A Bell-state-based authenticated multi-party quantum key agreement method and system

Abstract

The present invention discloses a Bell-state-based authenticated multi-party quantum key negotiation method and system, with m-1 participants, P i (i=1,2,...,m‑1), each of which holds its own n-bit secret string #imgabs0# Each participant has an identity information ID of length l i In order to ensure the legitimacy of the participants’ identities, P i (i = 1, 2, …, N-1) require identity authentication with a semi-trusted third party, P0, and each participant shares #imgabs1# with P0. After executing the following steps, these participants will obtain a negotiated key #imgabs3# of approximately #imgabs2# length. As can be seen, Bell states are leveraged to authenticate user identities with the help of a semi-trusted third party, resisting impersonation attacks. Bell states are used as information carriers and transmitted between participants. Encoding operations are designed using quantum state differentiation to ensure the correctness and security of the proposed protocol, which can resist collusion attacks among participants.

Description

Technical Field

[0001] The present invention relates to the field of information transmission technology, and in particular to a Bell-state-based authenticated multi-party quantum key negotiation method and system. Background Art

[0002] Quantum key agreement (QKA) is a key branch of quantum cryptography. It allows two or more users to reach consensus on the same key, with both parties having influence over the key. Compared to quantum key distribution, QKA prioritizes protocol fairness and user privacy. As a primary key management method, key agreement is a crucial cryptographic primitive and has been widely used in secure multi-party computation, access control, electronic auctions, and other fields.

[0003] In 2004, Zhou et al. proposed the first QKA protocol, in which two users leverage quantum teleportation to negotiate a key. Later, in 2013, Shi and Zhong proposed the first multi-party QKA protocol (MQKA) based on entanglement exchange. Unfortunately, both protocols were insecure. Subsequently, several MQKA protocols were proposed leveraging various properties of quantum mechanics. These protocols can be divided into three categories based on the transmission structure of signal particles: complete graph, tree, and ring. Compared to the first two types, ring MQKA (CMQKA) offers higher efficiency and feasibility. Therefore, most existing MQKA protocols belong to the third type. However, existing research has shown that most CMQKA protocols are insecure because they are vulnerable to collusion attacks. Furthermore, there is the possibility of impersonation attacks, which can occur during the actual execution of the protocol. The attacker can be an external attacker or a dishonest participant within the protocol. They hope to impersonate a legitimate participant and directly participate in the protocol, executing every step of the protocol without being detected and obtaining the final negotiated key or other participants' private information. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a Bell-state-based authenticated multi-party quantum key agreement method and system to prevent collusion attacks and ensure that the proposed protocol is correct and secure.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A Bell-state-based authenticated multi-party quantum key agreement method comprises the following steps:

[0007] S1, the third-party terminal P0 obtains the participant terminal P i(i=1,2,...,m-1) number (m-1), calculate the authentication information B of each participant terminal i , get the hash value of the third-party terminal

[0008] S2, each participant terminal P i Generate a set of random bit strings A i , then according to A i and holds the secret string Calculate the bit string C i ;

[0009] S3, each participant terminal P i Randomly generate n Bell states and obtain two ordered particle sequences:

[0010]

[0011]

[0012] Each participant terminal P i All will Send to the next participant terminal Among them, the last participant terminal P m-1 Q m-1→0 Sent to the first participant terminal P0;

[0013] S4. Assume l=1 and repeat the following m-1 times:

[0014] According to the received signal particle sequence Each participant P i (i=1,...,m-1) according to its string A i [l], B i [l] and C i [l] Perform encoding operations to obtain new

[0015] Each participant terminal P i All new Send to the next participant terminal Among them, the last participant terminal P m-1 Q m-1→0 Send to the first participant terminal P0, set l = l + 1;

[0016] S5. Each participant terminal P i For two particle sequences and R i Each pair of particles is measured in Bell state, and the measurement results are obtained

[0017] S6. All participant terminals P i according to Perform eavesdropping detection, if passed, all participants' terminals P i The key generated during the eavesdropping detection process will cause the protocol to be abandoned if it fails.

[0018] In order to solve the above technical problems, another technical solution adopted by the present invention is:

[0019] A Bell-state-based authenticated multi-party quantum key agreement system includes a third-party terminal and at least two participant terminals, wherein the third-party terminal and the participant terminals each include a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method when executing the computer program.

