CN105490804A - Two-party quantum key negotiation protocol based on three-particle GHZ state - Google Patents

Abstract

The present invention discloses a two-party quantum key negotiation protocol based on a three-particle GHZ state, comprising the following steps: step 1: Alice and Bob negotiate codes of quantum states; step 2: Alice prepares n+q GHZ states and divides all the particles into sequences; Alice sends a sequence SC to Bob; step 3: Bob selects and measures q sample particle(s); Alice selects measurement bases to measure corresponding particles; Bob calculates an error rate; and if the error rate is low, step 4 is performed, otherwise step 2 is performed; step 4: Alice performs a Bell measurement on two particles with the same sequence number in the sequences; Bob performs X-base measurement on the particles in the sequences; and Alice and Bob respectively obtain the same shared key according to measurement results and the codes of the quantum states. According to the present invention, the two-party quantum key negotiation protocol can resist existing participant attacks and external attacks as well as Trojan horse attacks, is safe in noiseless quantum channels and quantum noise channels, and can achieve a relatively high quantum bit efficiency.

Description

Based on two side's quantum key agreement protocols of three ions

Technical field

The invention belongs to quantum communications field, be specifically related to a kind of quantum key and consult (Quantumkeyagreement) agreement, particularly a kind of two side's quantum key agreement protocols based on three ions.

Background technology

Quantum cryptography is the new technology of communication and network security, and its fail safe is ensured by fundamental principles of quantum mechanics.Be the different of computationally secure mostly from conventional cipher, quantum cryptography can realize unconditional security, has attracted a large amount of concern thus.It is the new important branch of of quantum cryptography that quantum key consults (QKA) agreement, it allows participant to consult a classical shared secret key by disclosed quantum channel, and the contribution of each participant is identical, the subset that any one participant or participant are formed all can not independently determine this shared key.Utilization sub-key consults the shared secret key of (QKA) agreement foundation and the cryptographic algorithm of one-time pad, and communicating pair can realize the secure communication of unconditional security.

Existing most of quantum key agreement protocol is based on single-particle or Bell state, based on multiparticle Entangled State quantum key agreement can be counted on one's fingers, and they or the external attacks such as Te Luoyi wooden horse can not be resisted, be unsafe, or quantum bit rate is too low.

D.S.Shen, W.P.MaandL.L.Wang utilizes the Cluster State of four particles to propose a both sides QKA agreement in paper " Two-partyquantumkeyagreementwithfour-qubitclusterstates " (QuantumInf.Process.2014:2313-2324), and this agreement has the sub-bit efficiency of higher amount.The concrete steps of agreement are: the first, the Cluster State of some four particles of each self-generating of communicating pair A and B.Communication party A (communication party B) issues communication party B (communication party A) by being inserted after trick photon by the sequence that (first) particle is formed of the 3rd in Cluster State, and retains and its particle sequence.The second, after communicating pair receives corresponding particle sequence, perform eavesdropping monitoring together.3rd, the unitary transformation of the particle sequence execution that communicating pair just receives separately oneself.Then insert after inveigling photon and it is issued the other side mutually.4th, after communicating pair receives corresponding particle sequence, perform eavesdropping monitoring together.5th, communication party A (communication party B) performs respective unitary transformation to by the sequence that (the 3rd) particle is formed of first in Cluster State.Then both sides perform the measurement of cluster base to respective Cluster State, and both sides can obtain identical measurement result.The privacy key shared can be obtained according to coding and the correspondence of measurement result.This agreement Shortcomings part is: because this agreement is a Ping-Pong agreement, namely same particle has been transmitted one back and forth in quantum channel, and therefore this agreement cannot be resisted invisible photon eavesdropping (IPE) Trojan attack and be postponed photon Trojan attack.

W.Huang, Q.Su, X.Wu, Y.B.LiandY.Sun utilize the DF state of four particles to propose the both sides QKA agreement of an energy immunity associating noise in paper " Quantumkeyagreementagainstcollectivedecoherence " (Int.J.Theor.Phys.2014:2891-2901).The concrete steps of agreement are: the first, and communication party A generates two random bit strings, and an individual as shared key contributes string, and one as selecting the control string measuring base.The second, communication party A contributes string and selection to measure the sequence of the DF state of control string preparation four particles of base according to individual, and issues communication party B after inserting trick photon.3rd, after communication party B receives the sequence of DF state of four particles, both sides perform eavesdropping monitoring jointly.If by detecting, the individual that communication party B announces his shared key contributes string.4th, communication party A contributes string according to oneself and the individual of communication party B, can calculate the shared secret key of both sides.The control string of base is measured in 5th, the communication party A selection disclosing him.Utilize this to control string, communication party B can measure all DF states, and the individual that can obtain the shared key of communication party A according to measurement result contributes string.Therefore, communication party B also can calculate the shared secret key of both sides.This agreement Shortcomings part is: the quantum bit efficiency of this agreement is too low, and its quantum bit efficiency is only 10%.

