Semi-quantum mutual identity authentication method and system based on single particle

Abstract

The invention relates to a semi-quantum mutual identity authentication method and system based on a single particle. The method comprises the following steps: determining a shared identity authentication key; the first authentication party selects a first calculation base or a second calculation base to generate a quantum bit according to the key bit value, and sends all the generated quantum bits to the second authentication party; the second authentication party measures or rearranges the received quantum bits according to the key bit value and compares the measurement result with the corresponding initial state, and if the measurement result and the corresponding initial state are the same, the first authentication party is considered to be legal; and the first authentication party receives the rearranged quantum bits and measures the quantum bits, and then compares a measurement result with a corresponding initial state, and if the measurement result is the same as the corresponding initial state, the second authentication party is considered to be legal. According to the invention, the simplicity and practicability of the quantum authentication process can be improved, and the problems of high resource consumption, dependence on a third party and incapability of identifying illegal identities in the existing scheme are effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum cryptography, and in particular to a semi-quantum mutual identity authentication method and system based on single particles. Background Art

[0002] With the development of technologies such as the Internet, social media, cloud computing, and the Internet of Things, the amount of data generated and stored has increased rapidly. Individuals, businesses, and governments rely on this data for daily operations and decision-making, making it an extremely valuable asset, so information protection has become increasingly important. This challenge is closely related to the basic tasks of cryptography: identity authentication and confidentiality, and ensuring secure and reliable identity authentication has become a serious challenge. With the advancement of quantum computers, current cryptographic systems that protect digital identities and sensitive data are increasingly vulnerable to quantum-based attacks. In this context, quantum identity authentication that can resist quantum attacks and achieve secure identity confirmation has become a key solution, and a series of quantum identity authentication protocols based on pre-shared entangled states and entanglement exchange have emerged. However, due to the limitations of technology and its physical properties, pre-shared entangled states are difficult to store for a long time, resulting in the low practicality of these protocols.

[0003] In order to reduce the consumption of quantum resources and reduce the difficulty of implementation, Boyer et al. proposed a quantum key distribution protocol in which one of the participants is classical in 2007, thus proposing the concept of semi-quantum. Zhou et al. proposed two semi-quantum identity authentication protocols with single photons in 2019, which are used to authenticate quantum Alice and classical Bob respectively, but they cannot simultaneously realize mutual authentication between quantum Alice and classical Bob. In the same year, a mutual semi-quantum authentication protocol based on GHZ-like states and W states was proposed to determine the identities of the two participants and ensure the credibility of important information. However, due to the complexity and difficulty of generating and operating multi-particle entangled states, the implementation difficulty and resource consumption of the protocol are further increased.

[0004] Recently, a novel quantum identity authentication protocol has been proposed based on the idea of ​​controlled secure direct quantum communication scheme, which allows two participants Alice and Bob to authenticate each other's identities with the help of a third party. However, when the identity authentication fails, it is impossible to determine whether the identity of Alice or Bob is illegal, and the introduction of the third party complicates the protocol. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a single-particle-based semi-quantum mutual identity authentication method and system, which can improve the simplicity and practicality of the authentication process and effectively solve the problems of high resource consumption, dependence on third parties, and inability to identify illegal identities in existing solutions.

[0006] The technical solution adopted by the present invention to solve the technical problem is: to provide a semi-quantum mutual identity authentication method based on a single particle, comprising the following steps:

[0007] Determining an identity authentication key shared by the first authenticator and the second authenticator;

[0008] The first authenticator selects to generate a quantum bit using the first computing basis or the second computing basis according to each bit value of the identity authentication key, and sends all the generated quantum bits to the second authenticator;

[0009] The second authenticator measures the quantum bits generated by the first computing base to obtain a first measurement result, or rearranges the quantum bits generated by the second computing base and reflects the rearranged result to the first authenticator, and publishes a rearranged order;

[0010] The first authentication party receives the rearranged quantum bits and performs measurement to obtain a second measurement result, and rearranges the second measurement result according to the rearrangement order announced by the second authentication party, and then compares the rearranged second measurement result with the second initial state. If they are the same, the second authentication party is deemed to be legitimate, otherwise the authentication is terminated, wherein the second initial state is the initial state of the quantum bits generated by the second computing base;

[0011] The second authenticator obtains the first initial state published by the first authenticator and compares it with the first measurement result. If they are the same, the first authenticator is considered legitimate, otherwise the authentication is terminated. The first initial state is the initial state of the quantum bit generated by the first computing base.

