1-out-of-2 oblivious transfer using a flawed bit-string quantum protocol

Oblivious transfer (OT) is an important tool in cryptography. It serves as a subroutine to other complex procedures of both theoretical and practical significance. A common attribute of OT protocols is that one party (Alice) has to send a message to another party (Bob) and has to stay oblivious to whether Bob did receive the message. Specific (OT) protocols vary by exact definition of the task—in the all-or-nothing protocol, Alice sends a single bit-string message, which Bob is able to read with only 50% probability, whereas in a 1-out-of-2 OT protocol Bob reads one out of two messages sent by Alice. These two flavors of protocol are known to be equivalent. Recently, a computationally secure all-or-nothing OT protocol based on quantum states was developed by A. Souto et al. [Phys. Rev. A91,042306(2015)], which, however, cannot be reduced to a 1-out-of-2 OT protocol by standard means. Here we present an elaborate reduction of this protocol that retains the security of the original.