Summary of the invention

For the defect existed in above-mentioned prior art or deficiency, the object of the invention is to, a kind of two side's quantum key agreement protocols based on three ions are provided.

In order to realize above-mentioned task, the present invention adopts following technical scheme to be solved:

Based on two side's quantum key agreement protocols of three ions, specifically comprise the steps:

Step 1:Alice and Bob consults the coding of quantum state; | φ ⁺> _aB→ 0, | φ ^-> _aB→ 1, |+> _c→ 0, |-> _c→ 1;

Step 2:Alice prepares n+q GHZ state | η > _aBC, and all particles are divided into three orderly sequences:

S _a={ A ₁, A ₂..., A _n+q, S _b={ B ₁, B ₂..., B _n+qand S _c={ C ₁, C ₂..., C _n+q,

Wherein sequence S _a, S _b, S _crespectively by each GHZ state | η > _aBCparticle A, B, C form; Alice oneself reservation queue S _aand S _b, by sequence S _csend to Bob; N, q are the positive integer being greater than 1;

Step 3: when Bob receives sequence S _c, at random from sequence S _cin select q sample particles, select Z base or X base to measure at random to this q sample particles; Then, Bob by this q sample particles at sequence S _cin position and corresponding base of measuring tell Alice; Alice selects the measurement base of oneself according to the measurement base of Bob, and measures sequence S with the measurement base of oneself _aand S _bin corresponding particle, then measurement result is informed Bob by classical authenticated channel; Bob compares the measurement result of two people, and according to the measurement correlation calculations error rate of GHZ state; If error rate is lower than prespecified limit gate value, then perform step 4, otherwise, perform step 2;

Step 4:Alice is by sequence S _aand S _bin sample particles remove, obtain sequence S' respectively _aand S' _b; Bob is by sequence S _cin sample particles remove, obtain sequence S' _c;

S' _a=A ' ₁, A' ₂..., A' _n, S' _b=B ' ₁, B' ₂..., B' _nand S' _c=C ' ₁, C' ₂..., C' _n;

Alice is to sequence S' _aand S' _btwo particles that middle sequence number is identical perform Bell and measure; Bob is to sequence S' _cin particle perform X base and measure; According to the coding of the quantum state that Alice and Bob in measurement result and step 1 consults, Alice and Bob obtains the shared key of identical n-bit respectively.

Further, in described step 1, described Alice and Bob consults being encoded to of quantum state: | φ ⁺> _aB→ 0, | φ ^-> _aB→ 1, |+> _c→ 0, |-> _c→ 1.

Further, in described step 2,

Further, in described step 3, described Alice selects the measurement base of oneself specifically to refer to according to the measurement base of Bob: if the measurement base of Bob is Z base, then Alice selects base (| 00>, | 01>, | 10>, | 11>}) as oneself measurement base; If the measurement base of Bob is X base, then Alice select Bell base (| φ ⁺>, | φ ^->, | ψ ⁺>, | ψ ^->}) as the measurement base of oneself.

Further, in described step 3, the measurement correlation of described GHZ state refers to:

According to above formula, if to GHZ state | η > _aBCparticle A and B perform base is measured, and performs Z base measure particle C, then system with 1/2 probability be collapsed to state | 00> _aB| 0> _cwith | 11> _aB| 1> _c; If to GHZ state | η > _aBCparticle A and B perform Bell and measure, X base is performed to particle C and measures, then system with 1/2 probability be collapsed to state | φ ⁺> _aB|+> _cwith | φ ^-> _aB|-> _c.

Further, in described step 3, described limit gate value gets 0.1 ~ 0.2.

Beneficial effect of the present invention:

Two side's quantum key agreement protocols based on three ions of the present invention can not only be resisted existing participant and attack and external attack, and can resist Trojan horse attack.And be all safe on noiseless quantum channel and quantum noise channel.Further, this agreement also can reach higher quantum bit efficiency.The present invention can guarantee that communicating pair sets up the classical privacy key shared between them liberally.Utilize the cryptographic algorithm of this classical privacy key and one-time pad, communicating pair can realize the secure communication of unconditional security.

