Is cryptography an interesting field for research? I am now styding for first year bachelor's degree in Mathematics for IT. In the future I would like to major in the same field and possibly continue trying to get a Ph.D. But I still have options to take a different path.

Even though I have a long journey ahead, I am thinking about trying to write a "scientific bachelor's thesis" (that's how we call bachelor's thesis with scientific results on my university in my language) when the time comes.

Is cryptography a field with interesting and imporant problems to solve? I know about some interesting problems like P=NP and some stuff about (post-)quantum cryptography, but surely that's not what majority of problems are like.

So, is cryptography a field where it is easy to find meaningful and interesting problems to solve?

(I am not sure if this is the right place to ask this, so please inform me if I should ask somewhere else.)
Cryptography is a nice field in which not only problems to solve are a-plenty, but it is also one of these fields where individuals can make significant discoveries in a relatively short time. A PhD student in cryptography will typically write three or four articles during his thesis; by comparison, a "pure mathematics" PhD student will generally produce a single article in the same time. Informally, to make new advances, you have to first learn the existing science; in cryptography, this means getting up to date with about 40 years of research. In mathematics, that's closer to 200 years, hence the comparatively higher effort to reach the "publishable" state.

Moreover, cryptography is an applied field, by which I mean that it has immediate practical applications. This means money: you can make a very nice living out of cryptographic expertise. A PhD is a very good key to unlock such things (I have a PhD and I am a consultant in cryptography, and my experience is that both facts are related). Intellectual fulfilment is of primordial importance to a balanced life, and money does not make happiness; but money is still some super useful stuff, and being able to live out of doing intellectually rewarding things is a nice combination to achieve.

In any case, mathematics are always useful for anything related to computers. A lot of computer users and developers can get along with a very low understanding of the underlying principles, but the maths are what explains why computers work that way. Mathematics allow to look beyond the magic.