[0020] The present invention provides a method and system for authenticated multi-party quantum key agreement based on Bell states. Bell states are used as information carriers and transmitted between participants, who embed their secrets into traveling particles through specific encoding operations. In this way, all participants simultaneously obtain the same negotiated key at the end of the protocol, which is the sum of their secret inputs. Quantum state differentiation technology is used to design the encoding operations, ensuring that the proposed protocol is correct and secure, and can resist collusion attacks by multiple participants. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of a flow chart of a Bell-state-based authenticated multi-party quantum key agreement method according to an embodiment of the present invention;

[0022] Figure 2 A schematic diagram of data flow for modeling a database involved in an embodiment of the present invention;

[0023] Figure 3 This is a schematic structural diagram of a Bell-state-based authenticated multi-party quantum key agreement system according to an embodiment of the present invention;

[0024] Figure 4 This is a schematic structural diagram of a third-party terminal according to an embodiment of the present invention;

[0025] Figure 5 Schematic diagram of the structure of a participant terminal according to an embodiment of the present invention.

[0026] Description of labels:

[0027] 1. A Bell-state-based authenticated multi-party quantum key agreement system; 2. A third-party terminal; 3. A participant terminal. DETAILED DESCRIPTION

[0028] To illustrate the technical content, achieved objectives and effects of the present invention in detail, the following description is given in conjunction with the embodiments and accompanying drawings.

[0029] Please refer to Figures 1 to 2 , a method,

[0030] A Bell-state-based authenticated multi-party quantum key agreement method comprises the following steps:

[0031] S1, the third-party terminal P0 obtains the participant terminal P i (i=1,2,...,m-1) number (m-1), calculate the authentication information B of each participant terminal i , get the hash value of the third-party terminal

[0032] S2, each participant terminal P i Generate a set of random bit strings A i , then according to A i and holds the secret string Calculate the bit string C i ;

[0033] S3, each participant terminal P i Randomly generate n Bell states and obtain two ordered particle sequences:

[0034]

[0035]

[0036] Each participant terminal P i All will Send to the next participant terminal Among them, the last participant terminal P m-1 Q m-1→0 Sent to the first participant terminal P0;

[0037] S4. Assume l=1 and repeat the following m-1 times:

[0038] According to the received signal particle sequence Each participant P i (i=1,...,m-1) according to its string A i [l], B i [l] and C i [l] Perform encoding operations to obtain new

[0039] Each participant terminal P i All new Send to the next participant terminal Among them, the last participant terminal P m-1 Q m-1→0 Send to the first participant terminal P0, set l = l + 1;

[0040] S5. Each participant terminal P i For two particle sequences and R i Each pair of particles is measured in Bell state, and the measurement results are obtained

[0041] S6. All participant terminals P i according to Perform eavesdropping detection, if passed, all participants' terminals P i The key generated during the eavesdropping detection process will cause the protocol to be abandoned if it fails.

[0042] As can be seen from the above description, the beneficial effects of the present invention lie in: a Bell-state-based authenticated multi-party quantum key agreement method and system. Bell states are used as information carriers and transmitted between participants. Participants embed their secrets into traveling particles through specific encoding operations. In this way, all participants simultaneously obtain the same negotiated key at the end of the protocol, which is the sum of their secret inputs. Here, the encoding operation is designed using quantum state differentiation technology, ensuring that the proposed protocol is correct and secure, and can resist collusion attacks by multiple participants.

[0043] The step S1 specifically includes:

[0044] S1, the third-party terminal P0 obtains the participant terminal P i (i=1,2,...,m-1) number (m-1), generate random number r0 and make it public to all participant terminals, and obtain the random number r generated by all participant terminals i , select a hash function h from the hash family: 2 * →2 (m-1)n And make it public to all participant terminals, calculate the authentication information of each participant terminal To obtain the hash value of the third-party terminal In the formula, || represents string concatenation, ID i Represents the i-th participant terminal P i Identity information, r i A random number generated for participant i;

[0045] The calculation of the authentication information B of each participant terminal i It is calculated according to the following formula:

[0046]

[0047] Among them, the function It will Expand to a bit string of the same length as IDi||ri||r0, and then perform a bit-by-bit XOR operation on the two bit strings to obtain Perform a hash operation on the bit string to obtain the corresponding hash value Bi, where For participant P i The private key held.

