Hidden quantum communication method based on quantum error correction code

Abstract

The invention discloses a hidden quantum communication method based on a quantum error correction code. The method comprises the following steps: a sender and a receiver generate keys and appoint the quantum error correction code and a hash function; the sender encodes coverage information and hidden information to obtain a coverage message and a hidden message, the Hash function values of the hidden message and the hidden information are embedded into the coverage message and rotated, and the coverage message is sent to the receiver to become a coverage disturbance message; the receiver obtains a hidden disturbance message and the Hash function value through unwinding, decodes the hidden disturbance message and the coverage disturbance message to obtain hidden disturbance information and original coverage information, and compares the disturbance Hash function value of the hidden disturbance information with the Hash function value to decide whether to give up communication; and the receiver calculates a concealment standard to judge whether the communication is concealed or not. According to the method, the problem of using the quantum depolarization channel to carry out covert communication is solved, and the detection of attack behaviors and higher accuracy are realized.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a covert quantum communication method based on quantum error correction code. Background Art

[0002] In today's era, with the development of modern information and communication technology, protecting sensitive information is an urgent need for secure communication. Quantum communication provides an unconditionally secure communication method for the transmission of sensitive information and has become a technology that has attracted much attention. However, in quantum communication, although the monitor cannot decipher sensitive information, it can still detect the transmission of sensitive information and destroy or intercept it, so the quantum communication method may still be attacked by the monitor. For this reason, covert quantum communication, as a method of covertly transmitting sensitive information, has been widely studied.

[0003] Covert quantum communication aims to hide sensitive information as covert information in cover information. Covert quantum communication methods based on quantum image steganography can hide covert information in redundant information of carriers such as images or videos. Covert quantum communication based on quantum key distribution protocol can hide covert information in the distributed key stream, thereby reducing the risk of detection by the monitor. Covert quantum communication methods based on quantum dense coding can use quantum dense coding to hide covert information in the distribution of auxiliary entangled resources for transmission, and can detect attacks by monitors.

[0004] However, the above-mentioned covert quantum communication method only considers the hiding of hidden information, and does not consider the situation that hidden information is easily affected by noise and errors occur during transmission. In the quantum information world, quantum is very susceptible to interference from noise and errors occur. In covert quantum communication, confidential information is the object to be protected, and its transmission accuracy should be guaranteed. Therefore, improving the accuracy and security of confidential information in covert quantum communication methods is an urgent problem to be solved. Summary of the invention

[0005] The purpose of the present invention is to provide a covert quantum communication method based on quantum error correction code, introduce a hash function authentication mechanism to detect the monitor's attack, improve security, and at the same time improve the accuracy of the covert information by performing quantum error correction coding on the covert information.

[0006] In order to achieve the purpose of the present invention, the present invention provides a covert quantum communication method based on quantum error correction code, which comprises the following steps:

[0007] Step 1: Preparation of both parties:

[0008] Step 1-1: The sender and receiver generate a random key through a shared quantum entanglement resource;

[0009] Step 1-2: The sender and the receiver agree on a quantum error correction code corresponding to the concealed information, a quantum error correction code corresponding to the cover information, and a hash function;

[0010] Step 2: Sender preparation:

[0011] Step 2-1: The sender performs quantum error correction encoding on the hidden information to obtain a hidden message, and calculates a hash function value of the hidden information;

[0012] Step 2-2: The sender performs quantum error correction encoding on the coverage information to obtain a coverage message;

[0013] Step 2-3: The sender embeds the concealed message and the hash function value into the cover message according to the key;

[0014] Step 2-4: the sender rotates the concealed message and the hash function value embedded in the cover message according to the key, and randomly rotates another small part of the cover message according to the error rate of the depolarized channel, and sends the cover message to the receiver through the depolarized channel as a cover disturbance message;

[0015] Step 3: Receiver derotates and decodes:

[0016] Step 3-1: After receiving the coverage disturbance message, the receiver locates and derotates the rotated concealed disturbance message and the hash function value in the coverage disturbance message according to the key;

[0017] Step 3-2: The receiving party performs quantum error correction decoding on the concealed disturbance message to obtain concealed disturbance information, and recalculates the disturbance hash function value of the concealed disturbance information;

[0018] Step 3-3: The receiving party compares the hash function value obtained after derotation with the perturbation hash function value obtained by calculation. If they are the same, the concealed perturbation information has not been attacked, otherwise the communication is abandoned.

