The other answers have given good info, but speaking to your supposed factoring algorithm in particular - most of the internet's public key cryptography still r

The other answers have given good info, but speaking to your supposed factoring algorithm in particular - most of the internet's public key cryptography still relies on factoring problems. Your algorithm would be enormously useful and dangerous. You would likely be able to break anything that reduces to the hidden subgroup problem using it, which means you'd be breaking both elliptic curve and non-elliptic curve systems.