The advice you've been given seems to make sense to me. Here in the UK cryptography isn't offered as a first degree. To study it at university you need to gain a first (Bachelors) degree in a relevant subject, or combination of subjects, and then go on to take a Masters degree in cryptography. That appears to be roughly the same path that's been suggested to you.
I'd suggest that it's Pure Mathematics, rather than Computer Science, that's at the heart of cryptography, as you need a
really good grasp of number theory. See 'Career Opportunities' here:
http://mathematics.uonbi.ac.ke/node/1819