PhD in cryptography using elliptic curves I am currently a MSc student in number theory and considering switching to a phD in cryptography. I would like to use number theory techniques. (i.e. RSA, elliptic curves, etc). 

The purpose of all of this is to find a job outside of academia. I would like to find a job in the industry.  Here is my worry: in 10-20 years quantum computers will be able to "solve" these problems. Hence, number theory will become useless in cryptography.

Knowing this, will I be able to find a job in the industry in, say, 5 years? 
My thought is that I will eventually have to adapt but so will everyone else. Will this be a problem for my career?

Kind regards.
If you want to end up in the industry, I strongly doubt a PhD is a good investment of your time, regardless of the rest of this discussion.

I believe a general purpose quantum computer, the kind that will send us all to relearn all our algorithm theory, is far from certain in 20 years. I won't even be surprised if someone publishes tomorrow a serious proof it can't be built. 10-20 years ago people were making similar predictions, and though quantum annealing seems to have moved forward, general quantum computers have not advanced much.

In the industry, people won't want to hire you because of your specific thesis and maybe not even because of your field of study. A PhD shows you are intelligent, capable of independent research, capable of finding and reading the latest literature, etc. These are marketable skills.

I read many PhD resumes on a daily basis. And though we do machine learning and artificial intelligence work, I won't throw out a cryptography PhD resume. However the real question with any PhD resume is: can they build production grade software? I believe our own requirements are common in the industry.