Research On Some Issues Of Quantum Secure Communication

Quantum secure communication is a cross-subject which basessecure communication on the quantum mechanics law. It is a verysignificant issue. The research of classical algorithms and quantumalgorithms for solving hard problems brings great threat to the classicalsecure communication based on complex mathematic computation. Withthe development of classical computer and the experimental progress ofquantum computer, the difficulty for breaking a mathematic cryptosystemhas been reducing continually. Some of mathematic cryptosystems, such asRSA public key cryptosystem and E1Gamal public key cryptosystem, facegreat threat because they can be broken by quantum computer inpolynomial time. Quantum no-cloning theorem, Heisenberg uncertaintyprinciple and quantum entanglement guarantee that quantum keydistribution has the unconditional security and the ability of detectingeavesdropper, which makes quantum secure communication possess theexcellent capacity and the attractive foreground. Some research objects ofquantum secure communication are the problems posed by classical securecommunication, such as quantum key distribution, quantum identityverification, quantum secret sharing and quantum signature. The security ofcommunication is based on the law of physics instead of the hard problem.The other research objects, such as quantum teleportation and quantumdirect secure communication, have no classical counterpart.The contributions of this thesis are mainly on secure multipartyquantum summation, entanglement split and entanglement combination,threshold quantum cryptograph and probabilistic teleportation. Mainachievements in this dissertation are summarized as follows:1. Implicit addition module n+1 is proposed (n≥2). An augend is encoded on non-orthogonal quantum states. Addition operation ispermutation acting on the non-orthogonal quantum states. Securityoperation is basis transformation changing one of two non-orthogonalquantum states into the other. When a parter adds the addend to the augendreceived, he need not and can not measure the augend precisely. Only withagreements of all the parters, the addition result can be measured precisely.There is no classical counterpart of implicit addition.2. A protocol for secure n-parities quantum summation is presentedbased on implicit addition module n +1. A patter splits his addend into twoshares. In control mode, one by one, each patter detects eavesdropper, andencodes one share on the quantum carriers using implicit addition modulen+1. In message mode, one by one, each parter encodes the other share onthe quantum carriers. After all the shares have been added, the summationcan be measured. We prove that the protocol is quasisecure to Eve outside.The higher control mode rate is; the less eavesdropping information contentis. Especially, when control mode rate tends to 1, eavesdroppinginformation content tends to 0. We also prove that the collusion attack byn-1 legitimate patters inside cannot eavesdrop all the input information ofthe remainder in the protocol if n-1 parters do not leak their all the inputs.3. Using implicit addition module 4, we proposed (n,t) thresholdquantum banknote protocol. The number of qubits of the generatedquantum state by the threshold protocol does not exceed that of thequantum state generated by the original (nonthreshold) protocol. In issuingphase and checking phase, each parter encodes his share on the quantumcarriers by implicit addition module 4. 3 bits information is encoded on onenon-orthogonal two-qubit system. We strictly prove that when dishonestparters take the privilege of preparing fake quantum state to attack anotherpatter, they can only extract 2 bits from the 3 bits information while theyhave to introduce error probability 3/8.4. A quantum circuit to detect the quantum Trojan horse attack isdesigned. In order to detect whether a legitimate qubit is replaced by amulti-qubit string, we input one auxiliary qubit and one qubit (or one qubitstring) received into the circuit, and then measure the auxiliary qubit. For a multi-qubit string instead of a legitimate single qubit, the auxiliary qubitClips with probability1/2. The detection scheme makes every legitimatequbit and auxiliary qubit invariant. We can detect quantum Trojan horseattack according as whether the auxiliary qubit flips or not.5. The technology of quantum entanglement split and entanglementconbination is presented. In the quantum secret sharing based on reusableGHZ states to act as quantum key, by entanglement split, the legitimatecheater, called Bob, can split GHZ state shared by Alice, Bob, and Charlie(?) two EPR states: One is shared by Alice and Bob, and the other issha(?)d by Bob and Charlie. Bob can use the entanglement split tointercept-resend all secret bits, while introducing one data bit error at mostin the whole communication. In the quantum key distribution based onreusable EPR states to act as quantum key, by entanglement split, theeavesdropper Eve can split EPR state shared by Alice and Bob into twoEPR states: One is shared by Alice and Eve, and the other is shared by Boband Eve. Eve can use the entanglement split to intercept-resend all sharedkey bits, while introducing no error in the whole communication. Byentanglement combination, Eve can combine EPR state shared by Aliceand Eve and EPR state shared by Bob and Eve into one EPR state sharedhy Alice and Bob.6. A bidirectional protocol of probabilistic teleportation on theclients/server model is proposed, which leads to the maximal probability ofsuccessful teleportation. We find the character of partially entangledquantum channel transparent to clients in probabilistic teleportation. Toperform probabilistic teleportation via the generally entangled quantumchannel, the clients must know a unitary operator which can transforms thequantum channel into the clients' transparent quantum channel.