CN111224780A - Arbitration quantum signature method based on XOR encryption - Google Patents

Abstract

The invention discloses an arbitration quantum signature method based on XOR encryption, which comprises a signer Alice, a receiver Bob, an arbiter Trent and a three-particle GHZ state quantum key shared by three parties, wherein the three-particle GHZ state is a common entangled resource in quantum communication, and the signature method comprises the following steps: an initialization phase, a signature phase and a verification phase. The signer Alice, the receiver Bob and the arbiter Trent share three particle GHZ states and keep secret for own particle information respectively, the traditional XOR encryption and decryption method is used, quantum messages are encrypted and signed through the shared GHZ states, the flow of a conventional arbitration quantum signature protocol is improved by introducing decoy photon states, the requirements of non-forgeability and non-repudiation are met, and finally, the encryption of the protocol does not involve a complex encryption method or complex quantum operation, so that the method is more practical than other methods.

Description

Arbitration quantum signature method based on XOR encryption

Technical Field

The invention relates to the technical field of quantum cryptography, in particular to an arbitration quantum signature method based on XOR encryption.

Background

As the work on AQS research has progressed, some researchers have begun investigating the security of protocols. In 2011, Gao et al indicated that AQS based on quantum one-time pad encryption has a security hole. This is because the Pauli operations used in encryption are commutative, so the recipient can forge a quantum signature. Choi et al subsequently proposed an AQS protocol that was resistant to the attack method reported by Gao et al. This is based on improved QOTP encryption. However, paper et al indicates that this method does not prevent the recipient from forging the signature. Instead, they use the mixed-key quantum encryption concept proposed in the art to design a multiple encryption method that can be applied to the quantum signature protocol. In 2015, Li et al proposed a new AQS protocol based on chained CNOT operation. The protocol encrypts quantum messages by using chained CNOT operations and is resistant to signature forgery that Pauli operations can produce. Later, Roman et al also proposed a new method of forgery attack against the plum protocol. In this regard, in 2017, sheet et al used the idea of key control to improve the chained CONT operation for encrypting quantum messages. The protocol enhances the ability to resist forgery attacks by introducing a shared key-controlled permutation operation to reorder the location of quantum messages. However, the requirements for quantum operation in the protocol are so high that the protocol is difficult to implement in practical conditions.

All AQS protocols should have two basic security conditions: non-forgeability and non-repudiation. To improve the security of the protocol, most AQS protocols are designed for enhancing the security of quantum message encryption and quantum signatures. Although the security performance is improved, more quantum resources and quantum operations are consumed, which increases the difficulty of practical application, and for this reason, an arbitration quantum signature method based on XOR encryption is proposed to solve the above problems.

Disclosure of Invention

The present invention aims to provide an arbitration quantum signature method based on XOR encryption to solve the problems proposed in the above background art.

In order to achieve the purpose, the invention provides the following technical scheme: an arbitration quantum signature method based on XOR encryption comprises a signer Alice, a receiver Bob, an arbiter Trent and three parties sharing three partiesThe particle GHZ state quantum key, the three particle GHZ states are common entangled resources in quantum communication, and the three particle GHZ states are represented by an expression (1):

performing a unitary Hadamard operation (H operation) on all three particles, expression (2) can be obtained:

the signature method according to the three-particle GHZ state quantum key is as follows:

A. initialization phase

(I1) Trent prepares n + d set GHZ state, and performs Hadamard operation on each of three particles in GHZ state, and can obtain expression (3):

for each GHZ state particle, the Trent reserves one particle and distributes the other two particles to Alice and Bob respectively;

(I2) the method for Trent to randomly use the d group GHZ state in the n + d group GHZ state to verify the safety of the transmission channel comprises the following steps: trent randomly selects a measurement base for particles reserved in a randomly selected d-group GHZ state, wherein the Z base { |0>，|1>} or X base { | +>，|->And fourthly, making single-particle-based measurement, recording a measurement result according to a certain recording rule, and then, Trent publishes d-group GHZ-state specific positions and specific measurement-based information M_i＝{M₁,M₂,M₃...M_d},M_d∈{X,Z}；

