www.cems.uvm.edu/~voight/195N/**Instructor's Web Page:**http://www.cems.uvm.edu/~voight/**Prerequisites:**None.**Required Text:**Simon Singh, The Code Book, reprint edition, Anchor, 2000. There is also a coursepack, available at the bookstore.**Grading:**Weekly homework will count for 50% of the grade, class participation 10%, and a final paper will count for 40% in place of the final exam.**Final Exam:**Not applicable.

**Syllabus:**

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**Syllabus**

**Homework:**

Occasional homework will be given roughly on a weekly basis. Some homework assignments may include writing response essays. Others will be mathematical problems; be sure to show your work and explain how you got your answer. Cooperation on these homework problems is permitted (and encouraged), but if you work together, write the solution up on your own.

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**Homework #1 (due Friday, 4 September)**

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**Homework #2 (due Monday, 14 September)**

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**Homework #3 (due Wednesday, 16 September)**

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**Homework #4 (due Wednesday, 23 September)**

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**Homework #5 (due Wednesday, 30 September)**

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**Homework #6 (due Wednesday, 7 October) = Worksheet, Day #14**

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**Homework #7 (due Friday, 16 October)**

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**Homework #8 (due Wednesday, 11 December)**

**Class Participation:**

To encourage lively participation, the final grade includes a metric of your preparedness and responsiveness in class.

A Google group for the class has been created. On certain days of class discussion, you will be asked to send one or more questions, concerns, points of clarification or interest, etc. to the group concerning the reading on the day before each class. You are encouraged but not required to read the questions of your peers.

**Worksheets:**

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**Worksheet, Day #2 (Wednesday, 2 September)**

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**Worksheet, Day #3 (Friday, 4 September)**

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**Worksheet, Day #4 (Wednesday, 9 September)**

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**Worksheet, Day #8 (Friday, 18 September)**

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**Worksheet, Day #12 (Monday, 28 September)**

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**Worksheet, Day #14 (Friday, 2 October)**

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**Worksheet, Day #22 (Friday, 23 October)**

**Reading:**

The additional reading for the course can be obtained at Blackboard.

**Warning**: Readings many weeks in advance are subject to change.

Basic Cryptography |
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1 | 31 Aug | (M) | Introduction | |

2 | 2 Sep | (W) | Shift ciphers and congruences |
(0) S: pp. 1-14 (in chapter 1) (1) TW: pp. 1-4 (sections 1.1-1.1.1) (1) TW: pp. 12-14 (section 2.1) (1) TW: pp. 70-72 (section 3.3) |

3 | 4 Sep | (F) | Substitution ciphers | (1) TW: pp. 24-30 (sections 2.4-2.5) |

7 Sep | (M) | No class, Labor Day
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4 | 9 Sep | (W) | Frequency analysis |
(0) S: pp. 14-32 (in chapter 1) (2) HPS: pp. 4.10 (section 1.1.1) |

5 | 11 Sep | (F) | The Babington plot | (0) S: pp. 32-44 (in chapter 1) |

6 | 14 Sep | (M) | Cribs | (4) K: pp. 325-330 (in section 13.1) |

7 | 16 Sep | (W) | Vigenère cipher | (0) S: pp. 45-63 (in chapter 2) |

8 | 18 Sep | (F) | Kasiski test | (0) S: pp. 63-99 (in chapter 2) |

9 | 21 Sep | (M) | Displacement analysis |
(2) HPS: pp. 200-209 (sections 4.2.1-4.2.2) (1) TW: pp. 16-24 (section 2.3) |

The Enigma Machine: Mathematical Analysis |
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11 | 23 Sep | (W) | The mechanization of security | (0) S: pp. 101-124 (chapter 3) |

11 | 25 Sep | (F) | Basic functioning of the Enigma machine | (0) S: pp. 124-142 (chapter 3) |

12 | 28 Sep | (M) | Demonstration | (3) HS: pp. 83-88 (chapter 11) |

13 | 30 Sep | (W) | Simple Enigmas | (4) K: pp. 331-338 (section 13.2) |

14 | 2 Oct | (F) | Basic principles of counting | (2) HPS: pp. 190-196 (section 4.1) |

