It was recently announced that Benjamin Moody has factored an RSA-512 bit key in 73 hours using only public software and his desktop computer. The first RSA-512 factorization in 1999 required the equivalent of 8,400 MIPS years over an elapsed time of about 7 months. The announcement was made all the more intriguing in that it came from a mailing list associated with a user forum for Texas Instruments calculators.
The public key in question is used to verify signed OS binaries for the TI 83 Plus and the factorization means that
… any operating system can be cryptographically signed in a manner identical to that of the original TI-OS. Third party operating systems can thus be loaded on any 83+ calculators without the use of any extra software (that was mentioned in recent news). Complete programming freedom has finally been achieved on the TI-83 Plus!
The original post from Moody was not very informative, but the subsequent Q & A thread drew out more details. Moody used public source factoring software on a dual-core Athlon64 at 1900 MHz. Just under 5 gigabytes of disk was required and about 2.5 gigabytes of RAM for the sieving process. The final computation involved finding the null space of a 5.4 million x 5.4 million matrix.
Most security people would rightly claim that RSA-512 is known to be provide little security as a keylength, however this does not mean that 512-bit public keys are not in use today by companies other than Texas Instruments. By the way, someone is offering an RSA 512 factoring service with a “price indication” of $5000.
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