20120219, 18:23  #1 
Dec 2010
Monticello
3403_{8} Posts 
John Nash's letter to the NSA predecessors
All:
This was recently declassified. I think it may be of general interest. http://agtb.wordpress.com/2012/02/17...ertothensa/ Christenson 
20120219, 20:28  #2 
∂^{2}ω=0
Sep 2002
República de California
2×13×443 Posts 
Fascinating ... two comments:
1. "[Nash] is very well aware that this is a conjecture and that he cannot prove it. Surprisingly, for a mathematician, he does not even expect it to be solved. Even more surprisingly he seems quite comfortable designing his encryption system based on this unproven conjecture. This is quite eerily what modern cryptography does to this day: conjecture that some problem is computationally hard; not expect anyone to prove it; and yet base their cryptography on this unproven assumption." I wonder whether this might be another example of the same phenomenon that came up recently with respect to the alleged discovery of fasterthanlight particles at CERN. I immediately offered to bet anyone $1000 that the alleged discovery would vanish under scrutiny, on "winwin" strategy that most of the time such 'finds" do prove spurious  in which case there is no exciting 'new physics' but I win some money  but in the remote probability that the find is real, that will be cool enough that I won't mind losing the money. In the present case, we believe "hard" problems really are hard, but we have no proof as yet. So for a mathematician who also enjoys gambling (game theory), if someone did manage to find a polynomialtime way to crack some believedtobehard (and hence all, if we are speaking of "hard" in the formal NPcomplete sense) problem like integer factorization, that would be such a onceinalifetime amazing discovery, that the side effect of much of the world's digitalsecurity infrastructure effectively vanishing would be a price worth paying. 2. Not being a crypto guy, I had not previously heard of Clifford Cocks having invented the "RSA" encryption algorithm in 1973, four years before R,S, and A first published it. Cocks’ work remained classified until 1997  as does one of the article commenters, I wonder what if any the 'prior art' implications of that prior discoverywhichwaskeptsecret might be. Also, once the algorithm was published in 1977 by the researchers whose initials it now bears, what would be the point of keeping Cocks' work classified? Is this just the usual paranoidnationalsecurity apparatus M.O. of keeping as much stuff as possible classified for as long as possible, irrespective of the rationale for continued secrecy having vanished long ago? 
20120219, 20:48  #3  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
1011001101101_{2} Posts 
Quote:


20120220, 03:08  #4 
Romulan Interpreter
Jun 2011
Thailand
2×29×151 Posts 
That is really interesting material. Remember what I said somewhere here around, half year ago, quoting Fred Cohen (I love his books!): "we never approve" (for export, for use in software products, for making public, whatever) "something we can not decrypt".

20120220, 07:29  #5  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
24031_{8} Posts 
Quote:
Bureaucratic organizations, and especially intelligence organizations, usually move exceedingly slowly. 

20120220, 15:13  #6 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 

20120224, 04:23  #7 
"Jason Goatcher"
Mar 2005
5×701 Posts 
Not to be a troll, but what sort of security could we have if we decided to only base things on proven assumptions?
I honestly have no idea how this will be answered. If there are adequate ways to secure computers than we should use them, but if alternatives are significantly worse than the cryptographic method we use now than I don't see what choice we have in the matter. Edit: Is the problem cryptography in general, or just this particular method? Last fiddled with by jasong on 20120224 at 04:24 
20120224, 04:32  #8 
May 2003
60B_{16} Posts 
As I understand it, the only provably absolutely secure cryptosystem (currently, publicly known) is the use of onetime pads. But even that rests on the assumption that the enemy does not have access to those onetime pads, that the pads are sufficiently long, etc... which makes them illsuited to internet security.

20120224, 05:16  #9  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5,741 Posts 
Quote:


20120224, 15:07  #10  
Nov 2003
2^{2}×5×373 Posts 
Quote:
Cryptography", Notices AMS, Sept 2007. To say that it raised quite a stir is an understatement. Quote:
they do not. Quote:
existence of a subexponential algorithm is evidence for that. (but not a proof) Quote:


20120225, 16:39  #11  
Oct 2007
London, UK
1,307 Posts 
Quote:


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