Two-party quantum secret magnitude comparison method based on two-level bell state

Abstract

The present invention relates to the technical field of communications. Disclosed is a two-party quantum secret magnitude comparison method based on a two-level bell state. The present invention comprises the following steps: step I: protocol participants Alice and Bob respectively possessing their own secret values SA and SB, and Alice and Bob sharing a secure n-bit key KAB=KAB1KAB2KKABn by means of QKD; and step II: Alice and Bob sharing a collision-resistant hash function Hash(.) that is resistant to quantum algorithms, and with the assistance of a semi-trusted third party (TP), Alice and Bob completing the comparison between the magnitudes of the secret values of the two. By means of the present invention, an equality relationship and magnitude relationship between the secret values of the two participants, i.e. Alice and Bob, can be effectively determined; a quantum state prepared by the TP is a two-particle maximally entangled Bell state; and by means of the first eavesdropping detection, the absence of eavesdroppers and the honesty of the TP are verified.

Description

A method for comparing the magnitude of two-party quantum secrets based on two-level Bell states Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a method for comparing the magnitude of two-party quantum secrets based on a two-level Bell state. Background Art

[0002] Quantum cryptography is the product of the combination of cryptography and quantum mechanics. It is a method of establishing a shared key between the two communicating parties using quantum states as information carriers, using the principles of quantum mechanics, and transmitting through quantum channels. This method is called quantum key distribution. Its security is guaranteed by the uncertainty relationship in quantum mechanics and the quantum no-cloning theorem. Absolute security means that the eavesdropper has an extremely high IQ, adopts the most ingenious eavesdropping strategy, and uses all possible advanced instruments. Under these conditions, the key is still safe. There are two basic eavesdropping strategies for eavesdroppers: one is to measure the quantum state carrying classical information and obtain the required information from the measurement results. However, the basic principles of quantum mechanics tell us that the measurement of the quantum state will interfere with the quantum state itself, so this kind of eavesdropping The first method will inevitably leave traces and be discovered by legitimate users; the second method is to avoid direct quantum measurement and use a quantum replicator to copy the quantum state of the transmitted information. The eavesdropper transmits the original quantum state to the information receiver, and leaves the copied quantum state for measurement to steal information. In this way, no traces that can be discovered will be left. However, the quantum no-cloning theorem ensures that the eavesdropper will not succeed. Any physically feasible quantum replicator cannot clone a quantum state that is exactly the same as the input quantum state. Therefore, quantum cryptography can, in principle, provide a confidential communication system that cannot be deciphered or eavesdropped. At present, quantum key distribution is one of the most promising technologies in quantum information technology. With the development of quantum technology, information transmission can be realized in optical fiber channels or space channels of several kilometers.

[0003] In recent years, research on bell states has been ongoing at home and abroad, especially in the physical realization of bell states. In addition, efficiency improvement technology and security analysis have always been research hotspots in the field of quantum cryptography. In the existing quantum private comparison technology, a variety of quantum private comparison methods have been proposed. Existing quantum private comparison protocols generally use entangled states, and the methods generally adopt quantum state particles formed based on entanglement exchange. Both security and practicality are difficult to meet the needs of use. People have been looking for a more secure and practical quantum key sharing method.

[0004] Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for comparing the magnitude of two-party quantum secrets based on a two-level Bell state.

[0006] In order to solve the above technical problems, the basic concept of the technical solution adopted by the present invention is:

[0007] A method for comparing the magnitude of two-party quantum secrets based on a two-level Bell state comprises the following steps:

[0008] Step 1: Alice and Bob, participants in the protocol, each have their own secret value S A and S B , Alice and Bob share a secure n-bit key via QKD

[0009] Step 2: Alice and Bob share a quantum-resistant, collision-resistant hash function Hash(.). With the assistance of a semi-trusted third party (TP), Alice and Bob compare the size of their secret values.

[0010] Step 3: The semi-trusted third party TP prepares a sequence S containing 2n identical Bell states. The two particles of the Bell state are separated and form the sequence S. a and S b TP will S a and S b Sent to participants Alice and Bob respectively;

[0011] Step 4: The semi-trusted third party TP performs eavesdropping detection on Alice and Bob.

