professional education – Switching from math bachelor to computer science master, is a good job in it-security feasible?

I am not sure whether this belongs in this forum or not, please direct me to an appropriate forum to ask my question if it is off-topic. I decided to ask here because a lot of you have very well knowledge of the field.

I am currently doing a bachelor in mathematics but I want to switch over to computer science with a focus on security and privacy for my master studies. As far as I have read up until now it became blatantly obvious that I need a very deep knowledge of how it-systems work in order to implement cryptographic algorithms and related code for it-security in order to not add any vulnerabilities, hence the mantra “don’t roll your own crypto”.

Would it be reasonable to switch directly from my bachelor studies in math to a master program in computer science and expect to get a good job in it-security later on or should I consider completing a bachelor in computer science beforehand in order to have all the fundamentals I need?