Seems like if you really cared for the contents of a textarea, for instance, you could tokenize the text client side and encrypt each token with the client side private key then you could similarly encrypt the search tokens client side and search serverside not knowing what you were searching for.

However, I take your point. Lots of work, not quite the same. It still seems like the facility should be baked in though so that application's could make the proper tradeoffs.

Products like CipherCloud reportedly work like you suggest. Unfortunately it's not very secure.

If you split the text into words, discard case and encrypt each word, the NSA can just e-mail you a dictionary file, match the line numbers in the dictionary file ciphertext to line numbers in the dictionary file plaintext, and they've got your secret decoder ring (at least for every word in the dictionary file).

Seems super vulnerable to frequency analysis though. However, if this is a path you might want to go down, you might want to look at CryptDB, a research project that looks at keeping a server side encrypted database and allows for queries in a principled way: http://css.csail.mit.edu/cryptdb/

This is where we really need fully homomorphic encryption!

Something like text search should only need partially-homomorphic encryption. For example: encrypt each byte with the same key. Then to search, encrypt the bytes of your search term and send them to the backend. It should be able to find them without knowing what your search term was. There are issues with this exact scheme of course but you get the idea!

There is some research in this area, e.g. http://www.cs.berkeley.edu/~dawnsong/papers/se.pdf