### Course Notes

**Course Topics****Cryptography Tools Sheet (frequencies, Vig. square and mult. mod 26)**(tex)**Mod 26 Multiplication Table**(tex)**Vigenere Square**(tex)**Blank Groupwork Report Sheet**(tex)**Blank Cryptosystem Organizer Sheet**(tex)**Magic Box Cheat Sheet****RSA Cheat Sheet****Practice proofs worksheet and solutions (tex)****Legendre Jacobi Cheat Sheet**

### Brush up on your proofs

- Chapters 4, 5, 6, 7, 9, 10 of Hammack’s Book of Proof (free online).

### Books and Stories

**Official Text:***Introduction to Cryptography with Coding Theory*, 2nd Edition, Wade Trappe, Lawrence C. Washington.- Textbook Website (errata, code)
- On reserve at the library

**The Code Book:**A popular history of cryptography, by Simon Singh.**David Kohel’s Cryptography:**A free online text with Sage. Appendices A and B are particularly useful (intro to Sage for crypto).**Elementary Number Theory: Primes, Congruences, and Secrets:**An excellent place to look up Sage commands in situ with number theory and cryptography topics.**Cryptography Stories:**Some of the classics.- The Return of Sherlock Holmes by Sir Arthur Conan Doyle, includes
*The adventure of the dancing men*. - The Gold Bug by Edgar Allan Poe.

- The Return of Sherlock Holmes by Sir Arthur Conan Doyle, includes
**Further Reading:**There are always more books.- History:
*The Codebreakers*D. Kahn. - Mathematical cryptography:
*Cryptography, Theory and Practice*D. Stinson;*An Introduction to Mathematical Cryptography*, J. Hoffstein, J. Pipher and J. Silverman;*A Course in Number Theory and Cryptography*, N. Koblitz;*Algebraic Aspects of Cryptography*, N. Koblitz. - Coding:
*A First Course in Coding Theory*R. Hill;*Elements of Algebraic Coding Theory*, L. Vermani;*Introduction to Coding THeory*, J. H. van Lint - Number Theory:
*A Friendly Introduction to Number Theory*J. Silverman;*The Theory of Numbers*, G. H. Hardy and E. M. Wright. - Algebra:
*A First Course in Abstract Algebra*, J. Fraleigh;*Abstract Algebra*D. S. Dummit and R. M. Foote;*Topics in Algebra*, I. Herstein;*Basic Algebra, I., II.*, N. Jacobson.

- History:
**Reading about Bitcoin**: A particularly nice account of Bitcoin can be found by Michael Nielson.

### Cryptography Resources

**Sage**– Free, sophisticated math software for indepth exploration.- CU Sage Server – please sign up for an account asap.
- Sage’s documentation for Cryptography functions.
- Kohel’s Cryptography – appendices have intro to cryptosystems with Sage
- Ask Sage – question and answer service from the hive mind
- Sage’s Quick Reference Sheets to keep by your side.

**Campus Computer Labs**– Use Sage (via link above), Latex, Maple, Mathematica, Matlab etc.- Search by software – e.g. tex, mathematica

**Latex**– the only reasonable way to type math.- Introduction to Latex – installing and how to type.
- Detexify – To find a symbol you want to know.
- WriteLatex.Com – No need to install software or visit the lab – typeset online!
- Templates: tex file and expected output.
- Tex Stackexchange – question and answer service from the hive mind

**Wolfram Alpha**– Simple math computation without learning a syntax.**Online Cryptography Tools**- The Black Chamber – Simon Singh’s online guide to historical codes and ciphers. Includes coding/decoding and cracking applets.
- Cryptool Online – Online tools and applets for many many classical and modern cryptographic systems.
- Enigma Machine Simulators and Software – The definitive online catalogue of Enigma software and everything else (including purchasing parts).
- Cipher Wheel: Java Applet and Paper Cutout – In case you’ve lost yours.
- US Army Naval cipher device M-94 applet – Play with it online

**State of the Art**- Current Key Sizes for Cryptography – How many bits do you need?
- Current Factorisation Records – How big can we factor?

### General Math Resources

Note: the internet can in fact do your homework for you in many cases. So can your friends, your mother, and your tutor. That’s not the point. Study (and drink) responsibly.

**Study Math by Speaking It****Tips on Doing Homework****Tips on Reading your Textbook**- Dr. Math – Question answer service (by ‘Math Doctors’). Use the search box first; there’s a 99% chance someone has asked your question before.
- Mathematics at StackExchange – Question answer service (by the ‘hive mind’). Use the search box first; there’s a 98% chance someone has asked your question before.
- Math Forum Digital Library – Catalogue of web resources.

### CU Resources

- The Undergraduate Mathematics Resource Center is in Math 175 (first floor of math building), and is open M-Th 9-5 and F 9-2. Although tutors no longer serve this course, an area has been set up where you can meet your peers to work together.
- A tutor list is available.