It seems the TI-83+ operating system is protected using some form of code signing scheme using a 512 bit RSA key. That key has now been factored:
http://www.unitedti.org/index.php?showtopic=8888 Which apparently will allow custom operating systems to run on the device. While this certainly is not the first 512 bit RSA moduli to be factored, this may be the first one that was performed (publicly, at least) with the goal of breaking an existing system, rather than simply demostrating progress in algorithms and hardware. Interestingly, it was reportedly done with only a single machine, over the course of 73 days. Details on the computation are lower down in the thread: """ How did I do this? With the best tools I could find for the job. The best algorithm for factoring really large general numbers (i.e., numbers without any special properties) is the general number field sieve. The best currently-available implementation of the GNFS consists of a combination of the GGNFS and Msieve projects. It's really the guys behind these tools who deserve the credit for making this possible. While it does take a bit of work to get the tools set up correctly, most of what I did was sitting around waiting for it to finish, and every once in a while, telling the script to try another filtering run. smile.gif Some fun statistics: - The factorization took, in total, about 1745 hours, or a bit less than 73 days, of computation. (I've actually been working on this since early March; I had a couple of false starts and haven't been able to run the software continously.) - My CPU, for reference, is a dual-core Athlon64 at 1900 MHz. - The sieving database was 4.9 gigabytes and contained just over 51 million relations. - During the "filtering" phase, Msieve was using about 2.5 gigabytes of RAM. - The final processing involved finding the null space of a 5.4 million x 5.4 million matrix. """ --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to majord...@metzdowd.com