Embodiment

1, pre-knowledge

As everyone knows, | 0>, | 1>} defines Z base, |+>, |->} defines X base, wherein four Bell state are defined as follows:

They form one group of complete orthogonal basis in four-dimensional Hilbert space.GHZ state is the maximal entangled state of three particles, they form one group of complete orthogonal basis in octuple Hilbert space.In agreement of the present invention, we use a following GHZ state as quantum information source, namely

According to expression formula, if to GHZ state | η > _aBCparticle A and B perform Bell and measure, X base is performed to particle C and measures, then system with 1/2 probability be collapsed to state | φ ⁺> _aB|+> _cwith | φ ^-> _aB|-> _c.

2, quantum key agreement protocol of the present invention

Two side's quantum key agreement protocols based on three ions of the present invention, specifically comprise the steps:

Step 1:Alice and Bob consults the coding of following quantum state: | φ ⁺> _aB→ 0, | φ ^-> _aB→ 1, |+> _c→ 0, |-> _c→ 1;

Step 2:Alice prepares n+q GHZ state | η > _aBC, and all particles are divided into three orderly sequences:

S _a={ A ₁, A ₂..., A _n+q, S _b={ B ₁, B ₂..., B _n+qand S _c={ C ₁, C ₂..., C _n+q,

Wherein sequence S _a, S _b, S _crespectively by each GHZ state | η > _aBCparticle A, B, C form; Alice oneself reservation queue S _aand S _b, by sequence S _csend to Bob; N, q are the positive integer being greater than 1; Such as, n=64.

Step 3: when Bob receives sequence S _c, at random from sequence S _cin select q sample particles, select Z base or X base to measure at random to this q sample particles; Then, Bob by this q sample particles at sequence S _cin position and corresponding base of measuring tell Alice; Alice selects the measurement base of oneself according to the measurement base of Bob, and measures sequence S with the measurement base of oneself _aand S _bin corresponding particle, then measurement result is informed Bob by classical authenticated channel; Bob compares the measurement result of two people, and according to the measurement correlation calculations error rate of GHZ state; If error rate is lower than prespecified limit gate value, then perform step 4, otherwise, perform step 2;

Described limit gate value gets 0.1 ~ 0.2.

Above-mentioned Alice selects the measurement base of oneself specifically to refer to according to the measurement base of Bob: if the measurement base of Bob is Z base, then Alice selects base (| 00>, | 01>, | 10>, | 11>}) as oneself measurement base; If the measurement base of Bob is X base, then Alice select Bell base (| φ ⁺>, | φ ^->, | ψ ⁺>, | ψ ^->}) as the measurement base of oneself.

The measurement correlation of above-mentioned GHZ state refers to:

According to above formula, if to GHZ state | η > _aBCparticle A and B perform base is measured, and performs Z base measure particle C, then system with 1/2 probability be collapsed to state | 00> _aB| 0> _cwith | 11> _aB| 1> _c; If to GHZ state | η > _aBCparticle A and B perform Bell and measure, X base is performed to particle C and measures, then system with 1/2 probability be collapsed to state | φ ⁺> _aB|+> _cwith | φ ^-> _aB|-> _c.

Step 4:Alice is by sequence S _aand S _bin sample particles remove, obtain sequence S' respectively _aand S' _b; Bob is by sequence S _cin sample particles remove, obtain sequence S' _c;

S' _a=A ' ₁, A' ₂..., A' _n, S' _b=B ' ₁, B' ₂..., B' _nand S' _c=C ' ₁, C' ₂..., C' _n;

Alice is to sequence S' _aand S' _btwo particles that middle sequence number is identical perform Bell and measure; Bob is to sequence S' _cin particle perform X base and measure; According to the coding of the quantum state that Alice and Bob in measurement result and step 1 consults, Alice and Bob obtains the shared key of identical n-bit respectively.

According to expressed measurement correlation is known, and the shared key that Alice and Bob obtains is identical.

4 fail safes and efficiency analysis

The QKA agreement of a safety can not only resist external attack, and can resist participant's attack.