[0012] Further, the selecting, according to each bit value of the identity authentication key, to generate a quantum bit using the first computing basis or the second computing basis comprises:

[0013] If the current bit value of the identity authentication key is 0, a quantum bit is generated using the first computing basis, otherwise a quantum bit is generated using the second computing basis.

[0014] Furthermore, the first measurement result is obtained by measuring using the first computing base, and the second measurement result is obtained by measuring using the second computing base.

[0015] Furthermore, the first calculation basis is a Z basis, and the second calculation basis is an X basis.

[0016] Furthermore, the quantum bits are randomly generated based on the first computing basis or the second computing basis.

[0017] The present invention also provides a single-particle-based semi-quantum mutual identity authentication system, comprising an edge computing device and a distributed node;

[0018] The edge computing device is used to negotiate with the distributed node to determine a shared identity authentication key, and select a first computing base or a second computing base to generate a quantum bit according to each bit value of the identity authentication key, and then send all the generated quantum bits to the distributed node; the edge computing device is also used to receive the quantum bits rearranged by the distributed node and measure them to obtain a second measurement result, and then compare the second measurement result with the second initial state. If they are the same, the distributed node is considered to be legitimate, otherwise the authentication is terminated, wherein the second initial state is the initial state of the quantum bit generated by the second computing base;

[0019] The distributed node is used to measure the quantum bits generated by the first computing base according to the bit value of the identity authentication key to obtain a first measurement result, or to rearrange the quantum bits generated by the second computing base and reflect them to the edge computing device; the distributed node is also used to obtain the first initial state published by the edge computing device and compare it with the first measurement result. If they are the same, the edge computing device is considered legal, otherwise the authentication is terminated, wherein the first initial state is the initial state of the quantum bits generated by the first computing base.

[0020] Further, the selecting, according to each bit value of the identity authentication key, to generate a quantum bit using the first computing basis or the second computing basis comprises:

[0021] If the current bit value of the identity authentication key is 0, a quantum bit is generated using the first computing basis, otherwise a quantum bit is generated using the second computing basis.

[0022] Further, measuring the quantum bits generated by the first computing basis to obtain a first measurement result according to the bit value of the identity authentication key, or rearranging the quantum bits generated by the second computing basis, includes:

[0023] If the current bit of the identity authentication key is 0, the quantum bits generated by the first computing base are measured to obtain a first measurement result; otherwise, the quantum bits generated by the second computing base are rearranged.

[0024] Furthermore, the first measurement result is obtained by measuring using the first computing base, and the second measurement result is obtained by measuring using the second computing base.

[0025] Furthermore, the first calculation basis is a Z basis, and the second calculation basis is an X basis.

[0026] Furthermore, the quantum bits are randomly generated based on the first computing basis or the second computing basis.

[0027] Furthermore, the distributed node rearranges and reflects the quantum bits through a coil deployed at the communication interface, and measures the quantum bits through a low-precision single-particle detector deployed at the communication interface.

[0028] Furthermore, the edge computing device generates quantum bits through a single-photon source deployed at the communication interface, and measures the quantum bits through a low-precision single-particle detector deployed at the communication interface.

[0029] Furthermore, the method also includes the step of establishing a communication link between the edge computing device and the distributed node if both are legal.

[0030] Beneficial Effects

[0031] Due to the adoption of the above-mentioned technical scheme, the present invention has the following advantages and positive effects compared with the prior art: the authentication method of the present invention is based on single-particle resources, which significantly reduces the use of quantum resources, reduces the complexity of the system and the difficulty of operation; the present invention does not rely on the participation of a third party, reduces the structural complexity of the protocol, and can achieve two-way identity authentication between the first authenticator as a powerful quantum communicator and the second authenticator as a classical participant through simple measurement operations; if the authentication process fails, the method proposed by the present invention can immediately distinguish which identity among the communicators is illegal, providing a guarantee for further security protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of a first embodiment of the present invention;

[0033] Figure 2 is a graph showing the relationship between the probability p of detecting an Eve impersonation attack and the length n of the identity authentication key according to the first embodiment of the present invention;

[0034] Figure 3 Schematic diagram of a system according to a second embodiment of the present invention. DETAILED DESCRIPTION

[0035] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the appended claims of the application equally.

