CN105245332B - Two side's quantum key agreement protocols based on four particle χ states - Google Patents
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Abstract
The invention discloses a kind of two side's quantum key agreement protocols based on four particle χ states：Step 1：Alice and Bob consults the coding of quantum state；Step 2：Alice prepares n χ state | χ00>ABCDAnd all particles are divided into four orderly sequences, select 2m and inveigle photon insetion sequence to be sent to Bob；Step 3：Bob is gone to measure corresponding trick photon with correct measurement base, and measurement result is informed into Alice；Alice compares measurement result and inveigles the original state of photon, calculates error rate；Step 4 is performed if error rate is low, otherwise performs step 2；Step 4：Alice performs Bell measurements to particle, and Bob performs to sequence
Description
Technical Field
The invention belongs to the field of Quantum communication, and particularly relates to a Quantum key agreement (Quantum key agreement) protocol, in particular to a two-party Quantum key agreement protocol based on a four-particle x state.
Background
Quantum cryptography is a new technology for communication and network security, and the security of the quantum cryptography is ensured by the basic principle of quantum mechanics. Unlike traditional cryptography, which is mostly computational security, quantum cryptography enables unconditional security, thereby attracting much attention. The Quantum Key Agreement (QKA) protocol is a new important branch of quantum cryptography that allows participants to agree on a classical shared secret key over a public quantum channel, and the contributions of the participants are the same, and any one participant or a subset of participants cannot independently determine the shared key. By using a shared secret key established by a Quantum Key Agreement (QKA) protocol and an encryption algorithm of a one-time pad, two communication parties can realize unconditional and safe secret communication.
Most of the existing quantum key agreement protocols are based on single particle or Bell state, quantum key agreement yield numbers based on multi-particle entangled state, and they either can not resist external attacks such as Trojan horse and the like, are unsafe or have too low quantum bit rate.
D.S. Shen, W.P.Ma and L.L.Wang, in the paper "Two-party Quantum key arrangement with four-Quantum cluster states" (Quantum inf.Process.2014: 2313-2324), proposed a Two-party QKA protocol with higher Quantum bit efficiency. The protocol comprises the following specific steps: first, both parties a and B each generate some four-particle cluster states. The correspondent a (correspondent B) inserts the sequence consisting of the third (first) particle in the cluster state into the decoy photon and sends it to the correspondent B (correspondent a), and retains and its particle sequence. Secondly, after both communication parties receive the corresponding particle sequences, eavesdropping monitoring is carried out together. Thirdly, the two communication parties perform their unitary transformation on the received particle sequences. And then after inserting the decoy photons, sending the decoy photons to each other. Fourthly, after both communication parties receive the corresponding particle sequences, the interception monitoring is carried out together. Fifth, the correspondent a (correspondent B) performs a respective unitary transformation on the sequence constituted by the first (third) particles in the cluster state. Then both sides perform cluster-based measurements on their respective cluster states, and both sides will obtain the same measurement result. And obtaining the shared secret key according to the correspondence of the codes and the measurement results. The protocol has the following defects: since the protocol is a Ping-Pong protocol, i.e., the same particle is transmitted back and forth in the quantum channel, the protocol cannot resist Invisible Photonic Eavesdropping (IPE) trojan attacks and delayed photonic trojan attacks.
In the paper "Quantum key element against noise collection coherence" (int.j. The. Theor. Phys.2014: 2891-2901), the two-party QKA protocol capable of immunizing combined noise is proposed by w.huang, q.su, x.wu, y.b.li and y.sun using the DF state of four particles. The protocol comprises the following specific steps: first, correspondent a generates two random bit strings, one as the individual contribution string of the shared key and one as the control string of the selected measurement basis. Secondly, the communication party A prepares a sequence of DF state of four particles according to the personal contribution string and the control string of the selected measuring base, inserts the decoy photon and sends the decoy photon to the communication party B. Thirdly, after the communication party B receives the DF state sequence of four particles, the two parties jointly execute eavesdropping monitoring. If detected, correspondent B publishes his personal contribution string sharing the key. Fourth, the correspondent a can calculate the shared secret key of both parties from the personal contribution strings of itself and the correspondent B. Fifth, correspondent a discloses his control string that selects the measurement basis. With this control string, the correspondent B can measure all DF states, and from the measurement result, the personal contribution string of the correspondent a's shared key can be obtained. Therefore, the communication party B can also calculate the shared secret key of both parties. The protocol has the following defects: the qubit efficiency of this protocol is too low, and its qubit efficiency is only 10%.
