For the record, GCHQ created RSA in 1973 and then DH in 1974:

* https://en.wikipedia.org/wiki/Public-key_cryptography#Histor...

DH qua DH was invented in 1976, and RSA qua RSA in 1977.

What does qua mean here?

There is "RSA" as implemented by GCHQ in 1973, and there is "RSA" as RSA like we generally know it by the three folks that it was named after. There is "DH" as implemented by GCHQ in 1974, and there is "DH" as DH like we generally know by the two folks that it was named after.

The concept "x" as we (generally) know x is what qua means. (Because words can mean and point to potentially many concepts.)

I'm assuming "by": as in those algorithms were created by the people whose names are now associated with them in those years

"as"

He means DH, as in Diffie Hellman, was not the first approach to key exchange. The difference is that in the UK we did what we usually do: we squandered an amazing innovation and let some other country benefit from it.

I do wonder what the capabilities of GCHQ are today - I guess it’ll be interesting to see in 50 years or whenever it is assuming it gets declassified…

Did it really invent RSA, such that there was any actual capability of performing asymmetric encryption or signatures?

I thought it was more like, one guy there had a pretty good idea that it was possible that he wrote about, but never developed it into anything practical.

Am I mistaken, and the whole working system was described?

A PDF scan of the paper is now available, so you can judge for yourself:

* https://web.archive.org/web/20180928121748/https://www.gchq....

IANAM (mathematician), but the formulae look RSA-like, though given the compute at the time, it may have been (too) expensive to try implementing.

The "pretty good idea" (Ellis' "non-secret encryption") was published about in 1969. Clifford Cocks found a workable algorithm for it — using prime factorization as the trapdoor function — in 1973. No cryptosystem was ever developed around the idea, by Cocks or GCHQ in general; they just sat on it as a classified secret. Then, in 1977, RSA was independently invented and published as both an algorithm and a full cryptosystem.

I would definitely say that Cocks and RSA both independently discovered what we refer to as the RSA algorithm. We should maybe call it the Cocks–RSA algorithm.

There is no provable claim by GCHQ for any of this. They are professionally liars and deceivers. The first public, peer-reviewed publishers are the ones that get the credit. GCHQ claims are just unproven British government propaganda from people that have agreed on record that they will lie, deceive and hide the truth.

It's certainly conceivable this claim was made by them just an attempt to look good.

If so it was an inept attempt, not that "inept" rules it out.

But I do generally assume that when organisations point at their mistakes, its not a failed attempt to look good.