Perform math on encrypted data without ever decrypting it

It's been interesting to watch this story roll downhill.

It started out as "fully homomorphic encryption using ideal lattices." http://portal.acm.org/citation.cfm?id=1536414.1536440

Then it got covered by the tech press: "Do calculations on encrypted data."

http://www.ddj.com/security/218101417

And is now in Forbes and probably other publications for highbrow laypeople: "IBM's Blindfolded Calculator."

This process has been talked about elsewhere:

http://www.phdcomics.com/comics/archive.php?comicid=1174

Not practical technology yet, note the "multiply the necessary computing time by around 1 trillion" part of the article.

Discussed on HN already, here:

http://news.ycombinator.com/item?id=657859

And here:

http://news.ycombinator.com/item?id=678975

I don't know anything about this area at all, but I remember in a cryptography lecture, being told you can perform arithmetic on un-padded standard RSA, is this similar to that. I imagine this could be very useful for banks possibly in databases, to for instance increase and decrease peoples funds, without standard employees seeing the total ammount of money in the account.

One should be able to do something similar with analysis of images. You can’t scramble them though...