Quantum Oblivious Transfer and Bit Commitment through a Trusted Initializer

Abstract:
Secure function computation is a network primitive allowing a client to calculate function values on data which is being held private by another client on the same network without disclosing sensitive information. It can be realized through cryptographic primitives such as Bit Commitment and Oblivious Transfer. Unconditionally secure Bit Commitment and Oblivious Transfer are provably impossible, both in the classical and quantum communication framework. Due to their connections with relevant functionalities, cryptographers have sought assumptions to circumvent the impossibility results. In this work, we show that quantum Bit Commitment and Oblivious Transfer can be implemented with information-theoretic security if a quantum trusted initializer is available. Our results stem from those of Rivest, who proposed similar classical protocols. We further show that if the initializer is corrupted after the setup phase and collaborates with one of the parties, the protocols remains secure for the other one.