# Oblivious Transfer (OT)

## What is 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.

## Rabin OT

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
$b$
$R$
, and with probability
$\frac{1}{2}$
sends # to
$R$
to signify that a bit was sent, but the information was lost in the transfer.
• The result is,
$R$
$b$
or # but S does not know which output
$R$
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

## 1-2 OT

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
$b_i$
$b_{1-i}$
.
• $S$
knows that
$R$
has one of the bits, but not which one. 1-2 OT

## Rabin OT == 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.