force attacks. I did some calculations and it looks like it will take, given a perfectly effecient computer, the combined energy of 509,485,193 average supernovas to brute force a 256 bit key. I was just wondering if
I'd be interested to see those calculations. If 128 bit keys would require sqr(509485193) supernovas, I think we probably don't need to go much higher with the number of bits. OTOH, if the feds can somehow figure out how to convert all the matter in the solar system into energy, they might be able to get enough energy... e=mc^2... But, there wouldn't be anywhere to put the computers. :) While we're exchanging calculations.... I've done some simple calculations myself (which have probably already been done, but anyway...), regarding 128 bit keys, assuming a billion (10**9) computers trying a billion keys per second... I heard it would take an average of 6 billion years to crack a 128 bit key with those resources, but my calculations (using GNU bc v1.02 under FreeBSD) figure it at over 5 trillion years... echo "2^128 / 10^9 / 10^9 / (60 * 60 * 24 * 365.25)" | bc 10782897524556 With commas, that's 10,782,897,524,556 years. Cut that in half (for average cracking time), it comes to 5,391,448,762,278 years. I don't know where I heard the 6 billion year figure, it might have been in the Wired Cypherpunks article, but I think I read it somewhere else as well... Is my calculation okay? Similar calculation... Assume you have a 384 bit key that you want to brute-force, and you have 10^73 computers trying 10^9 calculations per second. (Last I heard, 10^73 is the number of particles in the universe). echo "2^384 / 10^73 / 10^9 / (60 * 60 * 24 * 365.25)" | bc 124857423240026108488221664 That's an impressive number. :) As an aside, I've heard that "billion" and "trillion" are different in different parts of the world... Western British billion 10^9 10^12 trillion 10^12 10^18 A British friend mentioned to me that they are different... We checked with American and British dictionaries to get those figures. AFAICS, Canada seems to use the American system. Weird, eh? ===================================================================== | Steve Reid - SysAdmin & Pres, EDM Web (http://www.edmweb.com/) | | Email: steve@edmweb.com Home Page: http://www.edmweb.com/steve/ | | PGP Fingerprint: 11 C8 9D 1C D6 72 87 E6 8C 09 EC 52 44 3F 88 30 | | -- Disclaimer: JMHO, YMMV, IANAL. -- | ===================================================================:)