[omazurov]

Galois (finite) fields are very much relevant in error correction codes and cryptography. Any time you want to manipulate bytes (or words) as numbers which you can add/subtract and multiply/divide you end up learning about finite fields. In fact, doing CRC or even XOR sums you are already making the first step towards the topic.

A recent problem I needed a solution for: given n blocks of data of equal length generate all possible XOR sums of the blocks in-place (no additional memory). The answer is an irreducible polynomial of degree n with a primitive root over GF(2).

[diminoten]

Most people aren't building crypto, though (at least they really shouldn't be).

And maybe the answer found the problem you're describing, not the other way around. You were taught to look for and solve problems a certain way, so problems appear with those characteristics.