A fun project would be: factor Mersenne numbers! Naive trial division -> optimize your code by only trying valid candidates (you’ll learn about quadratic residues, Jacobi symbol etc.) -> You’ll soon realize that trial division only goes so far, motivated to learn new approaches. The P−1 method may impress you, it’s powerful. Enjoy coding that. -> But then, you’ll be frustrated by even stronger opponents here and there beyond M100, which the P−1 method can’t factor. Now you’ll be so ready, even determined, to learn ECM. At this point, you’ll find using elliptic curves is actually not so difficult, because it’s just like P−1. And yay, 20- or 30- digit numbers are no longer your enemies, they’re just small fish, elliptic curves rule!
Before you know it, you’ll have a clear, intuitive vision about “an elliptic curve over a finite field”. Try to understand why ECM works. Try to count the number of points. Everything you experience with ECM is related to ECC too.
I’m not that good; know enough to know that I don’t really know much. Just a hobbyist; posted ℍappy ℍamilton Day! here.
The scary part is, that the US can do something like this if it wants to. A service provider saying “We’re privacy-friendly. Your email address is all we ask.” could end up this way. Think about so-called bullet-proof hosting providers or so-called trusted no-long VPN providers.
The only safe way, if any, may be that you never show them your IP… (much less any identifying information)