| The bit commitment primitive is a key ingredient in two party cryptography where both participants want to compute a public function of their private inputs. Since the discovery of the impossibility theorem stating that unconditionally secure quantum bit commitment cannot exists, quantum cryptography in the two party case must rely on assumptions. We are considering quantum computational assumptions. Those assumptions have to be different from their classical cousins since factoring large integers, a computational assumption widely in use nowadays, is under attack by a quantum algorithm.; We are interested in the possibility of basing the bit commitment and oblivious transfer cryptographic primitives on quantum computational assumptions. We show that those two primitives can be constructed if we assume that quantum one-way permutations exist. In the case of oblivious transfer, the security proof is incomplete. |
