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Spr2019: MAT4930 2H22, Number Theory & Cryptography MWF7 [13:55-14:45] LIT207 (CE)

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

(Previous versions of [Spring 2016] and [Spring 2013] and [Spring 2011] NT&MC have nice photos of the class.)

MAT4930 2H22 : NT&Math-Crypto counts as an Upper-division math-elective.

Welcome sign

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

It is accessible to anyone with an introductory NT course or who has read the first chapter or two of a beginning NT text.

(I'd like you to know What a prime number is, and What mathematical induction is and What an equivalence relation is. Also helpful is how to “add two numbers mod N”, and what the Euler phi function is.)

Good choices [all these books are in Marston Science Library, on campus] for self-study are:

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).


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).
In all of my courses, attendance is absolutely required (excepting illness and religious holidays). In the unfortunate event that you miss a class, you are responsible to get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.


Resources from a previous incarnation of the course

Approx. Syllabus

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

Various math czars who help out.

Time Computer/Proj Blackboard Humor E-Problems Phone
? ? ? ? ?



Web Resources on The Web

  1. If she saw this, AM HERE ABE SLANEY (TAotDM) , WWSKnow?
  2. The decipherment of a substitution cipher appears in The Gold Bug, by Edgar Allan Poe.
  3. Wikipedia. See also Primality testing and links to original AKS article and improvement.
  4. Historical Cryptography (Trinity College)>.
  5. MathPages. (I haven't reviewed this.)
  6. Sample chapters from the Handbook of Applied Cryptography. (I have not reviewed this book.)

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.

End-of-semester NT Individual Project

Prof.

The  IP (pdf),  is due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , no later than   2PM, Thur., 25Apr2019.

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.



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____End: Number Theory