(I3) According to the information published by Alice and Bob, Trent calculates the quantum transmission error rate according to the expression (2), if the error rate exceeds a certain threshold value, the quantum channel is considered to be unsafe due to wiretapping, at the moment, all entangled particles are discarded, the protocol is terminated, on the contrary, the communication channel can be considered to be safe, and three parties continue to complete the protocol by using the remaining n groups of GHZ states;

B. signature phase

(S1) Alice prepares the signed quantum message as in expression (4):

wherein | a_i|²+|b_i|²1 and Alice prepares three identical quantum messages

Simultaneously randomly generating an n-bit binary parameter r, and then encrypting | P>To quantum pseudorandom string | P'>As expressed by expression (5): l P'>＝E_r(|P>)；

(S2) Alice uses the particle sequence A of n groups of GHZ states to make three copies of | P'>Performs a controlled not gate (CNOT) operation, as in expression (6):

(S3) Alice prepares enough decoy photon states | D>，|D>Is randomly in { |0>,|1>,|+>,|->One of the four single particle states, then Alice will trick the photon state | D>Insert | P'>And two other sets of particle sequences

To form two new particle sequences { | P'>,|D>And

then the two groups of particle sequences are respectively sent to Trent and Bob;

C. verification phase

(V1) after the Trent receives the particle sequence sent by Alice, the Alice tells the Trent the detailed information of the decoy photon state | D > so that the Trent can measure and calculate the error rate to finish the eavesdropping detection, if the error rate is zero or is lower than a specific threshold value, the eavesdropping behavior can be considered to be absent, the Trent removes the decoy photon state | D > and declares the protocol to continue, and if not, the protocol is terminated;

(V2) when Bob receives the particle sequence, he detects the presence or absence of eavesdropping on the communication channel in the same way. If eavesdropping behavior is found, the protocol is terminated. Otherwise, Bob deletes the decoy photon state | D>Then using the particle sequence B in the n groups of GHZ states held by him to one of the particle sequences

Perform a CNOT operation, such as expression (7):

(V3) Bob prepares the decoy photon state | D again as shown in (S3)>Then randomly inserted into

Formation of a novel particle sequence

Bob then sends this new particle sequence to Trent, leaving another particle sequence in his hand

(V4) after Trent receives the particle sequence from Bob, it performs eavesdropping detection in the same way as before, and if no eavesdropping behavior is detected, Trent will remove the decoy photon state | D>And using the particle sequence T in the n groups of GHZ states in the hand to pair the particle sequences

Perform a CNOT operation, such as expression (8):

and verified by quantum state comparison techniques, then Trent prepares the bait photon state | D in the same way>And randomly insert

Form a newOf the particle sequence

And send it to Bob;

(V5) Bob receives the particle sequence, performs channel security check according to the previous method, and determines whether to continue the protocol and store Alice's quantum signature.

In a preferred embodiment, the unitary Hadamard operation H is:

and

the expression (2) shows that under the condition of taking z group as measuring base to measure single particle group, the measuring result of GHZ state after H conversion is written into binary number, wherein '0' represents measuring result |0>And "1" represents the measurement result |1>It can be easily found that the measurement results of the three particles satisfy the classic exclusive-or relationship.

In a preferred embodiment, in step a, the recording rule is as follows, "0" represents the measurement results { |0>, | + >, and "1" represents the measurement results { |1>, | - >.

