Oblivious transfer protocol to retrieve k elements

A_guest

11/2/23, 9:55 AM

The sever holds the N encrypted elements, each element is associated with an index (unencrypted). The receiver wants to retrieve only k-out-N elements using k-out-N OT. The motivation for using OT is to retrieve only k elements, not all N elements, retrieving N elements results in storage overhead on the device (receiver) and another motivation is that the server should not learn which elements have been retrieved.

As the elements are encrypted so the receiver does not hold the private key, the receiver performs operations on encrypted data (element) using homomorphic encryption. We can utilize PIR by retrieving N elements at the beginning of the session, then the server cannot learn which elements have been retrieved, but, the problem of storage overhead still remains we do not want to retrieve all N elements.

It feels difficult to understand that whether OT solves this problem? My question is that using OT the server (sender) still sends all N elements and the receiver can only decrypt what he asks for?

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oblivious-transfer

protocol-design

pir

poncho

11/2/23, 1:12 PM

Is the limitation you have the amount of storage the receiver can store, or the amount of data that the server can send to the receiver?

JAAAY

11/2/23, 1:14 PM

If you are worried about storage on the client side and client has only enough space for k elements, the client of course parse the received messages sequentially discarding every message that doesn't fit to its selection. Of course if you want to process those k elements in combination you need storage for all of them otherwise (for example if you want to do homomorphic addition or multiplication) there are ways that you only need space for less than k (I guess probably only two) elements for example. But all of this is really theoretical and it may differ in practice.

A_guest

11/2/23, 2:09 PM

@poncho, @JAAAY; the reason for using OT is to retrieve only k elements, as each element is already encrypted so we don't need to worry about the malicious user. But, if the sends everything in response to k elements, then PIR looks more efficient than OT, especially in this case. ?

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EN: Oblivious transfer protocol to retrieve k elements

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