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.
- 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.
- 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 – 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 – 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
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.