Came here to post a summary but you did a better job than I could.
> A few companies/research groups are working on bridging
> the gap between the extremes (unencrypted/fully
> homomorphic encryption) in order to come up with a good
> compromise between security and cost.
I just wanted to add that plain text vs homomorphic encryption is indeed a security and cost trade-off.
Fully vs partially homomorphic encryption is a trade-off between supported operations and cost. Fully homomorphic systems allow arbitrary computations while partially homomorphic systems do not, hence the lack of support for standard SQL.
Fully vs partially homomorphic encryption is a trade-off between supported operations and cost. Fully homomorphic systems allow arbitrary computations while partially homomorphic systems do not, hence the lack of support for standard SQL.