4.1 participants attack

Below, explanation dishonest participant can not be obtained alone this shared key by us.Without loss of generality, suppose that Alice is a dishonest participant, she wants to allow the l bit in shared key be 0, and she needs to measure sequence S' with Bell base _aand S' _bin corresponding l to particle.But according to the characteristic of Quantum Entangled States, what measurement result was random is | φ ⁺> _aBwith | φ ^-> _aB, namely Alice with 50% probability obtain 0 or 1.Therefore, every in l bit random is 0 or 1.So Alice cannot any one bit in Independent Decisiveness shared key.So this agreement can be resisted participant and be attacked.

4.2 external attack

Suppose that Eve is a listener-in wanting to steal shared key, the possible method that she attacks has: Trojan horse attack, measurement-multi-sending attack, intercepting and capturing-multi-sending attack and tangle-measure attack.

Trojan horse attack: in this agreement, because each photon in quantum channel is only transmitted once, therefore Eve successfully can not perform invisible photon eavesdropping (IPE) Trojan attack and postpone photon Trojan attack.

Measurement-multi-sending attack: Eve can to sequence S _cin particle perform measurement-multi-sending attack.But the measurement of Eve will affect sequence S _a, S _band S _cthe state of middle sample particles, makes no longer to meet between corresponding three particles to tangle correlation.In the eavesdropping of second step detects, Alice and Bob can with 1-(3/4) ^mthe probability of (m represents the quantity for detecting the sample GHZ state that this is attacked) finds the attack of Eve.

Intercepting and capturing-multi-sending attack: if Eve performs intercepting and capturing-multi-sending attack, first she intercept and capture sequence S _c, then send her forgery sequence to Bob.After agreement terminates, she is again to sequence S _cin particle perform corresponding measurement.But, the sequence S that the particle in the sequence that Eve forges and Alice retain _aand S _bin corresponding particle do not meet and tangle correlation, therefore not by the safety monitoring of second step.When m sample GHZ state is used to monitor this eavesdropping attack, corresponding eavesdropping verification and measurement ratio is 1-(1/2) ^m.Therefore, the intercepting and capturing-multi-sending attack of Eve also have failed.

Tangle-measure attack: Eve also can go to tangle this transmission particle (sequence S with oneself pre-prepd auxiliary particle _cin particle), then transmission particle is issued Bob again.After agreement terminates, she measures corresponding auxiliary particle again, thus extracts the useful information about shared key.If tangling of Eve is operating as U, and there is U (| 0>|E>)=a|0>|e ₀₀>+b|1>|e ₀₁> and U (| 1>|E>)=c|0>|e ₁₀>+d|1>|e ₁₁> sets up, wherein | and e ₀₀>, | e ₀₁>, | e ₁₀> and | e ₁₁> is by the well-determined pure state of unitary transformation U, and | a| ²+ | b| ²=1, | c| ²+ | d| ²=1.Obviously, CNOT conversion is the special circumstances of unitary transformation U.GHZ state through Eve tangle operation after, system becomes:

If Eve wants to be detected by eavesdropping at second step, the unitary transformation U of Eve must satisfy condition b=c=0 and a|e ₀₀>=d|e ₁₁>.As equation a|e ₀₀>=d|e ₁₁when > sets up, Eve can not distinguish auxiliary photon a|e ₀₀> and d|e ₁₁>, thus Eve does not obtain the useful information of shared key by observing auxiliary photon.But, if a|e ₀₀> ≠ d|e ₁₁the attack of >, Eve will disturb sample state | η > _aBC.Therefore, the attack of Eve will be found by Alice and Bob.The eavesdropping verification and measurement ratio of each trick photon is:

4.3 quantum noise channels

In quantum noise channel, the span of quantum bit error rate (QBER) τ introduced by noise is similar at 2%-8.9%, and it depends on the situation of channel as factors such as distances.If the quantum bit error rate that the attack of Eve is introduced is less than τ, so she just can hide her attack with noise.According to above-mentioned safety analysis, in this agreement, the eavesdropping verification and measurement ratio of each trick photon is at least 25%, and it is much larger than τ.Therefore, suitable eavesdropping detectability gate value is selected can to guarantee that this agreement is also safe on quantum noise channel.

According to above-mentioned analysis, this agreement is all safe on noiseless quantum channel and quantum noise channel.

