Now we know you need both private and public key, but you haven't clarify what kind of range you're talking about. Are you talking about range of private key or range of public key?
OP, you need to have a shorter range of private keys that you want the associated public keys to. You may also want to choose a different dissertation topic.
okay well how about a smaller more applicable range then.. its not written in stone... lol .
There are approximately 2^160 possible bitcoin addresses. There are an estimated approximately 2^63 grains of sand on Earth.
The relationship between a private key and a public key is not linear, if you want an explanation regarding the relationship between private keys and public keys, you can watch the video at the bottom of this webpage.
I can also assure you that a lot of resources has been devoted into trying to find a way to calculate a private key based on a public key, not only for ecdsa but other encryption methods as well.