Actually homomorphic encryption is currently based on a problem about ideal lattices which is very different than factoring. The same complaint applies—we don’t really know if the problem is hard, just that we haven’t been able to solve it.
The cryptographic operation I am describing is sufficiently limited (since you control the code of the adversary) that it is plausible that we will develop unconditional proof techniques, however, long before proving P != NP. I think it would be interesting to develop such techniques, and quarantining code may turn out to be useful.
Actually homomorphic encryption is currently based on a problem about ideal lattices which is very different than factoring. The same complaint applies—we don’t really know if the problem is hard, just that we haven’t been able to solve it.
The cryptographic operation I am describing is sufficiently limited (since you control the code of the adversary) that it is plausible that we will develop unconditional proof techniques, however, long before proving P != NP. I think it would be interesting to develop such techniques, and quarantining code may turn out to be useful.