[0048] From the above description, it can be seen that a method for calculating authentication information is given.

[0049] Furthermore, the step S2 specifically includes:

[0050] Each participant terminal P i Generate a random string of (m-1)n bits:

[0051] A i ={A i [1],A i [2],…,A i [m-1]|A i [k]=a i 1 [k]…a i n [k],a i j [k]∈{0,1}};

[0052] Where A i is the i-th participant terminal P i The generated random string;

[0053] Each participant terminal P i According to its own random string A i and holds the n-bit secret string The calculation results in a string of m-1 n-length bit strings:

[0054] C i ={C i [1],C i [2],…,C i [m-1]|C i [k] = c i 1 [k]...c i n [k],c i j [k]∈{0,1}};

[0055] in, And k=1,2,...,m-1,j=1,2,...,n.

[0056] In this embodiment, the value corresponding to the third-party terminal P0 is A0=C0=00…0

[0057] From the above description, it can be seen that the calculation method and specific implementation method of the secret string are given.

[0058] Furthermore, in step S3, in the two ordered particle sequences, the initial state of each two quantum pairs is:

[0059]

[0060] From the above description, we can see that the constraints for generating two particle sequences are given.

[0061] Furthermore, in step S4, each participant P i According to its string A i [l], B i [l] and C i [l] The encoding operation is performed on the sequence The jth particle Perform local unitary operation to get new

[0062] It can be seen from the above description that the encoding operation is realized.

[0063] Furthermore, the j-th particle Perform local unitary operations, specifically:

[0064] Perform unitary operation in:

[0065] U 0,0 =I=|0><0|+|1><1|,U 0,1 =X=|0><1|+|1><0|;

[0066] U 1,0 =Z=|0><0|-|1><1|,U 1,1 =iY=|0><1|-|1><0|;

[0067]

[0068] It can be seen from the above description that a specific implementation of the unitary operation is given.

[0069] Furthermore, the step S5 specifically includes:

[0070] Each participant terminal P i For two particle sequences and R i For each pair of particles, Bell state measurements are performed and the results are obtained:

[0071]

[0072] According to n measurement results, it is deduced in

[0073] It can be seen from the above description that a specific implementation method of Bell state measurement and Si is given.

[0074] Furthermore, the step S6 specifically includes:

[0075] The third-party terminal P0 calculates a bit sequence of length n based on B0, namely All participant terminals P i According to the bit sequence D Divide into sample sequences and information sequence

[0076] Each participant terminal P i Calculate δ based on D = (d1×2 n-1 +d2×2 n-2 +…+d n ×2 0 ) modulo n1 and disclose T i ', Each participant terminal P i String m into T i 'The new n1 bit sequence T' and its own T i For comparison, if all T i are equal to T', then all participants accept K=K0=K1=…=K m-1 as the original negotiated key, otherwise the protocol is abandoned.

[0077] From the above description, it can be seen that a specific method for eavesdropping detection is given.

[0078] Furthermore, the sequence is converted according to the bit sequence D Divide into sample sequences and information sequence Specifically:

[0079] If d j If the value is equal to 0, the corresponding bit is selected As samples to form a sample sequence The remaining bits form the information sequence

[0080] From the above description, it can be seen that the sequence is converted into Divide into sample sequences and information sequence

[0081] A Bell-state-based authenticated multi-party quantum key agreement system includes a third-party terminal and at least two participant terminals, wherein the third-party terminal and the participant terminals each include a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method when executing the computer program.

[0082] The present invention is applied to information transmission with multiple participants to avoid collusion attacks.

[0083] Please refer to Figures 1 to 2 , embodiment 1 of the present invention is:

[0084] A Bell-state-based authenticated multi-party quantum key agreement method comprises the following steps:

[0085] S1, the third-party terminal P0 obtains the participant terminal P i (i=1,2,…,m-1) number (m-1), calculate the authentication information B of each participant terminal i , get the hash value of the third-party terminal

[0086] Specifically, the third-party terminal P0 obtains the participant terminal P i (i=1,2,…,m-1) number (m-1), generate random number r0 and make it public to all participant terminals, and obtain the random number r generated by all participant terminals i , select a hash function h:2 from the hash family * →2 (m-1)n And make it public to all participant terminals, calculate the authentication information of each participant terminal To obtain the hash value of the third-party terminal In the formula, || represents string concatenation, ID i Represents the i-th participant terminal P i Identity information, r i A random number generated for participant i.