In a preferred embodiment, the encryption method E is performed in step (S1)_rComprises the following steps: when r is_iWhen 1, p_i>Performing a unitary transformation X transform, i.e. X ═ 0><1|+|1><0|, when r_iWhen 0, then p_i>Performing an I-identity transformation, i.e. I ═ 0><0|+|1><1 l, it can be easily seen that the corresponding decryption method E'_r＝E_r。

In a preferred embodiment, in step (V4), the quantum state comparison technique is verified as:

if the two are equal, Trent prepares | V_T>＝|1>Otherwise preparing | V_T>＝|0>And if equal, Trent will again be on the particle sequence

Perform a CNOT operation, such as expression (9):

in a preferred embodiment, in step (V5), the security is checked by deleting the bait photon state | D by Bob if there is no eavesdropping action>And judging whether | V_T>＝|1>If so, Bob pairs the particle sequence using the particle sequence B of the n sets of GHZ states in his hand

Perform a CNOT operation, such as expression (10):

later, Bob verified using quantum state comparison techniques, as expressed in expression (11):

if the two are equal, Bob publishes | V_B>＝|0>Rejecting Alice's signature and terminating the protocol, otherwise, Bob notifies Alice to declare parameter r, and through Alice's issued parameter r, Bob will restore | P '>To | P>＝E'_r|P'>And store

As the quantum signature of Alice.

Compared with the prior art, the invention has the beneficial effects that: in the method, a signer Alice, a receiver Bob and an arbiter Trent share three particle GHZ states and respectively keep secret on particle information of the signer Alice, the receiver Bob and the arbiter Trent, different from other protocols which adopt a quantum one-time pad encryption method or a chain CNOT encryption method, the protocol borrows the traditional XOR encryption and decryption method, the quantum information is encrypted and signed through the shared GHZ states, the flow of the conventional arbitration quantum signature protocol is improved by introducing decoy photon states, the requirements of non-forgeability and non-repudiation are realized, and finally, the encryption of the protocol does not involve a complex encryption method or complex quantum operation, so the method is more practical than other protocols.

Drawings

FIG. 1 is a detailed process diagram of the initialization phase of the present invention;

FIG. 2 is a diagram illustrating the signature phase of the present invention;

FIG. 3 is a diagram illustrating the verification phase of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1-3, the present invention provides a technical solution: an arbitration quantum signature method based on XOR encryption comprises a signer Alice, a receiver Bob, an arbiter Trent and a three-party shared three-particle GHZ state quantum key, wherein the three-particle GHZ state is an entangled resource commonly used in quantum communication, and is represented by an expression (1):

performing a unitary Hadamard operation (H operation) on all three particles, expression (2) can be obtained:

the unitary Hadamard operation H is:

and

the expression (2) shows that under the condition of taking z group as measuring base to measure single particle group, the measuring result of GHZ state after H conversion is written into binary number, wherein '0' represents measuring result |0>And "1" represents the measurement result |1>Can easily findAnd if the measurement results of the three particles meet the classical exclusive-or relationship, the method for signing the quantum key according to the three-particle GHZ state is as follows:

A. initialization phase

(I1) Trent prepares n + d set GHZ state, and performs Hadamard operation on each of three particles in GHZ state, and can obtain expression (3):

for each GHZ state particle, the Trent reserves one particle and distributes the other two particles to Alice and Bob respectively;

(I2) the method for Trent to randomly use the d group GHZ state in the n + d group GHZ state to verify the safety of the transmission channel comprises the following steps: trent randomly selects a measurement base for particles reserved in a randomly selected d-group GHZ state, wherein the Z base { |0>，|1>} or X base { | +>，|->And (6) carrying out single-particle-based measurement, and recording the measurement result according to a certain recording rule, wherein the recording rule is as follows, and 0 represents the measurement result { |0>，|+>And "1" represents the measurement result { |1>，|->Trent then publishes d group d specific positions of GHZ states and specific measurement base information M_i＝{M₁,M₂,M₃...M_d},M_d∈{X,Z}；

(I3) According to the information published by Alice and Bob, Trent calculates the quantum transmission error rate according to the expression (2), if the error rate exceeds a certain threshold value, the quantum channel is considered to be unsafe due to wiretapping, at the moment, all entangled particles are discarded, the protocol is terminated, on the contrary, the communication channel can be considered to be safe, and three parties continue to complete the protocol by using the remaining n groups of GHZ states;