[0019] Step 3-4: The receiving party performs quantum error correction decoding on the coverage disturbance message to obtain the original coverage information;

[0020] Step 4: Calculate the concealment standard based on the error rate of the actual depolarization channel and the error rate of the monitored depolarization channel believed by the monitor to determine whether the communication is concealed.

[0021] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, a covert quantum communication method based on quantum error correction code is implemented.

[0022] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a covert quantum communication method based on quantum error correction codes.

[0023] Compared with the prior art, the significant improvements of the present invention are: (1) the present invention performs quantum error correction encoding on the cover information so that it can be embedded in the hidden information to prevent detection by the monitor; (2) the present invention improves the accuracy of the hidden information by performing quantum error correction encoding on the hidden information; (3) the present invention realizes the detection of the monitor's attack behavior and improves security by introducing a hash function authentication mechanism.

[0024] In order to more clearly illustrate the functional characteristics and structural parameters of the present invention, further description is given below in conjunction with the accompanying drawings and specific implementation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0026] Figure 1 It is a model diagram of the concealed quantum communication system of the present invention;

[0027] Figure 2 It is a comparison diagram of simulation results in the present invention;

[0028] Figure 3 It is the concealment standard diagram in the present invention. DETAILED DESCRIPTION

[0029] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0030] A concealed quantum communication method based on quantum error correction code of the present invention is combined with Figure 1 The present invention uses quantum error correction codes to realize covert quantum communication on a depolarized channel. In the presence of a monitor, covert quantum communication is performed in a manner with a low detection probability. The specific contents are as follows:

[0031] Step 1: Preparation of both parties:

[0032] Step 1-1: The sender and receiver generate a random binary key through the shared quantum entanglement resource, the length of which is:

[0033]

[0034] Where N is the coverage message |φ C > quantum number, M is the hidden message |φ S >, h is the hash function value f of the hidden information |S> h (S) quantum number;

[0035] Step 1-2: The sender and the receiver agree on a quantum error correction code corresponding to the hidden information |S>, such as the [M, k2] quantum repetition code, and a quantum error correction code corresponding to the cover information |C>, such as the [N, k1] quantum error correction code, and a hash function.

[0036] Step 2: Sender preparation:

[0037] Step 2-1: For the hidden information |S>, the sender performs the [M, k2] quantum repetition coding to obtain the hidden message |φ s >, and calculate the hash function value f of the hidden information |S) h (S):

[0038] f h (S)=((((b×α+s0)×α+s1)×α+s2)…×α+s n-1 )mod H;

[0039] Where b is the initial hash value, α is the multiplication factor, and H is the large prime number used for modulus;

[0040] Step 2-2: For the coverage information |C>, the sender performs the [N, k1] quantum error correction coding to obtain the coverage message |φ C >

[0041] Step 2-3: The sender uses the key in the overlay message |φ C > randomly selects M quanta with the hidden message |φ s ) is replaced, and the overlay message |φ is randomly selected according to the key C >h quanta and the hash function value f h (S) make a replacement;

[0042] Step 2-4: For the depolarized channel △(ρ):

[0043] △(ρ)=(1-q)ρ+q / 3(XρX+YρY+ZρZ);

[0044] Wherein, q is the error rate of the depolarized channel, ρ is the input of the depolarized channel, X represents the bit flip error in the depolarized channel, Y represents the phase flip error in the depolarized channel, and Z represents the error of simultaneous bit and phase flip in the depolarized channel;

[0045] The sender performs a key operation on the overlay message |φ C >The hidden message embedded in |φ S > and the hash function value f h (S) performs rotation, i.e., performs X, Y or Z operation according to the key and randomly rotates the cover message |φ C >another (qN-Mh) quanta; then the rotated cover message |φ C >Sent to the receiver through the depolarized channel △(ρ) to become the coverage disturbance message |φ C ′>.

[0046] Step 3: Receiver derotates and decodes:

[0047] Step 3-1: For the received coverage disturbance message |φ C ′>, the receiver locates and derotates the overlay disturbance message |φ according to the key C The hidden perturbation message |φ rotated in ′> S ′> and the hash function value f h (S);

[0048] Step 3-2: The receiver derotates the concealed disturbance message |φ S ′>Perform the [M, k2] quantum error correction decoding to obtain the hidden disturbance information |S′>, and recalculate the disturbance hash function value f h (S′):

[0049] f h (S′)=((((b×α+s′0)×α+s′1)×α+s′2)…×α+s′ n-1 )mod H;

[0050] Where b is the initial hash value, α is the multiplication factor, and H is the large prime number used for modulus;

[0051] Step 3-3: The receiver compares the derotated hash function value f h (S) and the calculated perturbation hash function value f h (S′), if they are the same, then the hidden disturbance information |S′> has not been attacked, that is, it is the same as the hidden information |S>, otherwise the receiving party abandons this communication;

[0052] Step 3-4: The receiving party receives the coverage disturbance message |φ C ′>Perform the quantum error correction decoding [N, k1] to obtain the original coverage information |C>.