5 efficiency analysiss

For a QKA agreement, Cabello quantum bit efficiency is defined as: wherein c represents the quantity of the classical bit of negotiation, the quantity of the quantum bit used in q presentation protocol.Therefore, our the quantum bit efficiency of agreement is: the wherein quantity of GHZ state in n presentation protocol, m represents the quantity of the GHZ state as sample.Make m=n, Wo Menyou

Claims (6)

1., based on two side's quantum key agreement protocols of three ions, it is characterized in that, specifically comprise the steps:

Step 1:Alice and Bob consults the coding of quantum state; | φ ⁺> _aB→ 0, | φ ^-> _aB→ 1, |+> _c→ 0, |-> _c→ 1;

Step 2:Alice prepares n+q GHZ state | η > _aBC, and all particles are divided into three orderly sequences:

S _a={ A ₁, A ₂..., A _n+q, S _b={ B ₁, B ₂..., B _n+qand S _c={ C ₁, C ₂..., C _n+q,

Wherein sequence S _a, S _b, S _crespectively by each GHZ state | η > _aBCparticle A, B, C form; Alice oneself reservation queue S _aand S _b, by sequence S _csend to Bob; N, q are the positive integer being greater than 1;

Step 3: when Bob receives sequence S _c, at random from sequence S _cin select q sample particles, select Z base or X base to measure at random to this q sample particles; Then, Bob by this q sample particles at sequence S _cin position and corresponding base of measuring tell Alice; Alice selects the measurement base of oneself according to the measurement base of Bob, and measures sequence S with the measurement base of oneself _aand S _bin corresponding particle, then measurement result is informed Bob by classical authenticated channel; Bob compares the measurement result of two people, and according to the measurement correlation calculations error rate of GHZ state; If error rate is lower than prespecified limit gate value, then perform step 4, otherwise, perform step 2;

Step 4:Alice is by sequence S _aand S _bin sample particles remove, obtain sequence S ' respectively _awith S ' _b; Bob is by sequence S _cin sample particles remove, obtain sequence S ' _c;

S ' _a={ A ₁', A ' ₂..., A ' _n, S ' _b={ B ₁', B ' ₂..., B ' _nand S ' _c={ C ₁', C ' ₂..., C ' _n;

Alice is to sequence S ' _awith S ' _btwo particles that middle sequence number is identical perform Bell and measure; Bob is to sequence S ' _cin particle perform X base and measure; According to the coding of the quantum state that Alice and Bob in measurement result and step 1 consults, Alice and Bob obtains the shared key of identical n-bit respectively.

2. as claimed in claim 1 based on two side's quantum key agreement protocols of three ions, it is characterized in that, in described step 1, described Alice and Bob consults being encoded to of quantum state: | φ ⁺> _aB→ 0, | φ ^-> _aB→ 1, |+> _c→ 0, |-> _c→ 1.

3., as claimed in claim 1 based on two side's quantum key agreement protocols of three ions, it is characterized in that, in described step 2, $|\mathrm{\η}{>}_{ABC}=\frac{1}{\sqrt{2}}{\left(\right|000>+|111>)}_{ABC}.$

4. as claimed in claim 1 based on two side's quantum key agreement protocols of three ions, it is characterized in that, in described step 3, described Alice selects the measurement base of oneself specifically to refer to according to the measurement base of Bob: if the measurement base of Bob is Z base, then Alice selects base (| 00>, | 01>, | 10>, | 11>}) as oneself measurement base; If the measurement base of Bob is X base, then Alice select Bell base (| φ ⁺>, | φ ^->, | ψ ⁺>, | ψ ^->}) as the measurement base of oneself.

5., as claimed in claim 1 based on two side's quantum key agreement protocols of three ions, it is characterized in that, in described step 3, the measurement correlation of described GHZ state refers to:

$|\mathrm{\η}{>}_{ABC}=\frac{1}{\sqrt{2}}{\left(\right|000>+|111>)}_{ABC}=\frac{1}{\sqrt{2}}\left(\right|{\mathrm{\φ}}^{+}{>}_{AB}|+{>}_C+|{\mathrm{\φ}}^{-}{>}_{AB}|-{>}_C);$

According to above formula, if to GHZ state | η > _aBCparticle A and B perform base is measured, and performs Z base measure particle C, then system with 1/2 probability be collapsed to state | 00> _aB| 0> _cwith | 11> _aB| 1> _c; If to GHZ state | η > _aBCparticle A and B perform Bell and measure, X base is performed to particle C and measures, then system with 1/2 probability be collapsed to state | φ ⁺> _aB|+> _cwith | φ ^-> _aB|-> _c.

6., as claimed in claim 1 based on two side's quantum key agreement protocols of three ions, it is characterized in that, in described step 3, described limit gate value gets 0.1 ~ 0.2.