Encryption and Uncertainty...

Two tidbits I encountered in the last 24 hours that I found interesting, and so am passing along (perhaps, in some odd way, there's even a tiny thread of linkage between the two!??):

1)  RSA encryption researchers make "an astonishing find" (essentially that encryption keys aren't nearly as random as one might expect):
http://www.pcworld.com/article/2897772/researchers-find-same-rsa-encryption-key-used-28000-times.html

and,

2)  Ed Frenkel advocating the importance of human uncertainty in science (I couldn't agree more) -- even scientists who acknowledge uncertainty, nonetheless often fall into the trap of assuming certainty about specific matters. The epistemological nature of uncertainty is difficult to internalize (I think) because we must operate in our daily lives as if we are certain of a great many things... but this ought not detract from the importance of recognizing uncertainty in a scientific perspective... anyway, read Ed and the Facebook discussion that follows (be sure to click on "See More" to expand Ed's full initial response):

http://tinyurl.com/ljam3lm

p.s.  -- the Lawrence Krauss New Yorker piece that is referenced (and inspired Ed's response) is here:
http://www.newyorker.com/news/news-desk/teaching-doubt?intcid=mod-latest 

"The Keys to the Keydom"

An interesting piece below from Brian Hayes on vulnerability of the RSA encryption system, based upon occasional shared prime number factors (nothing that wasn't already known, but nicely-explained and interesting storyline):

http://bit-player.org/2013/the-keys-to-the-keydom

From the article:

"...The output was a list of 64,081 compromised keys for TLS hosts, about 0.5 percent of all such keys collected...
"The good news is that none of the weak keys are guarding access to major web servers hosting bank accounts or medical records or stock markets or military installations. Most of them are found in embedded networked devices, such as routers and firewalls. That’s also the bad news. A programmer with malicious intent who can gain control of a well-placed router can make a lot of mischief."

P vs. NP vs. NSA

Since the press leaks regarding NSA subversion of online encryption through various means, dicey articles (and forum discussion) have begun speculating as to whether or not the agency may be working with a quantum computer, or even might have already proven P = NP (but for obvious reasons would never disclose such a proof -- cue in "Travelling Salesman" movie). Not much to back up such speculation… but always fun guessing, I s'pose. Here's one 'popular' piece (focused on RSA encryption, no actual mention of P vs. NP):

http://www.dailydot.com/politics/nsa-rsa-encryption-crack-prime-numbers/

And for those up to more of a challenge, here's a recent take from the always interesting, excellent Scott Aaronson:

http://www.scottaaronson.com/blog/?p=1517

A Prime Example...

of what prime numbers are good for...

A very brief (simplified) introduction to RSA encryption via YouTube:

RSA Keys... How Weak?

Rather technical, but still very interesting discussion of the recent concerns over RSA encryption from the "Gödel's Lost Letter" blog (if RSA interests you, a must-read):

http://rjlipton.wordpress.com/2012/03/01/do-gaps-between-primes-affect-rsa-keys/

RSA Encryption

A fairly straightforward explanation of RSA encryption here:

http://inversezen.com/2010/11/the-rsa-algorithm/