CN115189868A - Authenticated multi-party quantum key agreement method and system based on Bell state - Google Patents

Authenticated multi-party quantum key agreement method and system based on Bell state Download PDF

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CN115189868A
CN115189868A CN202210749870.3A CN202210749870A CN115189868A CN 115189868 A CN115189868 A CN 115189868A CN 202210749870 A CN202210749870 A CN 202210749870A CN 115189868 A CN115189868 A CN 115189868A
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participant
terminal
participant terminal
bit
party
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高丽贞
林崧
黎卫英
郭躬德
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Fujian Fuzhou Culture And Education Vocational Secondary School Fuzhou No 23 Middle School
Fujian Normal University
Xiamen Institute of Technology
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Fujian Fuzhou Culture And Education Vocational Secondary School Fuzhou No 23 Middle School
Fujian Normal University
Xiamen Institute of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/002—Countermeasures against attacks on cryptographic mechanisms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these

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Abstract

The invention discloses an authenticable multi-party quantum key agreement method and system based on Bell state, wherein m-1 participants, P i (i =1, 2.... M-1), which each hold its own n-bit secret string
Figure DDA0003720789660000011
Each participant has an identity information ID of length l i . To ensure the validity of the participant's identity, P i (i =1,2, \ 8230;, N-1) requires the assistance of a semi-trusted third party P 0 Authentication is accomplished and they are separately associated with P 0 Sharing
Figure DEST_PATH_FDA0003720789630000025
. After performing the following steps, the participants will obtain a length of about
Figure DDA0003720789660000012
Is negotiated a key
Figure DDA0003720789660000013
It can be seen that the identity of the user is authenticated with the help of the semi-trusted third party by using the characteristics of the Bell state, so that the impersonation attack is resisted. The Bell states are used as information carriers and are transmitted among participants, and the encoding operation is designed by utilizing quantum state discrimination, so that the proposed protocol is ensured to be correct and safe, and collusion attack of the participants can be resisted.

