Course Notes

• • • Cryptography Tools Sheet (frequencies, Vig. square and mult. mod 26) (tex)
    • Mod 26 Multiplication Table (tex)
    • Vigenere Square (tex)
    • Blank Cryptosystem Organizer Sheet (tex)

Research / Modern Developments in Cryptography

• Steven Galbraith’s Blog on mathematical cryptography developments.
• Recent interesting article The Uneasy Relationship between Mathematics and Cryptography.  It’s one researcher’s experience of the recent history and conflict in the field.  Very interesting read.
• eprint server (where new research appears)
• Major cryptography conferences, most of which have video recorded talks:  see the IACR Events Website.

Brush up on your proofs

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

Brush up on your programming

• • • learnpython.org — I recommend you work through the tutorials in order (start at the header “Welcome”; the bit before is an ad for something else).

Books and Stories

• • • Official Text: Introduction to Cryptography with Coding Theory, 2nd Edition, Wade Trappe, Lawrence C. Washington.
      • Textbook Website (errata, code)
      • Available on reserve in Canvas
    • The Code Book: A popular history of cryptography, by Simon Singh.
      • On Google Books
    • David Kohel’s Cryptography: A free online text with Sage. Appendices A and B are particularly useful (intro to Sage for crypto).
      • Download the PDF
      • Locally hosted copy
    • Elementary Number Theory: Primes, Congruences, and Secrets: An excellent place to look up Sage commands in situ with number theory and cryptography topics.
      • Download the PDF
    • 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.
    • Further Reading: There are always more books.
      • A practical guide for developers:  Series Cryptography, by Jean-Philippe Aumasson
      • 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 Theory: 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.
    • Reading about Bitcoin: A particularly nice account of Bitcoin can be found by Michael Nielson.

Sage

• • • Sage – Free, sophisticated math software for indepth exploration.
    • SDSU Sage Tutorial – good choice for an intro
    • 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.

Latex

• • • Latex – the only reasonable way to type math.
    • My Latex introduction
    • Introduction to Latex – installing and how to type.
    • detexify – To find a symbol you want to know.
    • overleaf.com – No need to install software or visit the lab – typeset online!
    • Tex Stackexchange – question and answer service from the hive mind

Online Cryptography Tools

• • • • Wolfram Alpha – Simple math computation without learning a syntax 
      • Compute any multiplication table mod n
      • Boxentrique – Online encrypt/decrypt for classic ciphers and more.
      • 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.
      • 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.

• • • Proof of Concept, my blog/resource site for math majors
    • Study Math by Speaking It
    • Tips on Doing Homework
    • Tips on Reading your Textbook
    • 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

CU Resources

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