Learning Cryptography in any way is never going to be free, when you could have spent that time building a SaaS or doing LeetCode exercises to land a Google job. In fact most people's life choices are very expensive through this lens.

Can anyone elaborate on how CS Ph.D.'s are 'free'? Does this apply to UK universities?

I'm aware of scholarships but I'm not from an under-represented background nor am I a genius. I suppose the student loan would cover the costs but I don't consider that free.

I've dropped out of a PhD programme in the UK (many years ago) so perhaps I can help.

It is usual for PhD students to have tuition and a small stipend for their living expenses paid for by government. The government knows perfectly well it needs some supply of researchers, the old ones eventually die so you need to train new ones and a PhD course is how you do that.

A particular university Computer Science department might have say, six slots this year for PhD students. It needs not only the money (which you could if you're wealthy just pay for yourself) but also experienced staff willing to supervise these students which may be a more limiting factor. If it has eight capable applicants versus six slots then yes, you might get refused, but it's rare for there to be a huge imbalance between the number of applicants and available slots such that you'd need to be a "genius".

If you have a good (say first or upper second honours) undergraduate degree in the same or closely related area, and you can find a PhD topic and a doctoral supervisor, in Computer Science they can probably make the money happen.

You will not be wealthy (the stipend is small), but you should be too busy to notice and you're hanging out with other students who haven't got any money anyway.

But it beats on the fun part if you are into it.

Cryptography is one of those areas that I believe a PHD actually helps. And going through it automatically proves that you have what is needed for future jobs.