B. signature phase

(S1) Alice prepares the signed quantum message as in expression (4):

wherein | a_i|²+|b_i|²1 and Alice prepares three identical quantum messages

Simultaneously randomly generating an n-bit binary parameter r, and then encrypting | P>To quantum pseudorandom string | P'>As expressed by expression (5): l P'>＝E_r(|P>) And an encryption method E_rComprises the following steps: when r is_iWhen 1, p_i>Performing a unitary transformation X transform, i.e. X ═ 0><1|+|1><0|, when r_iWhen 0, then p_i>Performing an I-identity transformation, i.e. I ═ 0><0|+|1><1 l, it can be easily seen that the corresponding decryption method E'_r＝E_r；

(S2) Alice uses the particle sequence A of n groups of GHZ states to make three copies of | P'>Performs a controlled not gate (CNOT) operation, as in expression (6):

(S3) Alice prepares enough decoy photon states | D>，|D>Is randomly in { |0>,|1>,|+>,|->One of the four single particle states, then Alice will trick the photon state | D>Insert | P'>And two other sets of particle sequences

To form two new particle sequences { | P'>,|D>And

then the two groups of particle sequences are respectively sent to Trent and Bob;

C. verification phase

(V1) after the Trent receives the particle sequence sent by Alice, the Alice tells the Trent the detailed information of the decoy photon state | D > so that the Trent can measure and calculate the error rate to finish the eavesdropping detection, if the error rate is zero or is lower than a specific threshold value, the eavesdropping behavior can be considered to be absent, the Trent removes the decoy photon state | D > and declares the protocol to continue, and if not, the protocol is terminated;

(V2) when Bob receives the particle sequence, he detects the presence or absence of eavesdropping on the communication channel in the same way. If eavesdropping behavior is found, the protocol is terminated. Otherwise, Bob deletes the decoy photon state | D>Then using the particle sequence B in the n groups of GHZ states held by him to one of the particle sequences

Perform a CNOT operation, such as expression (7):

(V3) Bob prepares the decoy photon state | D again as shown in (S3)>Then randomly inserted into

Formation of a novel particle sequence

Bob then sends this new particle sequence to Trent, leaving another particle sequence in his hand

(V4) after Trent receives the particle sequence from Bob, it performs eavesdropping detection in the same way as before, and if no eavesdropping behavior is detected, Trent will remove the decoy photon state | D>And using the particle sequence T in the n groups of GHZ states in the hand to pair the particle sequences

Perform a CNOT operation, such as expression (8):

and verified as follows by a quantum state comparison technology:

if the two are equal, Trent prepares | V_T>＝|1>Otherwise preparing | V_T>＝|0>And is combined withAnd if equal, Trent will again be on the particle sequence

Perform a CNOT operation, such as expression (9):

subsequently, Trent prepares bait photon state | D in the same manner>And randomly insert

Formation of a novel particle sequence

And send it to Bob;

(V5) when Bob receives the particle sequence, channel security checks are performed as before, and if there is no eavesdropping action, Bob deletes the bait photon state | D>And judging whether | V_T>＝|1>If so, Bob pairs the particle sequence using the particle sequence B of the n sets of GHZ states in his hand

Perform a CNOT operation, such as expression (10):

later, Bob verified using quantum state comparison techniques, as expressed in expression (11):

if the two are equal, Bob publishes | V_B>＝|0>Rejecting Alice's signature and terminating the protocol, otherwise, Bob notifies Alice to declare parameter r, and through Alice's issued parameter r, Bob will restore | P '>To | P>＝E'_r|P'>And store

As the quantum signature of Alice.