[0053] Step 4: Calculate the concealment standard based on the error rate of the actual depolarization channel and the error rate of the monitored depolarization channel believed by the monitor to determine whether the communication is concealed;

[0054] For the actual depolarization channel △ r (ρ):

[0055] Δ r ρ)=(1-r)ρ+r / 3(XρX+YρY+ZpZ);

[0056] Wherein, r represents the error rate of the actual depolarization channel;

[0057] For the monitoring depolarization channel △ p (ρ):

[0058] △ p (ρ)=(1-p)ρ+p / 3(XρX+YρY+ZpZ);

[0059] Where p represents the error rate of the monitoring depolarization channel and r = p + δ p , δ p The channel error rate difference represents the difference between the actual depolarization channel error rate and the monitored depolarization channel error rate. The concealment criterion is:

[0060]

[0061] in, and represent the actual depolarization channel for transmitting N quanta and the monitored depolarization channel as believed by the monitor, respectively; || ||◇ represents the diamond norm used to characterize the difference between the actual depolarization channel and the monitored depolarization channel as believed by the monitor; ε represents the upper limit of the concealment standard reached by the concealed quantum communication system, and

[0062] Example

[0063] An embodiment of the present invention is described in detail as follows. The simulation is implemented using Python 3.8 and runs in a PyCharm environment. [3, 1] quantum repetition code and [7, 1] quantum error correction code are selected for the hidden information |S> and the cover information |C> respectively. A one-bit quantum state |0> is selected as the hidden information |S>, and a three-bit quantum state |000> is selected as the cover information |C>. For the depolarized channel △(ρ), the depolarized noise quantum circuit provided by the Qiskit module is selected for simulation. Combined with Figure 2 , the accuracy of the covered information decreases as the actual depolarization channel error rate p increases. The reason is that the actual depolarization channel error rate, represents the depolarization noise. When the actual depolarization channel error rate, increases, the information transmitted in the channel is more susceptible to interference from the depolarization noise, thereby reducing the accuracy. Secondly, compared with other covert communication methods, when the actual depolarization channel error rate p is high, the accuracy of the covert information using the present invention will be significantly improved, thanks to the error correction capability of the quantum error correction code corresponding to the covert information.

[0064] In addition, for the concealment standard of concealed quantum communication, combined with Figure 3 , for the transmission of a coverage message of 1024 quantum numbers |φ C >The hidden quantum communication method, as the channel error rate difference δ p As the channel error rate difference δ p <0.1, the concealment criterion decreases with the increase of the error rate of the actual depolarized channel. Therefore, when the channel error rate p of the actual depolarized channel is large enough and the channel error rate difference δ p If it is small enough, the monitor will not be able to detect the hidden information.

[0065] It should be noted that, in this article, the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus.

[0066] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A covert quantum communication method based on quantum error correction code, characterized in that: The following steps are involved: Step 1: Preparation of both parties: Step 1-1: The sender and receiver generate a random key through a shared quantum entanglement resource; Step 1-2: The sender and the receiver agree on a quantum error correction code corresponding to the concealed information and a quantum error correction code corresponding to the cover information and a hash function; Step 2: Sender preparation: Step 2-1: The sender performs quantum error correction encoding on the hidden information to obtain a hidden message, and calculates a hash function value of the hidden information; Step 2-2: The sender performs quantum error correction encoding on the coverage information to obtain a coverage message; Step 2-3: The sender embeds the concealed message and the hash function value into the cover message according to the key; Step 2-4: the sender rotates the concealed message and the hash function value embedded in the cover message according to the key, and randomly rotates another small part of the cover message according to the error rate of the depolarized channel, and sends it to the receiver through the depolarized channel to become a cover disturbance message; Step 3: Receiver derotation and decoding: Step 3-1: After receiving the coverage disturbance message, the receiver locates and derotates the rotated concealed disturbance message and the hash function value in the coverage disturbance message according to the key; Step 3-2: The receiving party performs quantum error correction decoding on the concealed disturbance message to obtain concealed disturbance information, and recalculates the disturbance hash function value of the concealed disturbance information; Step 3-3: The receiving party compares the hash function value obtained after derotation with the perturbation hash function value obtained by calculation. If they are the same, the concealed perturbation information has not been attacked, otherwise the communication is abandoned. Step 3-4: The receiving party performs quantum error correction decoding on the coverage disturbance message to obtain the original coverage information; Step 4: Calculate the concealment standard based on the error rate of the actual depolarization channel and the error rate of the monitored depolarization channel believed by the monitor to determine whether the communication is concealed.