[0036] The first embodiment of the present invention relates to a single-particle based semi-quantum mutual identity authentication method. First, it is assumed that the first authenticator Alice is a powerful quantum communicator, while the second authenticator Bob has only classical capabilities. When accessing a quantum channel, the classical Bob can only perform the following four operations: (a) generate quantum bits in a fixed computational basis (Z basis) {0, 1}; (b) measure quantum bits on a fixed Z basis {0, 1}; (c) reflect quantum bits without interference; (d) reorder quantum bits (through different delay lines). For communicators, ensuring security by authenticating the other party's identity before communication is an effective measure.

[0037] Alice and Bob pre-share a key sequence As the authentication key, n is the number of bits of the authentication key. Assume that the quantum channel is noiseless and lossless. In order to achieve mutual authentication between Alice and Bob, Figure 1 Specific steps of the protocol shown are described.

[0038] Step 1: Alice authenticates the key K i (i=1,2,…,n) Generate each identity authentication qubit Q i Specifically, if K i is 0, Alice randomly generates a quantum bit Q in the Z basis {0, 1} i , otherwise she randomly generates qubits Q in the X basis {+, -} i . Alice then sends these qubits to Bob.

[0039] Step 2: After receiving the sequence, Bob performs corresponding operations on each quantum bit according to the pre-shared authentication key.

[0040] ①For K i = 0, Bob measures it in the Z basis and obtains MR Z result;

[0041] ②For K i =1, Bob randomly reorders the quantum bits and reflects the rearranged result to Alice, while publishing the rearranged order.

[0042] Step 3: After receiving all reflected qubits, Alice measures them in the X basis and obtains the measurement results. At the same time, the initial state IS of the qubits generated in the Z basis is announced. Z .

[0043] Step 4: Bob sends his measurement results to MR ZCompare with the initial state IS published by Alice Z , if MR Z With IS Z If the reflected qubits are different, the protocol restarts; otherwise, Bob recognizes Alice as the legitimate communicator and publishes the rearranged order of those reflected qubits.

[0044] Step 5: Alice restores the order of her measurement results according to the rearrangement order published by Bob to obtain MR X , by taking the measurement result MR X The initial state IS of the quantum bit generated in the X basis X By comparing, Alice can successfully authenticate Bob. If the comparison results are the same, Bob's identity is legitimate; otherwise, Bob is an illegal communicator.

[0045] The security of the above protocol is analyzed below. Assuming that the attacker Eve has full quantum capabilities, she can access the quantum channel and perform attack actions, pretending to be a legitimate participant or stealing the secret information of the authentication key. By specifically analyzing four different attack strategies, it is verified that the protocol proposed in this invention is resistant to these attacks.

[0046] (1) Impersonation attack

[0047] An impersonation attack is an attempt to gain unauthorized access to protected information or information systems by pretending to be a legitimate actor. Depending on who she is impersonating, Eve, the malicious attacker, can choose one of two strategies to perform an impersonation attack:

[0048] ① If the attacker Eve impersonates Alice, she will try to complete the false authentication by randomly generating and publishing the initial state. Since Eve knows nothing about the pre-shared authentication key K, she can only randomly generate each qubit in the Z basis or X basis. In addition, Eve must randomly publish the initial state in step 3 because she does not know which qubit should actually be prepared in the Z basis and eventually measured by Bob in the Z basis. The probability of each initial state published by Eve correctly is one in two.

[0049] If there are n2 quantum bits that can detect Eve's attack, then Eve's attack can be detected by Therefore, when n is large enough, it is difficult for Eve to be detected by eavesdropping.

[0050] ② If the attacker Eve pretends to be Bob, she will not be able to perform the correct operation on the correct qubit due to the lack of a pre-shared authentication key K. If Eve reflects qubits generated in the Z basis, or if she publishes an incorrect rearrangement of the order of these reflected qubits so that Alice arranges the measurements in the wrong order, she will introduce errors.

