It still grates me a little when they talk about "factoring large primes". I realize that what they mean, "factoring the product of two large primes," is a bit long-winded, but why not just "factoring large numbers"?
Interesting article, but I was left with a somewhat troubling question about British Intelligence. They developed this elegant crypto algorithm, but felt it may have a weakness which they were unable to find. Being spooks, wouldn't their next thought be, "What if our enemy develops this too and starts using it? We really need to find that weakness!"
Even Williamson believed that the whole venture was too risky. When he finally wrote up a revised version of his key scheme, he cited these reservations as the reason for the two-year delay. "I find myself in an embarrassing position," he wrote. "I have come to doubt the whole theory of nonsecret encryption. The trouble is that I have no proof that the method ... is genuinely secure." He conceded he could not find anything wrong with the system, though, "and would be grateful if anyone else can." No one did. But by then the GCHQ had tacitly concluded it wasn't worth the effort to implement a public key crypto system.
They tried, hard, to find weaknesses, but they couldn't, this was the problem.
Nick Patterson is mentioned early in this article as a mentor to Cocks (half of the Cocks-Ellis pair that originally invented what we know as RSA).
Patterson now applies his mathematical prowess to investigating human genetics at the Broad Institute http://www.nytimes.com/2006/12/12/science/12prof.html . (Sorry to continually add biological asides to all of these discussions.)
This reminds me of John Harrison's invention of the chronometer. In both cases, a modest Briton brought a solution to an "impossible problem" to the officials, who rejected it because it was too simple to be correct.
(John Harrison also had the problem that one of the officials came up with a rival, astronomical solution before his was accepted.)
"...public key is now ubiquitous, on every copy of Netscape and Lotus Notes - and may one day wind up in everyone's wallet as smartcards..."