2. The quantum hidden communication method based on quantum error correction code according to claim 1 is characterized in that: The length L of the random key generated by both communicating parties in step 1-1 is: Wherein, N is the quantum number of the covering interest, M is the quantum number of the concealed message, and h is the quantum number of the hash function value.

3. The covert quantum communication method based on quantum error correction code according to claim 1 is characterized in that: In step 2-1, the sender performs [M, k2] quantum error correction coding on the hidden information |S> to obtain the hidden message |φ S >, and calculate the hash function value f of the hidden information |S> h (S): f h (S)=((((b×α+s0)×α+s1)×α+s2)…×α+s n-1 )mod H; Where b is the initial hash value, α is the multiplication factor, and H is a large prime number used for modulo.

4. The covert quantum communication method based on quantum error correction code according to claim 1 is characterized in that: In step 2-3, the sender sends the overlay message |φ according to the key. C > select M quanta with the hidden message |φ S > Replace and select h quanta and the hash function value f according to the key h (S) is replaced.

5. The covert quantum communication method based on quantum error correction code according to claim 1 is characterized in that: The depolarization channel △(ρ) in step 2-4 is: Δ(ρ)=(1-q)ρ+q / 3(XρX+YρY+ZρZ); Wherein, q is the error rate of the depolarized channel, ρ is the input of the depolarized channel, X is the bit flip error in the depolarized channel, Y is the phase flip error in the depolarized channel, and Z is the bit and phase flip error in the depolarized channel; The sender performs a key operation on the overlay message |φ C >The hidden message embedded in |φ S > and the hash function value f h (S) is rotated and the coverage message |φ is randomly rotated C >(qN-Mh) quanta, the rotation of the covered message |φ C >Sent to the receiver through the depolarized channel △(ρ) to become the coverage disturbance message |φ C ′>.

6. The covert quantum communication method based on quantum error correction code according to claim 1 is characterized in that: In step 3-1, the receiver locates and derotates the received coverage disturbance message |φ according to the key C The hidden perturbation message |φ rotated in ′> S ′> and the hash function value f h (S).

7. The covert quantum communication method based on quantum error correction code according to claim 1 is characterized in that: In step 3-2, the receiving party sends the concealed disturbance message |φ S ′>Perform [M, k2] quantum error correction decoding to obtain the hidden disturbance information |S′> and calculate the disturbance hash function value f h (S′): f h (S′)=((((b×α+s′0)×α+s′1)×α+s′2)…×α+s′ n-1 )mod H; Where b is the initial hash value, α is the multiplication factor, and H is a large prime number used for modulo.

8. The covert quantum communication method based on quantum error correction code according to claim 1 is characterized in that: The actual depolarization channel △rρ) in step 4 is: △ r (ρ)=(1-r)ρ+r / 3(XρX+YρY+ZρZ); Wherein, r represents the error rate of the actual depolarization channel, ρ is the input of the actual depolarization channel, X is the bit flip error in the actual depolarization channel, Y is the phase flip error in the actual depolarization channel, and Z is the error of simultaneous bit and phase flip in the depolarization channel; The monitor considers the monitoring depolarization channel △ p (ρ): △ p (ρ)=(1-p)ρ+p / 3(XρX+YρY+ZρZ); Where p represents the error rate of the monitoring depolarization channel and r = p + δ p , δ p The channel error rate difference represents the difference between the actual depolarization channel error rate and the monitored depolarization channel error rate; The concealment criteria are: in, and denote the monitoring depolarization channel and the actual depolarization channel for transmitting N quanta, respectively; || ||◇ is the diamond norm that can be used to characterize the difference between the monitoring depolarization channel and the actual depolarization channel; ε denotes the upper limit of the concealment standard reached by the concealed quantum communication method; and 9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, a covert quantum communication method based on quantum error correction code as described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, a covert quantum communication method based on quantum error correction code as described in any one of claims 1 to 8 is implemented.

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