# 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 sender$S$sends a bit$b$into the OT machine.
- The machine then flips a coin, and with probability$\frac{1}{2}$sends$b$to the receiver$R$, and with probability$\frac{1}{2}$sends
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to$R$to signify that a bit was sent, but the information was lost in the transfer. - The result is,$R$received either$b$or
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but S does not know which output$R$received.

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:

- $S$sends an ordered pair of bits$(b_0, b_1)$into the 1-2-OT machine.
- $R$then gives the machine a bit$i$, indicating which input he would like to receive.
- The machine outputs the selected bit$b_i$and discards the other bit$b_{1-i}$.
- $S$knows that$R$has 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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