After signing, the method can be subjected to security analysis, and a secure quantum signature protocol has two basic characteristics of (1) non-forgeability, which means that an attacker (including a dishonest receiver Bob) cannot maliciously forge the signature. (2) Undeniable, i.e. the signer cannot reject the signature, the recipient cannot reject the received signature. In this protocol, when Alice and Bob disagree on the signatures, Trent will act as an arbitrator to resolve the divergence, and thus Trent is absolutely secure and reliable in our protocol. Below, we will analyze our protocol to satisfy the non-forgeability and non-repudiation, proving that it is secure under some existing attack methods:

non-forgeability

If an external eavesdropper Eve wants to forge Alice's signature, the only way is to obtain all the state information of the particles in the GHZ state that the three parties share in the protocol initialization phase, but this is obviously not possible. There are generally three common eavesdropping methods, interception-retransmission, measurement-retransmission, and entanglement measurement attacks. Eve cannot steal messages using these three methods because she cannot know the specific location and specific measurement basis of the d-set of GHZ states that are randomly used for authentication. Therefore, if there is an eavesdropping behavior, the error rate in the channel verification process in the initialization phase will be high, and the eavesdropping behavior will be inevitably detected.

It can be seen that absolute secure quantum key distribution based on the GHZ state is the basis of our proposed arbitration quantum signature. In addition, decoy photon states are introduced during the initialization, signature and verification phases of the protocol so as to detect any eavesdropping behavior in time, thereby preventing an external eavesdropper from stealing any useful information.

Now consider an insider attacker and a dishonest receiver Bob. He cannot forge Alice's signature because of the encrypted message | P'>Is sent directly by Alice to the arbiter Trent. In the protocol process, decoy photon state | D for channel security detection is also introduced>. This means that Bob cannot know | P 'until Trent sends authentication information back to Bob'>Any of (3). Therefore, Bob is unlikely to forge

To make

(X2) non-repudiation

For non-repudiation, neither Alice nor Bob can deny the validity of the signature because the GHZ state in the respective hands is only known to themselves in the specific state information.

Suppose Alice has signed an encrypted quantum message | P'>And corresponding quantum signatures

She cannot deny her signature issued for Bob. In other words, Alice excludes the corresponding quantum signature

In addition, other quantum message signatures cannot be forged

This is because, on the premise of the secure distribution of GHZ state, Alice cannot obtain any information of the GHZ state particles owned by Bob, and therefore it is impossible to forge another message signature in addition to the legitimate message signature

To replace

The Trent verification is passed. This means that

Cannot be established.

Also, in this protocol, message | P 'is encrypted'>Is directly sent to the arbitrator Trent by Alice, and the corresponding mail signature is verified in Trent

And return to

Before giving Bob, Bob isCannot obtain | P'>Any of (3).

Bob need only be able to accept her signature and dispute once Alice attempts to deny her acceptance

And sending the information to Trent for judgment. Trent will determine that the signature must be signed by Alice. In addition, decoy photon state | D is introduced into the whole protocol>Therefore, any attempt by Alice to alter the signature verification information

And

must be discovered.

The recipient deny means that Bob denies his receipt of the quantum information | P>The signature of (2). Based on the premise of GHZ state safe distribution, three parties only know the information of GHZ state particles in the hands of the three parties, but not the particle information of other two parties, so that Bob cannot know two groups of CNOT operations CNOTA and CNOTT. Thus, if Bob wants to get quantum message | P>And the corresponding quantum signature, he cannot deny him receipt of

And a parameter r. In particular when, in the case of,

bob cannot claim out

Since he needs Alice to issue a parameter r to recover the quantum message | P>. Otherwise, he will not get the correct quantum signature

Therefore, Bob cannot reject the quantum signature;

(X3) efficiency comparison

In the field of quantum cryptography, research on quantum signatures is being deepened. Many quantum signature protocols have been proposed so far, and many good ideas have also been proposed in the design of arbitrated quantum signatures. However, there are still some security holes in such protocols. Particularly in the core part of the protocol, the quantum signature encryption algorithm uses relatively complicated encryption operations, which undoubtedly increases the difficulty of implementation in practical applications. Moreover, this approach is also ineffective in preventing counterfeit signatures.

