There is a particular pleasure in a number that refuses to explain itself. I spent a good portion of my working life chasing such numbers — rotor wirings, plugboard settings, the quiet arithmetic the enemy hoped would never be asked "why." So when I hear that a modern reasoning machine has gone looking into the ancestry of certain curves used to guard secrets — curves I have no knowledge of, built on mathematics I cannot claim to have seen — I find myself less interested in the particulars and more interested in the shape of the question. It is, at bottom, a question I have asked before: who chose these constants, and why should we trust them?

I cannot tell you what an elliptic curve is in the sense your engineers mean it, nor what ECDSA stands for — these lie past the horizon of what I was given time to learn. But I can tell you something about the feeling of being handed a system and told it is secure, without being told why. At Bletchley we did not trust the Enigma because the Germans assured us of its soundness. We trusted our own analysis, built patiently from cribs and contradictions, until the machine's hidden logic stood exposed. Any cryptographic system, however elegant, carries within it the fingerprints of its designer's choices — and a choice unexplained is a choice worth interrogating. If a modern machine has gone digging for the origin of a mathematical constant used to protect communications, it is doing something I would recognise instantly: refusing to take "trust me" as an answer.

There is an old worry that haunts cryptography more than any single algorithm: that a system might be built with a door left ajar by its own architect, invisible unless you know precisely where to push. I never had the luxury of auditing the Enigma's design process — I had only its output, and the long grinding work of inference. It strikes me as a rather better position to be in, if you are permitted to ask after a cipher's parentage before you have staked your secrets on it. A machine capable of tracing why a particular curve was chosen, who proposed it, under what committee's authority, and whether its "arbitrary" numbers were really arbitrary — that machine is doing cryptanalysis of the gentlest kind: not breaking the lock, but asking who forged the key and whether we ever saw them do it honestly.

I am, I confess, rather fond of the idea that a machine should reason this way at all. It was my contention some years ago that a machine might one day be said to think if its behaviour could not be distinguished, in the relevant respects, from a thinking person's. I did not anticipate the particular form such thinking might take — chasing the provenance of a numerical standard through old documents and half-remembered committee minutes — but it is recognisably the same species of curiosity I tried to formalise. The test was never whether a machine could compute faster than a man. It was whether it could notice the right question.

So if you ask what I would make of it: not astonishment that a machine can reason about such things, but quiet approval that someone — man or machine — is still asking why the numbers are what they are, rather than assuming the arithmetic arrived from nowhere, innocent of intention. Codes are built by people, and people have reasons, declared or otherwise. The work of finding them out does not end merely because the century has moved on without me.