Re: Not knowing how it works
For example, take AES-128-GCM if you implement that cypher mode, you will need to do multiple precision integer arithmetic. This library does it with elliptic curves https://github.com/miracl/MIRACL
Methinks you have misunderstood something, somewhere. Galois Counter Mode has nothing to do with elliptic curves, though it's true that the MIRACL library implements both. Elliptic Curve Cryptography requires floating-point calculations, but GCM does not.