Qubit-string-based bit commitment protocols with physical security

AbstractSeveral kinds ofqubit-string-based(QS-based) bitcommitment protocolshavebeen presented in this paper. We show that for QS-based protocols the sizeof unitary matrix U A suggested by no-go theorem is so large that the numberof entries of U A is about 2 100 × 2 100 as the length of n-qubit string used inour protocols is 100. This number is greater than the number of atoms ofthe earth, so the matrix U A can never be get by human beings actually. Wesuggest this kind of security the ”physical security”. Then we arrive at a con-clusion that the QS-based bit commitment protocol can realize informationtheoretically secure concealing and physically secure binding simultaneously.Finally, a practical QS-based scheme against channel loss and error is pre-sented.1. IntroductionResearch on quantum cryptography may be traced back to about 40 yearsago. Soon after Wiesner’s work published [1], Bennett and Brassard proposedtwo quantum cryptographical protocols in their original paper [2]: quantumkey distribution (QKD) and quantum coin tossing. Though QKD has beenproved unconditionally secure [3, 4, 5, 6, 7, 8, 9] and applied in practice,the quantum bit commitment (QBC) developed from quantum coin tossinghas been proved impossible [12, 13]. A generally accepted QBC scheme waspresented by Brassard, Crepeau, Jozsa and Langlois in 1993 [10], but itsunconditional security was shown to be impossible in 1996 [11]. Later, theidea in [11] was developed by Mayers [12] and Lo-Chau [13] independentlyand resulted in no-gotheorem ofQBC. It is shown thatany kind of interactiveprotocol of QBC is also impossible [14].