Disclosure of Invention
In view of the above drawbacks and deficiencies of the prior art, an object of the present invention is to provide a quantum key agreement protocol based on GHZ state.
In order to realize the task, the invention adopts the following technical scheme to solve the problem:
a two-party quantum key agreement protocol based on a four-particle x state specifically comprises the following steps:
step 1: alice and Bob negotiate the following quantum state encodings;
step 2: alice prepares n χ states | χ 00 > ABCD And the n x states | x are combined 00 > ABCD All particles of (a) are divided into four ordered sequences:
S A ＝{A 1 ,A 2 ,…,A n }，S B ＝{B 1 ,B 2 ,…,B n }，
S C ＝{C 1 ,C 2 ,…,C n and S D ＝{D 1 ,D 2 ,…,D n }
Wherein the sequence S A ,S B ,S C ,S D Respectively formed by each x state | x 00 > ABCD The particles A, B, C and D; alice selects from the set { |0>,|1>,|+>,|->, randomly selecting 2m decoy photons, and randomly inserting the 2m decoy photons into the sequence S C And S D Ensuring that m decoy photons are inserted into each sequence to respectively obtain a new sequence S' C And S' D (ii) a Alice self-retaining sequence S A And S B Prepared from sequence S' C And S' D Sending the data to Bob; n and m are positive integers greater than 1;
and step 3: when Bob receives the sequence S' C And S' D Then, the information is informed to Alice through a classical authentication channel; alice publishes that the decoy photon is at sequence S' C And S' D Is associated with the corresponding measurement basis 0>,|1> + { | +>,|-> bob measures the corresponding decoy photons by using the correct measurement basis and informs the measurement result to Alice through a classical authentication channel; alice compares the measurement result with the initial state of the decoy photon, and calculates the error rate; if the error rate is lower than the predefined threshold value, executing step 4, otherwise, executing step 2;
and 4, step 4: alice pair sequence S A And S B Bell measurements are performed for every two particles with the same sequence number, and Bob performs on the sequence S C And S D Every two particles with the same middle sequence number executeBase measurement; and according to the measurement results of Alice and Bob and the quantum state codes negotiated by Alice and Bob in the step 1, obtaining the same shared secret key with 2n bits by Alice and Bob respectively.
Further, in step 1, the encoding of the quantum state negotiated by Alice and Bob: i phi + > AB →00， |ψ - > AB →01，|ψ + > AB →10，|φ - > AB →11，|00> CD →00，|01> CD →01，|10> CD →10， |11> CD →11。
Further, in the step 2,
further, in the step 3, the threshold value is 0.1 to 0.2.
The invention has the beneficial effects that:
the two-party quantum key agreement protocol based on the four-particle x state can ensure that two communication parties can establish shared classical secret keys between the two communication parties in a public way; by using the classic secret key and the one-time pad encryption algorithm, two communication parties can realize unconditional and safe secret communication, and obviously, the invention can resist the existing participant attack and external attack. Since each particle in the protocol of the present invention is transmitted only once, an attacker also cannot successfully perform a trojan horse attack. The protocol was found by analysis to be secure not only on noiseless quantum channels, but it is also secure on quantum noise channels. In addition, the quantum bit efficiency of the protocol of the invention is higher than that of the existing safe quantum key agreement protocol based on the multi-particle entangled state.