[0012] Step 5: After Alice and Bob delete the detection particles, the remaining particle sequences are recorded as and Alice uses her secret value S A to s a The particles in the unitary transformation operation Then, Alice (Bob) Insert several single photons as decoy states to obtain a new sequence Then Alice(Bob) will Send to TP;

[0013] Step 6: The semi-trusted third party TP performs eavesdropping detection with participants Bob and Alice.

[0014] Step 7: Semi-trusted third party TP from and Delete the decoy state and restore the sequence and Then, after pairing the photons at the same position in the two sequences, measurements are performed under the Bell basis;

[0015] Step 8: Alice and Bob verify the authenticity of the results published by TP.

[0016] Optionally, in step 1, S A (S B ) can be represented by a 2n-bit 0-1 sequence as

[0017] Optionally, in step 3, each Bell state Then TP separates all two particles in the Bell state, and the sequence composed of the first particle is recorded as S a , the sequence made by the second particle is denoted as S b .

[0018] Optionally, in step 3, the two-level quantum entangled state Bell state has four different states:

[0019] Optionally, in step 4, eavesdropping detection is: Alice and Bob receive S a and S b After that, particles at n positions are randomly selected to perform eavesdropping detection. They randomly negotiate to select a measurement basis (Z basis or X basis), measure the particles at these positions and compare the measurement results. If their measurement results are the same, there is no eavesdropping behavior and the TP has not made any malicious behavior. The protocol goes to the next step. Otherwise, the protocol is executed again.

[0020] Optionally, in step 5, the unitary transformation rule is as follows:

[0021] In the formula represents modular n addition, I, X, Y, Z are Pauli transformations, and Bob also uses the same rules to transform s b The particles in the unitary transformation operation In this way, Alice (Bob) will get a new sequence

[0022] Optionally, in step 6, the eavesdropping detection is: TP receives Finally, particles at n positions are randomly selected to perform eavesdropping detection. They randomly negotiate to select a measurement basis, measure the particles at these positions and compare the measurement results. If their measurement results are the same, there is no eavesdropping behavior or there is eavesdropping behavior, but the eavesdropping behavior is within the tolerable range, and the protocol goes to the next step. Otherwise, the protocol is re-executed.

[0023] Optionally, in step 7, if each measurement result is consistent with the initial Bell state If the measurement results are the same, TP announces that Alice and Bob’s secret values ​​are equal. If some of the measurement results are different from the initial Bell state, TP announces the minimum value k of the different positions.

[0024] Optionally, in step 8: If the secret values ​​published by Alice and Bob are equal, Alice and Bob calculate and The calculation results are exchanged. If the results are the same, the result announced by TP is considered correct. Otherwise, TP is considered untrustworthy and the protocol terminates.

[0025] Optionally, in step 8, if TP announces different minimum values ​​k among the single photon subscripts, Alice and Bob calculate and And exchange the calculation results. If the results are the same, continue to publish your own secret value and shared key k AB XOR value of 2 bits and If the two results are different, the result announced by TP is considered correct. At the same time, Alice and Bob and The value of can know the size of their secret value, otherwise, TP is considered untrustworthy and the protocol terminates.

[0026] After adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art. Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described below at the same time:

[0027] The present invention can effectively determine the equality and size relationship of the secret values ​​of two participants, Alice and Bob. The quantum state prepared by TP is the Bell state of the maximum entanglement of the two particles. The first eavesdropping detection verifies the non-existence of the eavesdropper and the honesty of TP. Alice and Bob simultaneously perform Pauli transformation on each quantum state without changing the measurement basis of the particle pair. Due to the entanglement of the particles, it is difficult for anyone to obtain the secret value of Alice and Bob through measurement. TP measures each quantum state to determine the equality or size relationship of the secret values ​​of Alice and Bob. The authenticity of the result published by TP is effectively verified by the hash function, effectively preventing TP from maliciously doing bad things. The protocol does not leak the secret information of any participant from beginning to end, and only uses the Bell state of two energy levels. Therefore, the protocol is not only secure but also practical.

[0028] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The drawings described below are only some embodiments. A person skilled in the art can derive other drawings based on these drawings without inventive effort. In the drawings:

[0030] FIG1 is a schematic diagram of a flow chart of an embodiment of the present invention;

[0031] FIG2 is a schematic diagram of a quantum secret comparison protocol model according to an embodiment of the present invention.

[0032] It should be noted that these drawings and textual descriptions are not intended to limit the conceptual scope of the present invention in any way, but rather to illustrate the concept of the present invention for those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0033] The present invention will now be described in further detail with reference to the accompanying drawings.