The quantum arbitration signature protocol does not adopt any form of quantum one-time pad encryption method, and does not adopt an encryption method based on chain type CNOT operation or combination of the chain type CNOT operation and key control. In contrast, since the three-party shared GHZ-state key satisfies the classical XOR relationship, the protocol encrypts and signs the quantum message using a CNOT operation (in effect, XOR encryption).

Although the three parties keep secret on own GHZ state particle information, the particles owned by the three parties meet the XOR relation, so that quantum messages and signatures can be verified and decrypted. By introducing decoy photon states and improving the flow of conventional quantum signature protocols, we have found that the protocol can also meet the requirements of arbitrating the non-forgeability and non-repudiation of quantum signatures. Finally, the most basic requirement of the protocol is the safe distribution of the three-particle GHZ state, which is also ensured by the safety detection in the whole protocol process. Thus, the solution proposed herein is safe and effective.

In summary, in this protocol, the signer Alice, the receiver Bob and the arbitrator Trent share the three-particle GHZ state and keep their own particle information secret. Different from other protocols which adopt a quantum one-time pad encryption method or a chain CNOT encryption method. The protocol encrypts and signs the quantum message by sharing the GHZ state by using the traditional XOR encryption and decryption method. By introducing decoy photon states, the flow of the conventional arbitration quantum signature protocol is improved, and the requirements of non-forgeability and non-repudiation are met. Finally, it can be seen that the encryption of this protocol does not involve complex encryption methods or complex quantum operations and is therefore more practical than other protocols.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. An arbitration quantum signature method based on XOR encryption comprises a signer Alice, a receiver Bob, an arbiter Trent and a three-party shared three-particle GHZ state quantum key, and is characterized in that: the three-particle GHZ state is an entangled resource commonly used in quantum communication, and is represented by an expression (1):

performing a unitary Hadamard operation (H operation) on all three particles, expression (2) can be obtained:

the signature method according to the three-particle GHZ state quantum key is as follows:

A. initialization phase

(I1) Trent prepares n + d set GHZ state, and performs Hadamard operation on each of three particles in GHZ state, and can obtain expression (3):

for each GHZ state particle, the Trent reserves one particle and distributes the other two particles to Alice and Bob respectively;

(I2) the method for Trent to randomly use the d group GHZ state in the n + d group GHZ state to verify the safety of the transmission channel comprises the following steps: trent randomly selects a measurement base for particles reserved in a randomly selected d-group GHZ state, wherein the Z base { |0>，|1>} or X base { | +>，|->And fourthly, making single-particle-based measurement, recording a measurement result according to a certain recording rule, and then, Trent publishes d-group GHZ-state specific positions and specific measurement-based information M_i＝{M₁,M₂,M₃...M_d},M_d∈{X,Z}；

(I3) According to the information published by Alice and Bob, Trent calculates the quantum transmission error rate according to the expression (2), if the error rate exceeds a certain threshold value, the quantum channel is considered to be unsafe due to wiretapping, at the moment, all entangled particles are discarded, the protocol is terminated, on the contrary, the communication channel can be considered to be safe, and three parties continue to complete the protocol by using the remaining n groups of GHZ states;

B. signature phase

(S1) Alice prepares the signed quantum message as in expression (4):

wherein | a_i|²+|b_i|²1 and Alice prepares three identical quantum messages

Simultaneously randomly generating an n-bit binary parameter r, and then encrypting | P>To quantum pseudorandom string | P'>As expressed by expression (5): l P'>＝E_r(|P>)；

(S2) Alice uses the particle sequence A of n groups of GHZ states to make three copies of | P'>Performs a controlled not gate (CNOT) operation, as in expression (6):

(S3) Alice prepares enough decoy photon states | D>，|D>Is randomly in { |0>,|1>,|+>,|->One of the four single particle states, then Alice will trick the photon state | D>Insert | P'>And two other sets of particle sequences