[0087] Specifically, it is calculated according to the following formula:

[0088]

[0089] Here, the function First Expand to a bit string of the same length as IDi||ri||r0, and then perform a bit-by-bit XOR operation on the two bit strings to obtain Finally, the bit string is hashed to obtain the corresponding hash value B i

[0090] S2, each participant terminal P i Generate a set of random bit strings A i , then according to A i and holds the secret string Calculate the bit string C i ;

[0091] Specifically, each participant terminal P i Generate a random string of (m-1)n bits:

[0092] A i ={A i [1],A i [2],...,A i [m-1]|A i [k]=a i 1 [k]...a i n [k],a i j [k]∈{0,1}};

[0093] Where A i is the i-th participant terminal P i The generated random string;

[0094] Each participant terminal P i According to its own random string A i and holds the n-bit secret string The calculation results in a string of m-1 n-length bit strings:

[0095] C i ={C i [1],C i [2],...,C i [m-1]|C i [k] = c i 1 [k]...c i n [k],c i j [k]∈{0,1}};

[0096] in, And k=1,2,...,m-1,j=1,2,...,n.

[0097] S3, each participant terminal P i Prepare n Bell states and obtain two ordered particle sequences:

[0098]

[0099] R i ={r i 1 ,r i 2 ,...,r i n};

[0100] Each participant terminal P i All will Send to the next participant terminal Among them, the last participant terminal P m-1 Q m-1→0 Sent to the first participant terminal P0.

[0101] Specifically, in the two ordered particle sequences, the initial state of each two-quantum pair is:

[0102]

[0103] S4. Assume l=1 and repeat the following m-1 times:

[0104] According to the received signal particle sequence Each participant P i (i=1,...,m-1) according to its string A i [l], B i [l] and C i [l] Perform encoding operations to obtain new

[0105] Each participant terminal P i All new Send to the next participant terminal Among them, the last participant terminal P m-1 Will Send to the first participant terminal P1, set l=l+1.

[0106] Specifically, each participant P i According to its string A i [l], B i [l] and C i [l] The encoding operation is performed on the sequence The jth particle Perform local unitary operation to get new

[0107]

[0108] in:

[0109] U 0,0 =I=|0><0|+|1><1|,U 0,1 =X=|0><1|+|1><0|;

[0110] U 1,0 =Z=|0><0|-|1><1|,U 1,1 =iY=|0><1|-|1><0|;

[0111]

[0112] S5. Each participant terminal P i For two particle sequences and R i Each pair of particles is measured in Bell state, and the measurement results are obtained

[0113] Specifically, each participant terminal P i For two particle sequences and R i For each pair of particles, Bell state measurements are performed and the results are obtained:

[0114]

[0115] According to n measurement results, it is deduced in

[0116] S6. All participant terminals P i according to Perform eavesdropping detection, if passed, all participants' terminals P i The key generated during the eavesdropping detection process will cause the protocol to be abandoned if it fails.

[0117] Specifically, the third-party terminal P0 calculates a bit sequence of length n based on B0, namely All participant terminals P i According to the bit sequence D Divide into sample sequences and information sequence Specifically, if d j If the value is equal to 0, the corresponding bit is selected As samples to form a sample sequence The remaining bits form the information sequence

[0118] Each participant terminal P i Calculate δ based on D = (d1×2 n-1 +d2×2 n-2 +…+d n ×2 0 ) modulo n1 and disclose T i ', Each participant terminal P i String m into T i 'The new n1 bit sequence T' and its own T i For comparison, if all T i are equal to T', then all participants accept K=K0=K1=…=K m-1 as the original negotiated key, otherwise the protocol is abandoned.

[0119] Please refer to Figure 3-5 , the second embodiment of the present invention is:

[0120] A Bell-state-based authenticated multi-party quantum key agreement system 1 includes a third-party terminal 2 and at least two participant terminals 3, wherein the third-party terminal and the participant terminal each include a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned embodiment 1 when executing the computer program.

