Crypto-busting boffins have broken a new record in their quest to find the prime factors in large numbers, and may soon threaten part of the encryption system used to secure retail websites.
Professor Arjen Lenstra of the Ecole Polytechnique Federale de Lausanne (EPFL) yesterday broke the news that computing clusters run by the EPFL, the University of Bonn, and NTT in Japan had managed to rip out the prime factors in a "whopping" 307-digit number.
On the face of it, this would seem to threaten the security of widely-used RSA 1024-bit encryption. The RSA algorithm uses two 150-odd digit primes to produce a 1024-bit code, similar in size to the one that Lenstra's computer clusters have factorised. The difficulty of extracting the prime factors involved in the creation of keys to the RSA code is what makes the algorithm secure.
Is the writing on the wall for 1024-bit RSA encryption?
"The answer to that question is an unqualified yes," says Lenstra.
However, the crypto prof then qualified his answer. The 307-digit monster his team has just broken wasn't a true RSA code but a so-called "special" number, describable in this case as 21039-1. RSA algorithms made up of two primes are harder to factorise. One might also note that even the special case 307-digit "behemoth" took 11 months and a century of computer time to crack.
The largest proper RSA number yet broken was a 200-digit "non-special" number whose two prime factors were identified in 2005 after 18 months of calculations that used over a half century of computer time. The 1024-bit numbers used in RSA encryption are around 100 orders of magnitude bigger than this. The writing may be on the wall for 1024-bit RSA: but as yet, um, nobody can read it.
However, Lenstra remains quietly confident.
"Last time, it took nine years for us to generalise from a special to a non-special hard to factor number," he said, referring to earlier efforts to break 155-digit numbers.
"I won't make predictions," he went on, "but let's just say it might be a good idea to stay tuned."
This would seem to indicate that Lenstra and his colleagues have even now moved on from 307-digit special numbers to similarly-sized non-special proper RSA numbers, and that he expects success within a few years. At that point, the writing would be on the 1024-bit RSA gravestone, not the wall. Crypto attackers would presumably need significant amounts of computer resources, but these aren't unobtainable. Large botnets, for instance, might conceivably be used in place of academic distributed projects or clusters.
Ari Juels, chief scientist at RSA Labs, told the Reg:
"Lenstra's result is consistent with the view of the scientific community that natural evolution in computing power will require the industry periodically to adopt longer key sizes. Indeed, Lenstra's result may confirm his prediction in 2001 that 1024-bit RSA keys will be within the reach of a concerted factoring effort by 2009...1024-bit RSA will reach the end of its effective lifetime around 2010...Our best estimate is that 2048-bit RSA keys will be suitably strong for use through 2030. Detailed scrutiny by the community of Lenstra's result may require some recalibration of key-lifetime recommendations."
Noted security brainbox Bruce Schneier commented more bluntly on the EPFL announcement in his blog, saying: "I hope RSA applications would have moved away from 1024-bit security years ago, but for those who haven't yet: wake up."
We're all RSA users on occasion: the padlock we see in our browser when logging onto a secure website such as a bank or web shopping checkout typically refers in part to an RSA handshaking process. We should probably all hope along with Bruce. ®