There is a new Internet draft on Fundamental Elliptic Curve Cryptography Algorithms by D. McGrew of CISCO and K. Igoe of the NSA. The NSA author might seem out of character for that particular 3-letter agency, but it's no secret that elliptic curves are the NSA’s preferred form of public key system over RSA. It is somewhat impressive that the authors would even attempt to write up such a complex mathematical topic using the ASCII formatting that the Internet Society has insisted on for several decades now. ASCII used to be the lowest common denominator for formatting in the 70’s, but surely now it is HTML or PDF.
Be that as it may, the document is well written and builds up elliptic curves from the basics of modular arithmetic, groups, finite fields before defining elliptic groups. Of course not all types of curves are examined – the document would need to be much longer than 20 pages – but it is self-contained. The section on the security of elliptic curves is a quite short however. After developing the required terminology and background, the authors focus on defining a method for elliptic curve signatures based on the work of two Japanese researchers Koyama and Tsuruoka. This signature variant was probably chosen to avoid any intellectual property issues with more well-known methods that are heavily patented, particularly with respect to efficient implementations.
An interesting read as long as you can handle sustained Courier font. If you are looking for some more background on elliptic curves for security please take a look at Luther Martin’s posts at Voltage, and 4 are listed below ASCII girl