Detailed Description
1. Preliminary knowledge
It is well known that { |0>,|1> forms Z base, { | +>,|-> forms an X group, wherein The four Bell states are defined as follows:
they form a set of completely orthogonal bases of four-dimensional Hilbert space, the Bell bases. The χ states are the most entangled states of the four particles, which form a set of completely orthogonal bases of 16-dimensional Hilbert space. In the protocol of the present invention we use a χ state as the quantum source, i.e., as follows
According to the expression, if x state is x 00 > ABCD Performing Bell measurements on particles A and B, and performing Bell measurements on particles C and DBased on the measurements, the system collapses to the state | φ with a probability of 1/4 + > AB |00> CD ，|ψ - > AB |01> CD ，|ψ + > AB |10> CD And | phi - > AB |11> CD 。
2. The invention relates to a two-party quantum key agreement protocol based on four-particle x state
The invention relates to a two-party quantum key agreement protocol based on a four-particle x state, which specifically comprises the following steps:
step 1: alice and Bob negotiate the encoding of the following quantum states: i phi + > AB →00，|ψ - > AB →01， |ψ + > AB →10，|φ - > AB →11，|00> CD →00，|01> CD →01，|10> CD →10，|11> CD →11。
And 2, step: alice prepares n χ states | χ 00 > ABCD And the n x states | x are combined 00 > ABCD All particles of (a) are divided into four ordered sequences:
S A ＝{A 1 ,A 2 ,…,A n }，S B ＝{B 1 ,B 2 ,…,B n }，
S C ＝{C 1 ,C 2 ,…,C n and S D ＝{D 1 ,D 2 ,…,D n }
Wherein the sequence S A ,S B ,S C ,S D Respectively formed by each x state | x 00 > ABCD The particles A, B, C and D; alice selects from the set { |0>,|1>,|+>,|->, randomly selecting 2m decoy photons, and randomly inserting the 2m decoy photons into the sequence S C And S D And ensuring that each sequence is just inserted with m decoy photons to respectively obtain a new sequence S' C And S' D (ii) a Alice self-retaining sequence S A And S B Prepared from sequence S' C And S' D Sending the data to Bob; n and m are positive integers greater than 1;
and step 3: when Bob received sequence S' C And S' D Then, the information is informed to Alice through a classical authentication channel; alice publishes that the decoy photon is at sequence S' C And S' D Is associated with the corresponding measurement basis 0>,|1> + { | +>,|-> bob measures the corresponding decoy photons by using the correct measurement basis and informs the measurement result to Alice through a classical authentication channel; alice compares the measurement result with the initial state of the decoy photon, and calculates the error rate; if the error rate is lower than the preset threshold value, executing the step 4, otherwise, executing the step 2; the threshold value is 0.1-0.2.
And 4, step 4: alice pair sequence S A And S B Bell measurements are performed for every two particles with the same sequence number, and Bob performs on the sequence S C And S D Every two particles with the same middle sequence number executeBase measurement; according to the measurement results of Alice and Bob and the amount negotiated by Alice and Bob in step 1Encoding of the sub-states, alice and Bob get the same shared secret key of 2n bits, respectively.
According toIt can be seen that the X state | X 00 > ABCD Performing Bell measurements on particles A and B, and performing Bell measurements on particles C and DBased on the measurements, the system collapses to the state | φ with a probability of 1/4 + > AB |00> CD ，|ψ - > AB |01> CD ，|ψ + > AB |10> CD And | phi - > AB |11> CD . Therefore, alice and Bob can get the same 2 n-bit shared key.
4 safety and efficiency analysis
A secure QKA protocol is not only resistant to external attacks, but also to participant attacks.
4.1 participant attack
We will now show that a dishonest participant cannot get this shared key alone. Without loss of generality, assuming that Alice is a dishonest participant, she wants the 2l bits in the shared secret to all be 0S, and she needs to use Bell-based measurement sequence S A And S B The corresponding pair of particles in (1). However, the measurement of each pair of particles is randomly | φ, depending on the nature of the quantum entangled state + > AB ，|ψ - > AB ，|ψ + > AB And | phi - > AB I.e., alice gets 00, 01, 10, or 11 with a 25% probability. Thus, every 2 bits of the 2l bits are randomly 00, 01, 10, or 11. Therefore, alice cannot decide independentlyAny one bit in the shared key. Therefore, the protocol is resistant to participant attacks.
4.2 external attacks
Assuming that Eve is an eavesdropper who wants to steal the shared key, there are possible ways she could attack: trojan horse attacks, measurement-replay attacks, interception-replay attacks, and entanglement-measurement attacks.
Trojan horse attack: in the present protocol, eve cannot successfully perform an Invisible Photonic Eavesdropping (IPE) trojan attack and a delayed photonic trojan attack because each photon in the quantum channel is transmitted only once.
Measurement-retransmission attack: eve can be on sequence S' C And S' D The particle in (a) performs a measurement-retransmission attack. However, the measurement of Eve will affect the sequence S' C And S' D The state of the decoy particles. In the second eavesdropping test, alice and Bob can detect the eavesdropping by 1- (3/4) m (m represents the number of decoy particles used to detect this attack) the Eve's attack was discovered.
Interception-retransmission attack: if Eve performs an intercept-retransmit attack, she first intercepts the sequence S' C And S' D And then send her forged sequence to Bob. When the agreement is over, she again matches sequence S' C And S' D The particles in (a) perform the corresponding measurements. However, eve does not know the position and initial state of the decoy particles, so her forged sequence cannot be monitored by eavesdropping in the second step. When m decoy particles are used to monitor this eavesdropping attack, the corresponding eavesdropping detection rate is 1- (1/2) m . Thus, the intercept-retransmit attack of Eve also fails.