[0121] In summary, the present invention provides a method and a terminal,

[0122] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent transformations made using the contents of the present invention's description and drawings, or directly or indirectly applied in related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A Bell-state-based authenticated multi-party quantum key agreement method, characterized in that: Including steps: S1. Third-party terminal Get the participant terminal P i The number of (m-1), i ranges from [1, m-1], calculates the authentication information of each participant terminal , get the hash value of the third-party terminal ; S2. Each participant's terminal Generate a set of random bits , then according to and holds the secret string Calculate the bit string ; S3, each participant's terminal Randomly generate n Bell states and obtain two ordered particle sequences: ； ； Each participant terminal All will Send to the next participant terminal , where the last participant terminal Will Sent to the first participant terminal ; S4, set , repeat the following m-1 times: According to the received signal particle sequence , each participant According to its string 、 and Perform the encoding operation to obtain the new , Each participant terminal All new Send to the next participant terminal , where the last participant terminal Will Sent to the first participant terminal ,make ; S5. Each participant's terminal For two particle sequences and Each pair of particles is measured in Bell state, and the measurement results are obtained ; S6. All participant terminals according to Perform eavesdropping detection, if passed, all participants' terminals The key generated during the eavesdropping detection process will cause the protocol to be abandoned if it fails.

2. The Bell-state-based authenticated multi-party quantum key agreement method according to claim 1, characterized in that: The step S1 specifically includes: S1. Third-party terminal Get participant terminal Generate a random number (m-1) And make it public to all participant terminals, and obtain the random numbers generated by all participant terminals , select a hash function in the hash family And make it public to all participant terminals, calculate the authentication information of each participant terminal = , to obtain the hash value of the third-party terminal , where Represents string concatenation, Represents the i-th participant terminal identity information, A random number generated for participant i; The calculation of the authentication information of each participant terminal It is calculated according to the following formula: ； Among them, the function It will Expand to a bit string of the same length as IDi||ri||r0, and then perform a bit-by-bit XOR operation on the two bit strings to obtain , perform hash operation on the bit string to obtain the corresponding hash value Bi, where For participants The private key held.

3. The Bell-state-based authenticated multi-party quantum key agreement method according to claim 2, characterized in that: The step S2 specifically includes: Each participant terminal Each produces a Random string of bit length: ； Where, is the i-th participant terminal The generated random string; Each participant terminal According to its own random string and holds the n-bit secret string The calculation results in a string of m-1 n-length bit strings: ； in, ,and .

4. The Bell-state-based authenticated multi-party quantum key agreement method according to claim 3, characterized in that: In step S3, the initial state of each quantum pair in the two ordered particle sequences is: 。 5. The Bell-state-based authenticated multi-party quantum key agreement method according to claim 4, characterized in that: In step S4, each participant According to its string 、 and The encoding operation is performed on the sequence The jth particle Perform local unitary operation to get new .

6. The Bell-state-based authenticated multi-party quantum key agreement method according to claim 5, characterized in that: The j-th particle Perform local unitary operations, specifically: Perform unitary operation ,in: ； ； 。 7. The Bell-state-based authenticated multi-party quantum key agreement method according to claim 6, characterized in that: The step S5 specifically includes: Each participant terminal For two particle sequences and For each pair of particles, Bell state measurements are performed and the results are obtained: ； According to n measurement results, it is deduced ,in .

8. The Bell-state-based authenticated multi-party quantum key agreement method according to claim 7, characterized in that: The step S6 specifically includes: Third-party terminals according to Calculate a bit sequence of length n, that is , all participant terminals According to the bit sequence will sequence Divide into sample sequences and information sequence ; Each participant terminal according to calculate Model and make it public , , each participant terminal String m Composed of new bit sequence With its own For comparison, if all are equal to , then all participants accept as the original negotiated key, otherwise the protocol is abandoned.

9. The Bell-state-based authenticated multi-party quantum key agreement method according to claim 8, characterized in that: The bit sequence will sequence Divide into sample sequences and information sequence Specifically: like If the value is equal to 0, the corresponding bit is selected As samples to form a sample sequence , The remaining bits form the information sequence .

10. A Bell-state-based authenticated multi-party quantum key agreement system, comprising a third-party terminal and at least two participant terminals, wherein the third-party terminal and the participant terminals each comprise 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 computer program, the method according to any one of claims 1 to 9 is implemented.

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