## 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:”

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:”

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,

614,966,266,413,770,127is the product of

5,174,413,344,875,007,990,519,123,187,

618,500,139,954,995,264,909,695,897,

020,209,972,309,881,454,541and

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.

Pretty cool. I remember implementing the RSA algorithm on a TI-57 calculator back in 1979, but the keys I could handle were even shorter than this.

Of course it would have been

reallycool if they had managed to factor the keyusinga TI-83 calculator ðŸ™‚Have you noticed that these numbers have been taken down elsewhere via (probably spurious) DMCA takedowns? Just curious what you’ll do if you get one of those…

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