Re: How far is the NSA ahead of the public crypto community?
An interesting datapoint I've always had on this question: Back in 1975 or so, a mathematician I knew (actually, he was a friend's PhD advisor) left academia to go work for the NSA. Obviously, he couldn't say anything at all about what he would be doing. The guy's specialty was algebraic geometry - a hot field at the time. This is the area of mathematics that studied eliptic curves many years before anyone realized they had any application to cryptography. In fact, it would be years before anyone on the outside could make any kind of guess about what in the world the NSA would want a specialist in algebraic geometry to do. At the time, it was one of the purest of the pure fields. The friend he used to advise bumped into this guy a few years later at a math conference. He asked him how it felt not to be able to publish openly. The response: When I was working at the university, there were maybe 30 specialists in the world who read and understood my papers. There aren't quite as many now, but they really appreciate what I do. -- Jerry - The Cryptography Mailing List Unsubscribe by sending unsubscribe cryptography to [EMAIL PROTECTED]
Re: How far is the NSA ahead of the public crypto community?
On May 8, 2008, at 19:08, Leichter, Jerry wrote: An interesting datapoint I've always had on this question: Back in 1975 or so, a mathematician I knew (actually, he was a friend's PhD advisor) left academia to go work for the NSA. Obviously, he couldn't say anything at all about what he would be doing. The guy's specialty was algebraic geometry - a hot field at the time. This is the area of mathematics that studied eliptic curves many years before anyone realized they had any application to cryptography. In fact, it would be years before anyone on the outside could make any kind of guess about what in the world the NSA would want a specialist in algebraic geometry to do. At the time, it was one of the purest of the pure fields. I've heard similar recollections of mathematicians from improbably abstract specialties being eagerly taken in by NSA, throughout the cold war. I've also heard it said that at one time NSA was the US's single largest employer of math PhDs. I don't know if that was actually true, but it certainly seems plausible. But it's also important to remember that crypto isn't the only area of the NSA mission that benefits from mathematical expertise. I suspect that while many of these NSA math PhDs were indeed doing cryptomathematics, a large fraction were (and are) working on other SIGINT problems such as signal processing, databases and searching, coding theory, machine learning, and so. Some of the (non-crypto) problems here seem rather specific to the NSA's domain, and so don't likely have an advanced civilian research community competing with them they way academic crypto does today. A couple of the papers from the 1970's hint (in redacted form, frustratingly) that the NSA then had large scale automatic systems for intercepting and processing morse code signals from large blocks of radio spectrum, which implies some pretty advanced (for that era) signal processing and computing, crypto aside. -matt - The Cryptography Mailing List Unsubscribe by sending unsubscribe cryptography to [EMAIL PROTECTED]
Re: How far is the NSA ahead of the public crypto community?
On 2008-05-09, Matt Blaze wrote: The guy's specialty was algebraic geometry - a hot field at the time. This is the area of mathematics that studied eliptic curves many years before anyone realized they had any application to cryptography. [...] I've heard similar recollections of mathematicians from improbably abstract specialties being eagerly taken in by NSA, throughout the cold war. I wouldn't say algebraic geometry is such a pure and abstract specialty in this context. It has its roots firmly planted in multivariate polynomial algebra, and even at that time it was quite clearly the field that was most intimately connected with mechanistic solutions to groups of nonlinear polynomial equations over finite fields. Which then is exactly what a mathematician sees when presented with a symmetric cryptosystem to break. As evidence of that, Hilbert's basis theorem (which underlies Groebner bases, which in case relinearization and the bunch are an independently discovered special case of) was well known and appreciated at that time. So, even if elliptic curve cryptography became later, the broader theory of algebraic geometry was *certainly* relevant to crypto even then, and should have easily been seen to be so. Some of the (non-crypto) problems here seem rather specific to the NSA's domain, and so don't likely have an advanced civilian research community competing with them they way academic crypto does today. Quite so. I think this is where one should be seeking for the signs of differential advantage. Not the broad fields of mathematical expertise which plausibly could have been acquired by the NSA for any of a number of reasons. A couple of the papers from the 1970's hint (in redacted form, frustratingly) that the NSA then had large scale automatic systems for intercepting and processing morse code signals from large blocks of radio spectrum, which implies some pretty advanced (for that era) signal processing and computing, crypto aside. Band agnostic, keying rate adaptable and error tolerant algorithms in this department most likely fall in the advanced category even today, especially if computationally thrifty. I've certainly never seen anything of the sort in what DSP literature I'm aware of. -- Sampo Syreeni, aka decoy - mailto:[EMAIL PROTECTED], tel:+358-50-5756111 student/math+cs/helsinki university, http://www.iki.fi/~decoy/front openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 - The Cryptography Mailing List Unsubscribe by sending unsubscribe cryptography to [EMAIL PROTECTED]