[0051] For Eve, The probability of reflecting back m qubits generated in basis X from qubits is Under this condition, the reflected The probability that k qubits out of qubits are in the wrong position is Where D(x) is the staggered formula e is a natural constant. For a qubit in the wrong position, the probability of passing detection is one in two. Now we can calculate the probability p that Eve cannot pass eavesdropping detection: When n is large enough, p is approximately 1, so it is difficult for Eve to pass eavesdropping detection. The relationship between p and n is as follows: Figure 2 shown.

[0052] (2) Intercept-Measure-Retransmit Attack

[0053] In an intercept-measure-replay attack, the attacker Eve tries to obtain some information about the authentication key without being detected. She can adopt the following two strategies.

[0054] Eve chooses to intercept the sequence that Alice sent to Bob in step 1 and measure each qubit. However, the only effect that the different authentication keys have on the qubits is the difference in the basis. Eve cannot infer the original basis of the particle from her measurements and therefore knows nothing about the key.

[0055] Eve intercepts the sequence sent by Alice and prepares a fake sequence in basis X, which she then resends to Bob in step 1. Afterwards, she intercepts the qubits reflected by Bob, measures them in step 2, and tries to get information about the operations performed by Bob. Although Eve can measure all qubits in basis X and knows the original states of these qubits, she cannot obtain the positions of these qubits originally through measurement. In addition, since Bob reordered the qubits, no one except Bob knows the original order before returning them to Alice.

[0056] In summary, Eve cannot know the state of the qubit with certainty through her measurements. More importantly, Alice and Bob can easily detect Eve’s presence in eavesdropping. Therefore, Eve cannot obtain any useful information from the intercept-measure-retransmit attack.

[0057] (3) Entanglement Measurement Attack

[0058] In an entanglement measurement attack, when a quantum bit is sent from Alice to Bob, the attacker Eve performs a unitary operation U F The sent qubit is entangled with the auxiliary qubit |ε>. F Afterwards, the following relationships should be established:

[0059] U F (|0>|ε>)=|0>|ε 00 >+|1>|ε 01 >,(1)

[0060] U F (|1>|ε>)=|0>|ε 10 >+|1>|ε 11 >,(2)

[0061]

[0062] where |ε 00 >,|ε 01 >,|ε 10 > and |ε 11 > represents the unnormalized state of Eve detection state.

[0063] Eve then lets the qubits continue to be sent to Bob. After the transmission, Eve measures the auxiliary qubit to obtain Bob's operation. When half of the qubits are reflected back to Alice by Bob, since Eve does not know the order in which Bob rearranged the qubits, she cannot perform another unitary operation on these qubits and their corresponding entangled auxiliary qubits to disentangle them. In order to pass eavesdropping detection without introducing any errors, it must meet the following conditions:

[0064] U F (|0|ε>)=|0>|ε 00 >,(5)

[0065] U F (|1>|ε>)=|1|ε 11 >,(6)

[0066]

[0067] According to the above equation, if Eve cannot be detected during eavesdropping, her measurement results cannot help her distinguish the initial preparation basis of the qubits, that is, the contents of the authentication key K. Therefore, Eve cannot extract any valuable information through the entanglement measurement attack.

[0068] (4) Trojan Horse Attack

[0069] Since our protocol is a two-way communication protocol, the attacker Eve may implement a Trojan horse attack to obtain secret information. She entangles invisible photons to the qubits sent from Alice to Bob to perform an invisible photon eavesdropping attack. By analyzing the invisible photons in those qubits sent by Bob to Alice, Eve tries to obtain Bob's operations. However, by applying photon number splitters and wavelength filter devices, malicious operations can be easily resisted.

[0070] The following further describes the implementation by comparing this implementation with the existing protocol.

[0071] As can be seen from Table 1 below, previous protocols have many problems and limitations. For example, protocols that only have one-way identity authentication capabilities need to be executed repeatedly to achieve two-way identity authentication, which increases the consumption of operations; protocols that require all communicators to have full quantum capabilities make their actual implementation difficult; the implementation of some protocols may need to rely on GHZ-like states and W states, and the requirements for generating and operating these multi-particle entangled states are more complex, further increasing the difficulty of protocol implementation and resource consumption. The attribute that the authentication failure cannot determine which participant's identity is illegal reduces the usability of the protocol; in addition, the participation of semi-trusted third parties also increases the complexity and trust risk of the protocol.

