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Spr2013: MAT4930 7554 Number Theory (Special Topics) MWF6 LIT221 (NW)

Number Theory & Cryptography We may use more advanced computing devices...



(A previous version of this course has two nice photos of the class.)
Welcome sign

This is a 1-semester course interested in Mathematical Cryptography (major topic) and other aspects of Coding: Data Compression and Error-correcting codes. We also did one example of an Isomorphism code.

It was accessible to anyone with an introductory course or who has read the first chapter or two of a beginning text. (Mainly, I'd like you to know how to “add two numbers mod N”, and what the Euler phi function is.) Good choices for self-study are:

Here are the Courageous Ones, who registered: (Click for a larger version. Which student has spinach in his teeth? [Perhaps it is visible in the photo at the page-bottom?])
2013Sprint NT/Crypto class


Various math czars who help out.

Chalk Phone Time Computer/Proj Blackboard Humor E-Problems
Dillon Baker Hannah! Thom everyone me Jackson & James G.

End-of-semester NT Individual project

Prof.

The Project-Y is due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , no later than   noon, Friday, 26Apr2013.

The project must be carefully typed, but diagrams may be hand-drawn.


At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist Checklist (pdf, 3pages) to earn full credit.

ENCODING: a b c d e f g h i j k l m n o p q r s t u v w x y z ' . ? ! , 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Three Examples of simple ciphers: CAESAR: Shift of 9: a b c d e f g h i j k l m n o p q r s t u v w x y z ' . ? ! , 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 0 1 2 3 4 5 6 7 8 MULTIPLICATIVE-CIPHER: Mult by 5: a b c d e f g h i j k l m n o p q r s t u v w x y z ' . ? ! , 0 5 10 15 20 25 30 3 8 13 18 23 28 1 6 11 16 21 26 31 4 9 14 19 24 29 2 7 12 17 22 27 AFFINE-CIPHER: Mult by 5, then add 9. x |-> [5*x]+9 (mod 32) a b c d e f g h i j k l m n o p q r s t u v w x y z ' . ? ! , 9 14 19 24 29 2 7 12 17 22 27 0 5 10 15 20 25 30 3 8 13 18 23 28 1 6 11 16 21 26 31 4

Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the ChecklistThe checklist (pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).


Photo of text cover Our textbook is An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics).
Authors: Jeffrey Hoffstein, Jill Pipher, J.H. Silverman ISBN: 978-0-387-77993-5
Year: 2008 Publisher: Springer
Marston: QA268 .H64 2008 Electronic: Chap. 1 and Chap. 2, Diffie-Hellman, etc. (Free for UF students)

The homepage of ... Mathematical Cryptography, with a link to its Errata sheet.
Here are links to this book at The Publisher's site and at Amazon.com.



Web Resources on The Web

  1. Wikipedia. See also Primality testing and links to original AKS article and improvement.
  2. Historical Cryptography (Trinity College)>.
  3. MathPages. (I haven't reviewed this.)
  4. Sample chapters from the Handbook of Applied Cryptography. (I have not reviewed this book.)

Approx. Syllabus

2013Sprint NT/Crypto class


Looking into the Future, here is part of the Spring 2014, NT & Cryptography, page:


Our syllabus mentioned some algorithms we will learn. There were some nice microquizzes during the semester.
The exams were:

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____End: Number Theory