On Friday, January 3, 2003, at 08:39 AM, Michael Cardenas wrote:
I see that you're entirely correct. I've read about half of Scheiner's applied cryptography, and I'm familiar with the fact that current algorithms' strength is based on factoring large primes,
Factoring large primes is easy.
Factoring large non-primes is the hard one.
and familiar with his estimates of 10^11 years for a 112 bit key, (given the caveat of no new scifi computing technology, from his book). And actually, in the chapter on key length he talks about biologocai systems and even about thermodynamics and computing machines in space that capture the energy of supernovas, giving a rather powerful upper bound, given that computation is bound by the laws of space and thermodynamics.As Bill said in his article directed at you a few days ago, the low-hanging fruit has been harvested, at least in terms of crypto qua crypto. There are interesting things to be done in the intersection zone between crypto/math and economics/game theory and reputation/belief. For example, how does money really work? I don't mean at the banal level, but at the level of why and how financial instruments are trusted or not trusted, how belief propagates through graphs, Bayesian and other causal theories, etc.
So, do you think that there are enough feasilbe research topics in cryptography to do graduate research in it, today? It seems that most of the work to be done is application, or solving the reimann zeta function and determining how primes come about.
I've had fun discussions with Dave Molnar on this, and he's well along in his studies at Harvard. Talk to him for ideas. (My own angle is looking at these systems through the lens of category theory and topos theory, my current interests. Use the usual search engines to find my articles on this, dating from around April 2002 to around mid-summer. I'm still doing this, but haven't felt any desire to write things up here on this list, where most subscribers are uninterested or have no background to follow along.)
However, and this is not directed at you in particular but at the "general" you: Unless one is very, very smart or creative or perhaps devious (in ways list members here sometimes are), there is not much good work for "spear carriers" (drones, engineers) to do in the research fringes. Just as in history (the study of history) there really is only room for a handful of topnotch thinkers and writers, and not much use for thousands of "Ph.D. in history" drones, the same is true in crypto and these newer areas of crypto.
Unless one is a Chaum or a Brands or a Goldreich, or one of about 20 others, tops, why bother? If one is a math major, or has a burning desire to understand the nature of the things I mentioned above (trust, belief, value, identity, credentials, etc.), going to grad school in these areas will likely just produce another drone with a Ph.D. who goes to work in the bowels of RSA or Verisign as an engineer. (If even that, as those companies have problems and crypto engineers are a dime a dozen because of the recession and high unemployment rates),
Someone not gifted at math or theory probably should get an engineering degree and make big bucks (someday, after this recession ends, after the U.S. has gone through all of the wars it is now planning) implementing the digital economy tools of 2008.
Of course, the same applies in most fields.
Follow your interests. But be realistic. (I did this in 1973-74 when I decided I was not likely to be the next Feynman or Wheeler and shifted my focus from gravitation and relativity to solid state physics, an area where there was a lot more low-hanging fruit and a lot more opportunities for employment for a non-Feynman like me. Since I've been retired, though, I have gotten back to studying these kinds of things, mainly because I don't have to publish or perish, don't have to fight for tenure, don't have to worry about people thinking I'm not a Feynman, and so on.)
--Tim May