[0034] Referring to FIG. 1-2 , this embodiment provides a method for comparing the magnitude of two-party quantum secrets based on a two-level Bell state, including the following steps:

[0035] Step 1: Alice and Bob, participants in the protocol, each have their own secret value S A and S B , Alice and Bob share a secure n-bit key via QKD

[0036] Step 2: Alice and Bob share a quantum-resistant, collision-resistant hash function Hash(.). With the assistance of a semi-trusted third party (TP), Alice and Bob compare the size of their secret values. Alice and Bob effectively verify the authenticity of the result published by TP through the hash function.

[0037] Step 3: The semi-trusted third party TP prepares a sequence S containing 2n identical Bell states. The two particles of the Bell state are separated and form the sequence S. a and S b TP will S a and S b Sent to participants Alice and Bob respectively;

[0038] Step 4: The semi-trusted third party TP performs eavesdropping detection on Alice and Bob.

[0039] Step 5: After Alice and Bob delete the detection particles, the remaining particle sequences are recorded as and Alice uses her secret value S A to s a The particles in the unitary transformation operation Then, Alice (Bob) Insert several single photons as decoy states to obtain a new sequence Then Alice(Bob) will Send to TP;

[0040] Step 6: The semi-trusted third party TP performs eavesdropping detection with participants Bob and Alice.

[0041] Step 7: Semi-trusted third party TP from and Delete the decoy state and restore the sequence and Then, after pairing the photons at the same position in the two sequences, measurements are performed under the Bell basis;

[0042] Step 8: Alice and Bob verify the authenticity of the results published by TP.

[0043] In step 1 of this embodiment, S A (S B ) can be represented by a 2n-bit 0-1 sequence as

[0044] In step 3 of this embodiment, each Bell state Then TP separates all two particles in the Bell state, and the sequence composed of the first particle is recorded as S a , the sequence made by the second particle is denoted as S b .

[0045] In step 3 of this embodiment, the two-level quantum entangled state Bell state has four different states:

[0046] In step 4 of this embodiment, eavesdropping detection is as follows: Alice and Bob receive S a and S b Finally, particles at n positions are randomly selected to perform eavesdropping detection. They randomly negotiate to select a measurement basis (Z basis or X basis), measure the particles at these positions and compare the measurement results. If their measurement results are the same, there is no eavesdropping behavior and TP has not made any malicious behavior. The protocol goes to the next step. Otherwise, the protocol is re-executed. Through the first eavesdropping detection, the absence of the eavesdropper and the honesty of TP are verified.

[0047] In step 5 of this embodiment, the unitary transformation rule is as follows:

[0048] In the formula represents modular n addition, I, X, Y, Z are Pauli transformations, and Bob also uses the same rules to transform s b The particles in the unitary transformation operation In this way, Alice (Bob) will get a new sequence Alice and Bob simultaneously perform Pauli transformations on each quantum state without changing the measurement basis of the particle pair. Due to the entanglement of the particles, it is difficult for anyone to obtain the secret value of Alice and Bob through measurement.

[0049] In step 6 of this embodiment, the eavesdropping detection is: TP receives After that, particles at n positions are randomly selected to perform eavesdropping detection. They randomly negotiate to select a measurement basis, measure the particles at these positions and compare the measurement results. If their measurement results are the same, there is no eavesdropping or there is eavesdropping, but the eavesdropping is within the tolerable range, and the protocol proceeds to the next step. Otherwise, the protocol is re-executed and each quantum state is measured through TP to determine the equality or size relationship of Alice and Bob's secret values.

[0050] In step 7 of this embodiment, if each measurement result is consistent with the initial Bell state If the measurement results are the same, TP announces that Alice and Bob’s secret values ​​are equal. If some of the measurement results are different from the initial Bell state, TP announces the minimum value k of the different positions.

[0051] In step eight of this embodiment: if the secret values ​​published by Alice and Bob are equal, Alice and Bob calculate and The calculation results are exchanged. If the results are the same, the result announced by TP is considered correct. Otherwise, TP is considered untrustworthy and the protocol terminates.

