It turns out that what I was attempting to do was create a form of ECDSA threshold signature protocol by just giving away multiple public keys and then having the two parties solve for the private.
I am currently working on building an application and I have a question about the triviality of deriving private keys from multiple public keys. I have read many places that it is possible to derive multiple public keys from a single private key but that publicly revealing more than one will jeopardize the private keys security. If I want to produce two public keys from a single private key (ECDSA) and derive the private key later using only the public keys, how much does knowing the two public keys help. Will two public keys easily yield a single private key? Will introducing more than two public keys reduce the amount of computation that it takes to derive a private key if it is computational difficult?