Encrypted search?

[Tyler Durden]

Got a crypto question here.

Let's say I push out a list I'd like to keep secret to some client machine. 
The user of that machine must enter some ID or other piece of information. I 
want the client machine to perform a search of that ID vs the contents of a 
list (again, resident locally on that machine), but I don't want the user to 
be able to see the other entries of that list.

Possible? Remember, after the initial push of data out to the client 
machine, no more messages are exchanged. This means the list must be sent in 
encrypted form.

When the search is performed, the "stupid" thing to do (I think...someone 
correct me) is to take the user's ID, encrypt it, and then determine if 
matches an encypted member of the list (and I don't see encrypted each entry 
individually as a desirable thing). I am assuming that this allows a savvy 
user to reverse-engineer the encryption.

Another option is one I don't have the background at this stage to 
understand. Let's assume the entire list has been encrypted in one shot. Is 
there some function such that when this encrypted list is convolved with the 
user ID a "Yes" or "no" can be obtained (indicating presence or absence from 
the list)?

If the answer is yes, I'd also like to know if knowing this is farily basic 
to most encryption professionals sphere of knowledge...

-TD

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