it's all just arithmetic, in fact, sign, odd/even, special forms of multiplication and division, the way that they write about it makes it a lot more confusing than it actually is when you cut through that
i don't obfuscate my meaning, i simplify it, because that's how i remember these things
one of the things that i think would help a lot with teaching people how cryptography works is scaling it down - they should show how a 32 bit elliptic curve signature works, then you would grasp it much easier what happens at 256 bits