[0072] Table 1 Comparison with previous quantum identity authentication protocols

[0073]

[0074] The quantum authentication protocol proposed in this implementation has the following advantages:

[0075] First, the protocol is based on single-particle resources, which significantly reduces the use of quantum resources and reduces the complexity and difficulty of operation of the system;

[0076] Secondly, the scheme does not rely on the participation of a third party, which reduces the structural complexity of the protocol. At the same time, two-way identity authentication between quantum and classical participants can be achieved through simple measurement operations.

[0077] In addition, if the authentication process fails, the protocol proposed by the present invention can immediately distinguish which identity among the communicators is illegal, which provides a guarantee for further security protection.

[0078] In summary, the present invention not only improves the simplicity and practicality of the authentication process, but also effectively solves the key problems of the existing solutions such as high resource consumption, reliance on third parties, and inability to identify illegal identities. It can be seen that the protocol proposed by the present invention has advantages over previous protocols.

[0079] The second embodiment of the present invention relates to a single-particle based semi-quantum mutual identity authentication system, which is used to perform the method in the first embodiment, such as Figure 3 As shown, it includes edge computing devices and IoT distributed nodes.

[0080] The operation of the power grid system depends on the communication and data exchange between a large number of devices and nodes. In particular, in the scenario of the power Internet of Things (IoT), edge-to-end communication is a key link. The communication network is responsible for transmitting control signals and data. The confidentiality of data during transmission is crucial to the security and stability of the power grid. If the identity authentication link is not secure, attackers may impersonate legitimate devices, thereby affecting the operation of the entire power grid. Specifically, when the power grid control center issues operation instructions to the distributed nodes of the power grid system, whether the illegal attackers impersonate the control center to issue false instructions, eavesdrop on the communication process to obtain instructions, or impersonate the distributed nodes to return error responses, it will affect the safe and stable operation of the power system.

[0081] Unlike classical identity authentication methods, quantum identity authentication uses the principles of quantum mechanics to build a secure identity authentication process, which can essentially prevent eavesdropping and man-in-the-middle attacks. It can ensure the authenticity of the identities of both parties in the system, thereby preventing data from being tampered with or stolen during transmission, preventing unauthorized devices from accessing the power grid system, and thus ensuring the communication security between the power grid control center and each distributed node.

[0082] In the edge-to-end communication scenario of the power Internet of Things, there are a large number of distributed equipment terminals (end devices) such as distributed energy, energy storage, charging piles and controllable loads. These equipment terminals often only have classical computing capabilities due to cost and performance limitations, while the grid edge computing devices (edge ​​devices) have stronger processing capabilities and can support full quantum identity authentication. Therefore, in this scenario, reasonable equipment deployment is required to ensure secure communication. The specific deployment plan is as follows:

[0083] The communication interface of the edge device is equipped with a single photon source and a high-precision single-particle detector. Coils and low-precision single-particle detectors are deployed at the communication interface of the distributed node to receive and operate quantum bits from the edge computing device.

[0084] When the edge computing device communicates with the IoT distributed node, both parties must first verify their identities. Using the pre-shared authentication key, the edge device uses a single-photon source to generate the authenticated qubits and distributes them to the distributed nodes. Based on the authentication key, the distributed node chooses to use a coil to rearrange and reflect the qubits, or to use a low-precision detector to measure the qubits in the Z basis. The edge device uses a high-precision detector to perform an X-basis measurement on the qubits reflected by the distributed node. The distributed node compares the measurement results with the results published by the edge device. If they are inconsistent, the communication will be cut off and the abnormal situation will be reported. Similarly, the edge computing device also compares the measurement results after restoring the rearranged order with the originally prepared state. If they are consistent, the identity of the distributed node is confirmed to be legal. Otherwise, it is deemed illegal, recorded and processed according to the process.

[0085] In this way, the two parties authenticate each other's identities and form an edge-to-end quantum authentication link, ensuring that the communication path from the edge computing device to the distributed node is secure and reliable. They can use pre-shared keys or execute quantum key distribution protocols to negotiate keys, and then conduct secure, confidential and reliable communication.

