Math 116

Announcements

• April 18 -
  Solutions to HW 1 are now posted on the professor's web page.
  Solutions to HW 2 and quiz 1 should be posted soon.
  I have started to compile a list of cryptography-related books, papers, and links below, which some of you might find interesting.

Crypto Books

• General

  Schneier, Bruce. Applied Cryptography.

  This book was considered for several years the bible of cryptography. Unfortunately, it's slightly outdated now (even though it's only ten years old), but it is still an excellent reference on many aspects of cryptography, and it requires very little mathematical background. Its chapter on cryptographic protocols is unsurpassed, and the book is worth owning for this alone.

  Stinson, Douglas. Cryptography: Theory and Practice.

  An excellent text on general cryptography, and more advanced than the textbook we are using. While not nearly as thorough as Applied Cryptography, this book is heavier on the theory and the mathematics. It also includes exercises.

• Mathematical

  Buchmann, Johannes. Introduction to Cryptography.

  This is a decent introduction to elementary number theory and public-key cryptography, but it is fairly long-winded for the material that it covers. Note that this book deals almost exclusively with basic public-key ciphers such as RSA, DSA, ElGamal-Diffie-Hellman, etc. It includes very little about symmetric ciphers, and virtually nothing about cryptographic protocols or the actual usage of cryptography in practice.

  Bressoud, David. Factorizaton and Primality Testing.

  This is not a book on cryptography, but rather a basic number theory book that might as well be subtitled, "What we know about how to crack RSA." It is a decent first text on elementary number theory (it was my first, not to mention the book that originally got me interested in cryptography), and it's an outstanding reference for anyone who wants to understand factoring algorithms, from the basic to the most high tech. It does not, unfortunately, cover the General Number Field Sieve (GNFS), the best publicly known factoring algorithm, but it does describe its predecessor, the Multiple Polynomial Quadratic Sieve (MPQS). Perhaps the most amazing thing about this book is that it manages to explain the "big guns" like MPQS and the elliptic curve factoring algorithm at a very elementary level, easily accessible to undergraduates. I believe it was out of print for several years, but it is apparently available again. Buy it while you can!

  Koblitz, Neal. A Course in Number Theory and Cryptography.

  I have not read this book, but it sounds like a very good supplement to the previous one in this list. It covers similar topics, but at a more advanced level, and it delves much more deeply into the actual cryptography. Note that this is a graduate text in mathematics, so it may be a difficult read.

• Historical

  Kahn, David. The Codebreakers.

  A voluminous tome, but a renowned source on the history of cryptography. It's worth owning just for the first chapter, which will have you on the edge of your seat as you discover how U.S. cryptanalysts uncovered the Japanese plot to attack Pearl Harbor only hours before the attack took place.

  Bauer, Friedrich. Decrypted Secrets.

  This book should probably also be listed in the mathematical section above, as it does contain a fairly high level of mathematical content, but of a different nature than the other books listed there. This book describes a lot of the nineteenth and early-to-mid-twentieth century history of cryptography (which is some of the most interesting history of the subject), but it also describes in excellent detail the mathematical principles behind the cryptosystems that were used in those times. Furthermore, it goes on to detail the cryptanalysis of such systems, both from a historical point of view and from a modern mathematical perspective. If you want to know exactly how Enigma worked, and exactly how it was cracked, including all the mathematical details, read this book.

  Stephenson, Neal. Cryptonomicon.

  This is not really a history book, but more like historical science fiction. Highly recommended.

Crypto Links

• Papers, etc.
  • A Method for Obtaining Digital Signatures and Public-Key Cryptosystems by Ron Rivest, Adi Shamir, and Len Adleman. The original RSA paper that established the world's first (publicly known) public-key cryptosystem.
  • Phil Zimmermann's web page - The original author of the PGP program. If you are interested in some of the ethical/political issues surrounding cryptography, this web site is a must read. See in particular his senate testimony and letters.
  • Bruce Schneier's web page - The author of Applied Cryptography maintains a web page with a lot of interesting information and links. See in particular his bibliography of crypto papers.
  • Ron Rivest's web page - Lots and lots of links.
  • The Stanford Applied Crypto Group
  • Ross Anderson's web page
• Software
  • PGP: Pretty Good Privacy, originally written by Phil Zimmermann, is a tool for encrypting files and email using public-key and conventional cryptography, with a "web of trust" paradigm for key management. (Note that this link is for the PGP International website, which will allow you to download one of the free, but full-featured, versions of PGP. You can also check out the commercial version if you like.
  • GnuPG: The GNU Privacy Guard, an open source alternative to PGP, which is essentially fully compatible with the original. If using software that is free-as-in-speech in addition to free-as-in-beer gives you a warm fuzzy feeling, try GPG. Note that even the freeware version of PGP has a nice graphical user interface and plugins for several popular email clients, whereas GnuPG is command-line only. There are graphical shells available for GnuPG, such as GPA.
  • OpenSSL: An open-source library and toolkit for the implementation of SSL and TLS, including numerous symmetric ciphers, hash functions, public-key algorithms, digital signature schemes, etc. Note that this is just a library to be used in other software, not an actual application.