[0052] In step eight of this embodiment, if TP announces the minimum value k in different single photon subscripts, Alice and Bob calculate and And exchange the calculation results. If the results are the same, continue to publish your own secret value and shared key k AB XOR value of 2 bits and If the two results are different, the result announced by TP is considered correct. At the same time, Alice and Bob and The value of can know the size of their secret value, otherwise, TP is considered untrustworthy and the protocol terminates.

[0053] The present invention is not limited to the above-described embodiments. Any structural changes made under the guidance of the present invention, which have the same or similar technical solutions as the present invention, should be understood to fall within the scope of protection of the present invention. The technologies, shapes, and structural parts not described in detail in the present invention are all well-known technologies.

Claims

1. A method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states, characterized in that, it includes the following steps: Step 1: The participants of the protocol, Alice and Bob, respectively have their own secret values S A and S B , and Alice and Bob share a secure n-bit key through QKD Step two: Alice and Bob share a collision - resistant hash function Hash(.) that resists quantum algorithms. With the assistance of a semi - trusted third party TP, Alice and Bob complete the comparison of the magnitudes of their secret values; Step 3: The semi-trusted third party TP prepares a sequence S containing 2n identical Bell states. The two particles of the Bell state are separated and form the sequence S a and S b , TP sends S a and S b to the participants Alice and Bob respectively; Step four: The semi - trusted third party TP performs eavesdropping detection with Alice and Bob; Step 5: After Alice and Bob delete the detected particles, the remaining particle sequences are respectively denoted as And Alice performs a unitary transformation operation on the particles in s based on her own secret value S A on s a by Next, Alice (Bob) is at Insert several single photons as decoy states to obtain a new sequence Then Alice (Bob) will Send to TP; Step six: The semi - trusted third party TP performs eavesdropping detection with the participating parties Bob and Alice; Step 7: The semi-trusted third party TP obtains from and Delete the decoy state and recover the sequence And Then pair the photons at the same positions in the two sequences and perform measurements in the Bell basis; Step eight: Alice and Bob verify the authenticity of the results announced by TP.

2. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 1, characterized in that, In step one, S A (S B ) can be represented by a 2n-bit 0-1 sequence as 3. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 1, characterized in that, In step three, for each Bell state (i = 1, 2, ..., 2n), TP separates the two particles of all Bell states, and the sequence formed by the first particles is denoted as S a , and the sequence formed by the second particles is denoted as S b .

4. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 3, characterized in that, In step three, there are four different states of the two-level quantum entanglement Bell state:

5. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 1, characterized in that, In step four, the eavesdropping detection is as follows: After Alice and Bob respectively receive S a and S b , randomly select the particles at n positions to perform eavesdropping detection, randomly select the measurement basis, measure the particles and compare the measurement results. If the measurement results are all the same, there is no eavesdropping behavior, and the protocol proceeds to the next step; otherwise, the protocol is executed again.

6. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 1, characterized in that, In step five, the unitary transformation rule is as follows: In the formula Denote modular n addition, I, X, Y, Z are Pauli transformations, and Bob also performs unitary transformation operations on the particles in s b in accordance with the same rules Alice (Bob) will get a new sequence 7. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 1, characterized in that, In step six, the eavesdropping detection is as follows: After TP receives , randomly select the particles at n positions to perform eavesdropping detection, negotiate and select a measurement basis, measure the particles and compare the measurement results. If the measurement results are all the same, there is no eavesdropping behavior, and the protocol proceeds to the next step. Otherwise, the protocol is executed again.

8. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 1, characterized in that, In step seven, if all measurement results are the same as the initial Bell state , the TP announces that the secret values of Alice and Bob are equal. If some measurement results are different from the initial Bell state, the TP announces the minimum value k of the positions where they are different.

9. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 1, characterized in that, In Step 8: If the secret values of Alice and Bob are equal, Alice and Bob respectively calculate and and exchange the results. If the results are the same, it is considered that the result announced by TP is correct; otherwise, TP is considered untrustworthy and the protocol terminates.

10. The method for comparing the magnitudes of two - party quantum secrets based on two - level Bell states according to claim 9, characterized in that, In step eight, if TP announces the minimum value k among different single-photon subscripts, Alice and Bob respectively calculate and and exchange the results. If the results are the same, they continue to announce the 2-bit XOR value of their secret values and the shared key k AB and If the two results are different, it is considered that the result announced by TP is correct. At the same time, Alice and Bob can know the magnitude of their secret values according to and Otherwise, it is considered that TP is untrustworthy and the protocol terminates.​

Images