15 | 5 Oct | (M) | Permutations | |

16 | 7 Oct | (W) | The plugboard | (4) K: pp. 338-347 (section 13.3) |

9 Oct | (F) | No class, Fall Recess
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17 | 12 Oct | (M) | The plugboard does not hide... |
(4) K: pp. 348-353 (section 14.1) (0) S: pp. 143-160 (in chapter 4) |

18 | 14 Oct | (W) | The Polish contribution | (9) T: pp. 419-439 (Rakus-Andersson) |

19 | 16 Oct | (F) | Beautiful Polish females |
(4) K: pp. 353-361 (section 14.2) |

20 | 19 Oct | (M) | Passing the torch |
(4) K: pp. 362-367 (section 14.3) (0) S: pp. 160-189 (in chapter 4) |

21 | 21 Oct | (W) | The Turing bombes |
(4) K: pp. 368-376 (section 15.1) (7) C: pp. 313-335 (chapter 6) |

22 | 23 Oct | (F) | The bombes at work |
(4) K: pp. 377-381 (section 15.2) (3) HS: pp. 132-137 (chapter 17) |

23 | 26 Oct | (M) | The Automatic Computing Engine | (7) C: pp. 362-394 (chapter 9) |

Cryptology and World War II: Historical Analysis |
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24 | 28 Oct | (W) | The Staff School memory |
(6) K: pp. 1-14 (chapter 1) (6) K: pp. 161-169 (chapter 13) |

30 Oct | (F) | No class, Cocurricular Exchange Day | ||

26 | 2 Nov | (M) | SHARK | (4) K: pp. 381-390 (section 15.3) |

27 | 4 Nov | (W) | The influence of Ultra in WW2 | (3) HS: pp. 1-13 (introduction) |

28 | 6 Nov | (F) | Hut 6, Hut 8, and naval Enigma |
(3) HS: pp. 89-99 (chapter 12) (3) HS: pp. 113-118 (chapter 14) |

The Life and Work of Alan Turing |
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29 | 9 Nov | (M) | "Relay Race" | (8) H: pp. 185-222 |

30 | 11 Nov | (W) | "Relay Race" and "On the Beach" | (8) H: pp. 222-241, 456-487 |

31 | 13 Nov | (F) | "On the Beach" | (8) H: pp. 487-527 |

32 | 16 Nov | (M) | The Turing test | (7) C: pp. 433-464 (chapter 11) |

33 | 18 Nov | (W) | Machines and intelligence | Braitenberg Vehicles |

34 | 20 Nov | (F) | From Turing to the information society | (9) T: pp. 59-74 (Cerqui) |

35 | 23 Nov | (M) | Discussion and wrap-up | |

25--27 Nov | (W--F) | No class, Thanksgiving Recess
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Modern Cryptography |
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36 | 30 Nov | (M) | Public key cryptography | (0) S: pp. 243-292 (chapter 6) |

37 | 2 Dec | (W) | GCDs and modular inverses |
(1) TW: pp. 66-68 (section 3.1.3) (1) TW: pp. 72-75 (section 3.3.1) |

38 | 4 Dec | (F) | Exponentiation and Fermat's little theorem |
(1) TW: pp. 78-79 (section 3.5) (1) TW: pp. 79-82 (section 3.6) |

39 | 7 Dec | (M) | RSA | (1) TW: pp. 164-169 (section 6.1) |

40 | 9 Dec | (W) | Integer factorization |

**Final Paper:**

In place of a final exam, there will be a final paper.

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**Final paper (due Thursday, 17 December)**

**Links:**

- Two Centuries On, a Cryptologist Cracks a Presidential Code.
- Enigma simulator by Dirk Rijmenant for Windows.
- Enigma simulator by Terry Long for Mac OS X (untested).
- Goodbye, passwords! from the New York Times.
- A list of additional reading for some of the topics we will cover, assembled by Menezes.
- Just one example of a failed cryptosystem in real life.
- PGP, IBM help Bletchley Park raise funds
- The Few Milliseconds of an HTTPS Connection
- Photos of the Enigma Machine
- Cat and Mouse