Entanglement-measurement attack: eve can also de-entangle this transport particle (sequence S ') with its pre-prepared auxiliary particle' C And S' D Particles in) and then resends the transmitted particles to Bob. When the protocol is over, she measures the corresponding helper particles again, thereby extracting useful information about the shared key. However, eve does not know the location of the decoy photon before eavesdropping detection, and her entanglement operation U must also be performed on the decoy photon. And the decoy state becomes as followsTwo particle entangled states of:
U(|0>|E>)＝a|0>|e 00 >+b|1>|e 01 >，
U(|1>|E>)＝c|0>|e 10 >+d|1>|e 11 >，
wherein | e 00 >，|e 01 >，|e 10 >, & | e 11 >, is a pure state uniquely determined by the unitary transformation U, and | a; & gtis non-linear 2 +|b| 2 ＝1， |c| 2 +|d| 2 And =1. Obviously, the CNOT transform is a special case of unitary transform U. If Eve wants to detect by eavesdropping in the second step, eve's unitary transformation U must satisfy the conditions b = c =0 and a | e 00 >＝d|e 11 &And (d) drying the steel. When equationWhen true, eve cannot distinguish the auxiliary photon a | e 00 >, and d | e 11 >, so that Eve cannot obtain useful information of the shared key by observing the auxiliary photons. However, if a | e 00 >≠d|e 11 &The attack of Eve will interfere with the decoy state | +> | -&And (d) drying the steel. Thus, eve's attack will be discovered by Alice and Bob. The eavesdropping detection rate of each decoy photon is:
4.3 Quantum noise channel
In quantum noise channels, the Quantum Bit Error Rate (QBER) τ introduced by the noise ranges approximately from 2% to 8.9%, depending on the channel conditions such as distance. If Eve's attack introduces a qubit error rate less than τ, she can hide her attack behavior with noise. According to the security analysis described above, the eavesdropping detection rate of each decoy photon in this protocol is at least 25%, which is much greater than τ. Therefore, choosing the appropriate eavesdropping detection threshold ensures that the protocol is also secure over quantum noise channels.
According to the above analysis, this protocol is secure over both noiseless quantum channels and quantum noise channels.
5 efficiency analysis
For a QKA protocol, the Cabello qubit efficiency is defined as:where c represents the number of classical bits negotiated and q represents the number of qubits used in the protocol. Thus, the qubit efficiency of our protocol is:wherein n represents the χ state | χ in the protocol 00 > ABCD M represents the number of decoy particles. Let m = n, we have
Claims (2)
1. A two-party quantum key negotiation method based on a four-particle x state is characterized by comprising the following steps:
step 1: alice and Bob negotiate the encoding of the following quantum states: i phi + > AB →00，|ψ - > AB →01，|ψ + > AB →10，|φ - > AB →11，|00> CD →00，|01> CD →01，|10> CD →10，|11> CD →11；
And 2, step: alice prepares n x states | x 00 > ABCD And the n x states | x |, are processed 00 > ABCD All particles of (a) are divided into four ordered sequences:
S A ＝{A 1 ,A 2 ,…,A n }，S B ＝{B 1 ,B 2 ,…,B n }，
S C ＝{C 1 ,C 2 ,…,C n and S D ＝{D 1 ,D 2 ,…,D n }
Wherein the sequence S A ,S B ,S C ,S D Respectively formed by each x state | x 00 > ABCD The particles A, B, C and D; alice selects from the set { |0>,|1>,|+>,|-> } randomly selects 2m decoy photons, and randomly inserts the 2m decoy photons into the sequence S C And S D Ensuring that m decoy photons are inserted into each sequence to respectively obtain a new sequence S' C And S' D (ii) a Alice self-retaining sequence S A And S B Prepared from sequence S' C And S' D Sending the data to Bob; n and m are positive integers greater than 1;
and step 3: when Bob received sequence S' C And S' D Then, the information is informed to Alice through a classical authentication channel; alice publishes that the decoy photon is at sequence S' C And S' D With the corresponding measurement basis 0>,|1> + { | +>,|-> }; bob measures the corresponding decoy photons by using the correct measurement basis and informs the measurement result to Alice through a classical authentication channel; alice compares the measurement result with the initial state of the decoy photon, and calculates the error rate; if the error rate is lower than the predefined threshold value, executing step 4, otherwise, executing step 2;
and 4, step 4: alice pair sequence S A And S B Every two of the same medium serial numbersBell measurements are performed for each particle, while Bob performs measurements on the sequence S C And S D Every two particles with the same middle sequence number executeBase measurement; according to the measurement results of Alice and Bob and the quantum state codes negotiated by Alice and Bob in the step 1, alice and Bob respectively obtain the same shared secret key with 2n bits;
2. the method of claim 1, wherein in step 3, the threshold value is 0.1-0.2.
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