[0086] By deploying full quantum and semi-quantum devices on edge devices and end devices respectively in the power Internet of Things and executing the quantum identity authentication protocol proposed in this invention, the security of edge-end communication can be ensured, thereby greatly improving the overall security and stability of the power grid system.

[0087] This invention provides an advanced and secure quantum identity authentication mechanism for the power grid system, which can effectively resist possible quantum computing attacks in the future and ensure the communication security, reliable operation and data confidentiality of the power system. As the power grid gradually transforms to intelligent, distributed management and automation, the application of quantum identity authentication protocols will become increasingly important and become a core component of power infrastructure security.

Claims

1. A semi-quantum mutual identity authentication method based on a single particle, characterized in that: The following steps are involved: Determining an identity authentication key shared by the first authenticator and the second authenticator; The first authenticator selects to generate a quantum bit using the first computing basis or the second computing basis according to each bit value of the identity authentication key, and sends all the generated quantum bits to the second authenticator; The second authenticator measures the quantum bits generated by the first computing base to obtain a first measurement result, or rearranges the quantum bits generated by the second computing base and reflects the rearranged result to the first authenticator, and publishes a rearranged order; The first authentication party receives the rearranged quantum bits and performs measurement to obtain a second measurement result, and rearranges the second measurement result according to the rearrangement order announced by the second authentication party, and then compares the rearranged second measurement result with the second initial state. If they are the same, the second authentication party is deemed to be legitimate, otherwise the authentication is terminated, wherein the second initial state is the initial state of the quantum bits generated by the second computing base; The second authenticator obtains the first initial state published by the first authenticator and compares it with the first measurement result. If they are the same, the first authenticator is considered legitimate, otherwise the authentication is terminated. The first initial state is the initial state of the quantum bit generated by the first computing base.

2. The method according to claim 1, characterized in that The step of selecting a first computing basis or a second computing basis to generate a quantum bit according to each bit value of the identity authentication key comprises: If the current bit value of the identity authentication key is 0, a quantum bit is generated using the first computing basis, otherwise a quantum bit is generated using the second computing basis.

3. The method according to claim 2, characterized in that The first measurement result is obtained by measuring using the first computing base, and the second measurement result is obtained by measuring using the second computing base.

4. The method according to claim 1, characterized in that: The first calculation basis is a Z basis, and the second calculation basis is an X basis.

5. The method according to claim 1, characterized in that The quantum bits are randomly generated based on the first computing basis or the second computing basis.

6. A semi-quantum mutual identity authentication system based on a single particle, characterized in that: Includes edge computing devices and distributed nodes; The edge computing device is used to negotiate with the distributed node to determine a shared identity authentication key, and select a first computing base or a second computing base to generate a quantum bit according to each bit value of the identity authentication key, and then send all the generated quantum bits to the distributed node; The edge computing device is further used to receive the quantum bits rearranged by the distributed node and measure them to obtain a second measurement result, and then compare the second measurement result with the second initial state. If they are the same, the distributed node is considered to be legitimate, otherwise the authentication is terminated, wherein the second initial state is the initial state of the quantum bit generated by the second computing base; The distributed node is used to measure the quantum bits generated by the first computing base according to the bit value of the identity authentication key to obtain a first measurement result, or to rearrange the quantum bits generated by the second computing base and reflect them to the edge computing device; the distributed node is also used to obtain the first initial state published by the edge computing device and compare it with the first measurement result. If they are the same, the edge computing device is considered legal, otherwise the authentication is terminated, wherein the first initial state is the initial state of the quantum bits generated by the first computing base.

7. The method according to claim 6, characterized in that The distributed node rearranges and reflects the quantum bits through a coil deployed at the communication interface, and measures the quantum bits through a low-precision single-particle detector deployed at the communication interface.

8. The method according to claim 6, characterized in that The edge computing device generates quantum bits through a single photon source deployed at the communication interface, and measures the quantum bits through a low-precision single particle detector deployed at the communication interface.

9. The method according to claim 6, characterized in that The method also includes the step of establishing a communication link between the edge computing device and the distributed node if both are legal.

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