Quantum oblivious mutual identification

Abstract

We consider a situation where two parties, Alice and Bob, share a common secret string and would like to mutually check their knowledge of that string. We describe a simple and efficient protocol based on the exchange of quantum information to check mutual knowl­edge of a common string in such a way that honest parties will always succeed in convincing each other, while a dishonest party interacting with an honest party will have vanishingly small probability of convinc­ing him. Moreover, a dishonest party gains only a very small amount of information about the secret string from running the protocol: whoever enters the protocol with no knowledge of the secret string would have to enter this protocol an exponential number of times in order to gain non-negligible information about the string. Our scheme offers an efficient identification technique with a security that depends on no computational assumption, only on the correctness of quantum mechanics. We believe such a system should be used in smart- cards to avoid frauds from typing PIN codes to dishonest teller machines.