PhD in Cryptography after Master's in Pure Mathematics I have done my Master's in Pure Mathematics.However as we had learnt Cryptography in our Master's Course ,I have developed an inclination towards it.

I have started liking coding theory in Cryptography. I like to write programs.
But I have seen that most  people in Cryptography are from Computer Science background.Should I do PhD in this subject as I am liking it now?

However I am unable to understand is there any prospect of that subject specially since I am a student of Pure Mathematics background.

Will I be able to get a job if I don't remain in Pure Mathematics anymore and start writing codes which are more inclined towards Computer Science.

I am puzzled.Please help me if there is any future of my liking.
My advice would be to find a way of getting some research experience associated with cryptography before committing to the idea of doing a Ph.D. in it. Several advantages to this:

a) you'll know that you'll like working on open problems in cryptography, as opposed to just liking learning about the field in the classroom;

b) it'll give you a sense of the types of research you might want to pursue, which would pave the way for a well-developed statement of purpose in your grad school applications;

c) it could help you make additional useful connections. A Ph.D. application supported by letters from cryptography professors attesting to your research potential in the field would make a lot of sense if you do indeed end up wanting to aim to do a Ph.D. in it.