What topics / books on mathematics are the minimum necessary for a programmer to learn cryptography?

Question

Programming

I’ve been working as a programmer for three years , I didn’t know mathematics, and even forgot, but then I was carried away by cryptography. During breaks, I began to engage in the implementation of PRNG (yeah, first of my bicycle, as soon as I finish, I will implement bbs, and then mt). That is, it is interesting not so much its practical application using ready-made tools as understanding and implementing existing algorithms, maybe creating new ones if there are enough brains. I would like to understand what you are doing, to see obvious holes and, if possible, avoid stupid mistakes that bring it all to naught.

Answer 1

Theory of algorithms
Theory of numbers
Probability theory (discrete).
Algebra

Answer 2

algolist.manual.ru/defence/intro.php
well, in general, cryptography is something on the border of science and art. After all, you need to protect the data so that they are not broken, but also so that they can then be decoded normally.