Shostack + Friends Blog Archive

Moore's Law is a Factor in This

I remember when Derek Atkins was sending mail to the cypherpunks list, looking for hosts to dedicate to cracking RSA-129. I remember when they announced that “The Magic Words are Squeamish Ossifrage.” How it took 600 people with 1,600 machines months of work and then a Bell Labs supercomputer to work through the data. I had a fun little stroll down memory lane reading about average machines not having more than 16MB of ram, and how they borrowed a server with 2, later 3 900 MB disks. 129 decimal digits fits in 430 bits. The RSA-129 paper concludes:

We conclude that commonly-used 512-bit RSA moduli are vulnerable to any organization prepared to spend a few million dollars
and to wait a few months.

Fast-forwarding to this week, David Molnar mentions that “We’re living in the future now:” [link to http://ephermata.livejournal.com/205656.html no longer works]

The 512-bit RSA key used for signing applications and firmware updates for the TI-83 has been factored. By some person working on his or her own. With one computer.

David links to “Calculator hackers crack OS signing key, opening a closed platform,” and following links, we get to “fun number theory facts:” [link to http://www.unitedti.org/index.php?showtopic=8888 no longer works]

Gentlemen,

A mathematical morsel for your entertainment and edification.

The number
6,857,599,914,349,403,977,654,744,967,
172,758,179,904,114,264,612,947,326,
127,169,976,133,296,980,951,450,542,
789,808,884,504,301,075,550,786,464,
802,304,019,795,402,754,670,660,318,
614,966,266,413,770,127

is the product of
5,174,413,344,875,007,990,519,123,187,
618,500,139,954,995,264,909,695,897,
020,209,972,309,881,454,541

and
1,325,290,319,363,741,258,636,842,042,
448,323,483,211,759,628,292,406,959,
481,461,131,759,210,884,908,747.

Originally published by adam on 24 Aug 2009
Last modified on 10 Oct 2022
Categories:   economics   information security   Security   Uncategorized