Oblivious Transfer (OT)
In cryptography, an Oblivious Transfer (OT) protocol is a type of protocol in which a sender transfers one of potentially many pieces of information to a receiver, but remains oblivious as to what piece (if any) has been transferred.
The first form of oblivious transfer was introduced in 1981 by Michael O. Rabin. Rabin oblivious transfer is a kind of formalization of "noisy wire" communication. The objective is to simulate a random loss of information. Formally, a Rabin OT machine models the following behavior:
- The sendersends a bitinto the OT machine.
- The machine then flips a coin, and with probabilitysendsto the receiver, and with probabilitysends
#toto signify that a bit was sent, but the information was lost in the transfer. - The result is,received eitheror
#but S does not know which outputreceived.
Note that this may be simulated by a sufficiently noisy wire, provided that the wire transmits faithfully a good proportion of bits and at the same time loses a good proportion of bits, replacing them with noise that is distinguishable from information.
Rabin Oblivious Transfer
Even, Goldreich and Lempel formulated a notion of oblivious transfer that has proven useful in various applications. In this situation:
- sends an ordered pair of bitsinto the 1-2-OT machine.
- then gives the machine a bit, indicating which input he would like to receive.
- The machine outputs the selected bitand discards the other bit.
- knows thathas one of the bits, but not which one.
1-2 OT
Theoretically, Rabin OT and 1-2 OT are equivalently. That is, given a black-box Rabin OT we can implement 1-2 OT, and vice versa.
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