To form two new particle sequences { | P'>,|D>And

then the two groups of particle sequences are respectively sent to Trent and Bob;

C. verification phase

(V1) after the Trent receives the particle sequence sent by Alice, the Alice tells the Trent the detailed information of the decoy photon state | D > so that the Trent can measure and calculate the error rate to finish the eavesdropping detection, if the error rate is zero or is lower than a specific threshold value, the eavesdropping behavior can be considered to be absent, the Trent removes the decoy photon state | D > and declares the protocol to continue, and if not, the protocol is terminated;

(V2) when Bob receives the particle sequence, he detects the presence or absence of eavesdropping on the communication channel in the same way. If eavesdropping behavior is found, the protocol is terminated. Otherwise, Bob deletes the decoy photon state | D>Then using the particle sequence B in the n groups of GHZ states held by him to one of the particle sequences

Perform a CNOT operation, such as expression (7):

(V3) Bob prepares the decoy photon state | D again as shown in (S3)>Then randomly inserted into

Formation of a novel particle sequence

Bob then sends this new particle sequence to Trent, leaving another particle sequence in his hand

(V4) after Trent receives the particle sequence from Bob, it performs eavesdropping detection in the same way as before, and if no eavesdropping behavior is detected, Trent will remove the decoy photon state | D>And using particles in n groups of GHZ states in his handSequence T vs. particle sequence

Perform a CNOT operation, such as expression (8):

and verified by quantum state comparison techniques, then Trent prepares the bait photon state | D in the same way>And randomly insert

Formation of a novel particle sequence

And send it to Bob;

(V5) Bob receives the particle sequence, performs channel security check according to the previous method, and determines whether to continue the protocol and store Alice's quantum signature.

2. An arbitrated quantum signing method based on XOR encryption according to claim 1, characterized by: the unitary Hadamard operation H is:

and

the expression (2) shows that under the condition of taking z group as measuring base to measure single particle group, the measuring result of GHZ state after H conversion is written into binary number, wherein '0' represents measuring result |0>And "1" represents the measurement result |1>It can be easily found that the measurement results of the three particles satisfy the classic exclusive-or relationship.

3. An arbitrated quantum signing method based on XOR encryption according to claim 1, characterized by: in step a, the recording rule is as follows, "0" represents the measurement result { |0>, | + >, and "1" represents the measurement result { |1>, | - >.

4. An arbitrated quantum signing method based on XOR encryption according to claim 1, characterized by: in step (S1), encryption method E_rComprises the following steps: when r is_iWhen 1, p_i>Performing a unitary transformation X transform, i.e. X ═ 0><1|+|1><0|, when r_iWhen 0, then p_i>Performing an I-identity transformation, i.e. I ═ 0><0|+|1><1 l, it can be easily seen that the corresponding decryption method E'_r＝E_r。

5. An arbitrated quantum signing method based on XOR encryption according to claim 1, characterized by: in step (V4), the quantum state comparison technique verifies that:

if the two are equal, Trent prepares | V_T>＝|1>Otherwise preparing | V_T>＝|0>And if equal, Trent will again be on the particle sequence

Perform a CNOT operation, such as expression (9):

6. an arbitrated quantum signing method based on XOR encryption according to claim 1, characterized by: in step (V5), the security is checked by deleting bait photon state | D by Bob if there is no eavesdropping action>And judging whether | V_T>＝|1>If so, Bob pairs the particle sequence using the particle sequence B of the n sets of GHZ states in his hand

Perform a CNOT operation, such as expression (10):

later, Bob verified using quantum state comparison techniques, as expressed in expression (11):

if the two are equal, Bob publishes | V_B>＝|0>Rejecting Alice's signature and terminating the protocol, otherwise, Bob notifies Alice to declare parameter r, and through Alice's issued parameter r, Bob will restore | P '>To | P>＝E’_r|P'>And store

As the quantum signature of Alice.

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