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Cryptology Syllabus Textbook: Making, Breaking Codes: An Introduction to Cryptology, Paul Garrett, Prentice-Hall, Inc., 2001. Paul Garrett's website: http://www.math.umn.edu/~garrett/crypto/ |
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Introduction to Important Algebraic Structures: Finite Groups, Rings, and Fields 1. Assignment: Read Garrett, Preface & Introduction, pp. xi-xix. 2. Summary of Algebraic Structures learned in standard math curriculum through calculus. 3. Assignment: Use Laboratory Experiences in Group Theory & Exploring Small Groups (ESG) software to investigate the symmetries of the triangle, square, and rectangle. 4. Discuss additive group of Zn, integers mod n, and the multiplicative group of units of Zn. Note that Zn is a field when n is prime, otherwise it's just a ring, since when n is composite Zn has some nonzero elements without multiplicative inverses. 5. Assignment: Use the description of the groups G1-G5 in terms of generators and equalities (obtained from the instructor) to construct the Caley table for each. 6. Assignment: Using the ESG software, determine which groups in the ESG library are isomorphic to each of the groups G1-G5 in 5. 7. Quiz 1:
Using your results in 6., write a proof that the group G5 is isomorphic
to the appropriate group that you found in the ESG library.
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Simple Ciphers 1. Assignment: Read Garrett, Chapter 1, pp. 1-16. NOTE: There are a significant number of errors in the book and you should check the two sources below BEFORE your read a section in the book or start to work on the corresponding Exercises. 3. Assignment: Shift Cipher Exercises, pp. 4-5. NOTE: On an assignment of Exercises in which specific numbers aren't given, you should read through all of the exercises and do enough of the routine ones that you understand what's going on. Regarding the exercises that require thought and/or a proof you should at least think about each one and have either a one sentence comment or a thoughtful question prepared and written down to discuss. 4. Assignment: Mod n Exercises, pp. 9-10. 5. (Pop) Quiz 2 on Shift Ciphers. 7. Assignment: Affine Cipher Exercises, pp. 16-17. 9. Assignment: Affine Cipher Frequency Attack Exercises, p. 38. Maple Worksheets for Affine Ciphers
11. Garrett Lecture Notes 05 (Anagrams, Permutations) 12. Assignment:
Cryptogram Exercises, p. 42.
13. Assignment:
Anagram Exercises, p. 47.
14. Assignment:
Permutations Exercises, p. 53.
15. Assignment:
Shuffles Exercises, pp. 55-56.
16. Assignment:
Block Interleavers Exercises, p. 57.
17. Assignment:
One-Time Pad Exercises, p. 13.
18. Garrett Lecture Notes 06 (OTP pp. 24-31)
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Modern Symmetric Ciphers 1. Assignment: Design Goals, DES, & AES. Read carefully pp. 96-107 and think about the Exercises. 2. SHW 2: Individually assigned Selected Homework presentation. 3. Data Encryption Standard (DES) Links. |
| Introduction to Java Programming |
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Useful Number Theory Results 1. Assignment: Read through Chapter 7. "The Integers," pp. 108-137, for the main definitions and results. Do the first three odd numbered exercises in each section. Beware serious error confusing "N" with "n" on pp. 113-114. NOTE: There are a significant number of errors in the book and you should check the two sources below BEFORE your read a section in the book or start to work on the corresponding Exercises. 2. Garrett Lecture Notes 07 (pp. 20-30, beware errors on p. 25 & 30) 3. SHW 3: Individually assigned Selected Homework presentation. 4. Quiz 3. (Applet
due Friday March 4)
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Public Key Ciphers 2. RSA 3. Quiz 4. (Wardlaw Article, Tuesday March 15)
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Sources for Midterm Presentations: Project Reviews & Proposals |
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Useful Applets & Links Tom Linton's Applets
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