Description

Authenticated multi-party quantum key agreement method and system based on Bell state
Technical Field
The invention relates to the technical field of information transmission, in particular to an authenticatable multi-party quantum key agreement method and system based on Bell state.
Background
Quantum key agreement protocol (QKA) is an important branch of quantum cryptography, which means that two or more users can agree on the same key, with both having an impact on the key. Compared with quantum key distribution, quantum key negotiation pays more attention to fairness of protocols and privacy of users. As a main key management method, key agreement is an important cryptographic primitive, and is widely applied in the fields of multiparty security calculation, access control, electronic auction and the like.
In 2004, zhou et al proposed the first QKA protocol, in which two users agreed on a key using quantum invisible states. Later, in 2013, shi and Zhong proposed the QKA protocol (MQKA) for the first multiple parties based on entanglement swapping. Unfortunately, however, both protocols are insecure. Subsequently, some MQKA protocols have been proposed using different properties of quantum mechanics. These protocols can be divided into three categories according to the transmission structure of the signal particles: full pattern, tree and ring. Compared with the former two types, the ring type MQKA (CMQKA) has higher efficiency and feasibility. Therefore, most of the existing MQKA protocols belong to the third type. However, the existing research shows that most CMQKA protocols are not secure because they cannot resist collusion attack, and in addition, there is a impersonation attack that can occur during the actual execution of the protocol, and the attacker can be an attacker outside the protocol or a dishonest participant within the protocol, and they want to impersonate a legitimate participant to directly participate in the protocol, normally execute each step of the protocol without being discovered, and obtain the final negotiation key or privacy information of other participants.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: an authenticatable multiparty quantum key agreement method and system based on Bell state are provided to prevent collusion attack and ensure the proposed protocol is correct and safe.
In order to solve the technical problems, the invention adopts the technical scheme that:
an authenticatable multi-party quantum key agreement method based on Bell state includes the steps:
s1, third party terminal P 0 Obtaining participant terminal P i (i =1, 2.., m-1), the authentication information B of each participant terminal is calculated i Obtaining the hash value of the third party terminal
Figure BDA0003720789640000021
S2, each participant terminal P i Generating a set of random bit strings A i Then according to A i And holding secret character strings
Figure BDA0003720789640000022
Calculating to obtain a bit string C i ；
S3, each participant terminal P i N Bell states were randomly generated, resulting in two ordered particle sequences:
Figure BDA0003720789640000023
Figure BDA0003720789640000024
each participant terminal P i All will
Figure BDA0003720789640000025
To the next participant terminal
Figure BDA0003720789640000026
Wherein the last participant terminal P m-1 Will Q m-1→0 To a first participant terminal P 0 ；
S4, setting l =1, repeatedly executing the following contents m-1 times:
according to the received signal particle sequence
Figure BDA0003720789640000027
Each participant P i (i = 1.., m-1) according to its character string a i [l]、B i [l]And C i [l]Performing coding operations to obtain
Figure BDA0003720789640000028
Each participant terminal P i All will be new
Figure BDA0003720789640000029
To the next participant terminal
Figure BDA00037207896400000210
Wherein the last participant terminal P m-1 Will Q m-1→0 To the first participant terminal P 0 Let l = l +1;
s5, each participant terminal P i For two particle sequences
Figure BDA00037207896400000211
And R i Each two-particle pair is subjected to Bell state measurement, and the Bell state measurement is obtained according to the measurement result
Figure BDA00037207896400000212
S6, all participant terminals P i According to
Figure BDA00037207896400000213
Performing eavesdropping detection, if passing, all participant terminals P i And eavesdropping the key generated in the detection process, and abandoning the protocol if the key does not pass the detection process.
In order to solve the technical problem, the invention adopts another technical scheme as follows:
an authenticatable multi-party quantum key agreement system based on Bell state comprises a third party terminal and at least two participant terminals, wherein the third party terminal and the participant terminals respectively comprise a memory, a processor and a computer program which is stored on the memory and can run on the processor, and the processor realizes the method when executing the computer program.
The invention has the beneficial effects that: an authenticatable multi-party quantum key agreement method and a system based on Bell state are disclosed, wherein Bell state is used as an information carrier and is transmitted among participants, and the participants embed their secrets into travel particles through specific encoding operations. In this way, all participants can obtain the same agreed-upon key, i.e. the sum of their secret inputs, at the end of the protocol at the same time. Here, the encoding operation is designed using quantum state discrimination techniques, ensuring that the proposed protocol is correct and secure, and can withstand collusion attacks by multiple participants.
Drawings
Fig. 1 is a schematic flowchart of an authenticatable multiparty quantum key agreement method based on a Bell state according to an embodiment of the present invention;
FIG. 2 is a data flow diagram of database modeling according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of an authenticatable multi-party quantum key agreement system based on the Bell state according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a third party terminal according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of a participant terminal according to an embodiment of the present invention.
Description of reference numerals:
1. an authenticable multi-party quantum key agreement system based on Bell state; 2. a third party terminal; 3. a participant terminal.
Detailed Description
In order to explain the technical contents, the objects and the effects of the present invention in detail, the following description is made with reference to the accompanying drawings in combination with the embodiments.
Referring to fig. 1-2, a method,
an authenticatable multi-party quantum key agreement method based on Bell state includes the steps:
s1, third party terminal P 0 Obtaining participant terminal P i (i =1, 2.., m-1), the authentication information B of each participant terminal is calculated i To obtain the hash value of the third party terminal
Figure BDA0003720789640000031
S2, each participant terminal P i Generating a set of random bit strings A i Then according to A i And holding secret character strings
Figure BDA0003720789640000032
Calculating to obtain a bit string C i ；
S3, each participant terminal P i N Bell states were randomly generated, resulting in two ordered particle sequences:
Figure BDA0003720789640000041
Figure BDA0003720789640000042
each participant terminal P i All will
Figure BDA0003720789640000043
To the next participant terminal
Figure BDA0003720789640000044
Wherein the last participant terminal P m-1 Will Q m-1→0 To a first participant terminal P 0 ；
S4, setting l =1, repeatedly executing the following contents m-1 times:
according to the received signal particle sequence
Figure BDA0003720789640000045
Each participant P i (i = 1...., m-1) according to its character string a i [l]、B i [l]And C i [l]Performing coding operations to obtain
Figure BDA0003720789640000046
Each participant terminal P i All will be new
Figure BDA0003720789640000047
To the next participant terminal
Figure BDA0003720789640000048
Wherein the last participant terminal P m-1 Will Q m-1→0 To the first participant terminal P 0 Let l = l +1;
s5, each participant terminal P i For two particle sequences
Figure BDA0003720789640000049
And R i Each two-particle pair is subjected to Bell state measurement, and the Bell state measurement is obtained according to the measurement result
Figure BDA00037207896400000410
S6, all participant terminals P i According to
Figure BDA00037207896400000411
Performing eavesdropping detection, if passing, all participant terminals P i And eavesdropping the key generated in the detection process, and abandoning the protocol if the key does not pass the detection process.
As can be seen from the above description, the beneficial effects of the present invention are: an authenticatable multi-party quantum key agreement method and a system based on Bell state are disclosed, wherein Bell state is used as an information carrier and is transmitted among participants, and the participants embed their secrets into travel particles through specific encoding operations. In this way, all participants can simultaneously obtain the same negotiation key, i.e. the sum of their secret inputs, at the end of the protocol. Here, the encoding operation is designed using quantum state discrimination techniques, ensuring that the proposed protocol is correct and secure, and can withstand collusion attacks by multiple participants.
The step S1 specifically includes:
s1, third party terminal P 0 Obtaining participant terminal P i (i =1,2,. Lam., m-1), generating a random number r 0 And is disclosed to all participant terminals and acquires the random numbers r generated by all participant terminals i Selecting a hash function h from the hash family: 2 * →2 (m-1)n And discloses to all participant terminals, calculates authentication information of each participant terminal
Figure BDA00037207896400000412
To obtain the hash value of the third party terminal
Figure BDA00037207896400000413
Where, | | represents a string connection, ID i Representing the ith participant terminal P i Identity information of r i A random number generated for participant i;
the authentication information B of each participant terminal is calculated i Specifically, the calculation is performed according to the following formula:
Figure BDA0003720789640000051
wherein the function
Figure BDA0003720789640000052
Is to be
Figure BDA0003720789640000053
Extending to a bit string with the same length as IDi ri r0, and then carrying out bit-by-bit XOR operation on the two bit strings to obtain the bit string
Figure BDA0003720789640000054
Performing hash operation on the bit string to obtain a corresponding hash value Bi, wherein
Figure BDA0003720789640000055
As participant P i The held private key.
As can be seen from the above description, a calculation method of the authentication information is given.
Further, the step S2 specifically includes:
each participant terminal P i Each generates a random string of (m-1) n bits long:
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}}；
in the formula, A i Is the ith participant terminal P i A generated random string;
each participant terminal P i According to its own random string A i And held n-bit secret string
Figure BDA0003720789640000056
Calculating to obtain a string of m-1 n long bit strings:
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}}；
wherein the content of the first and second substances,
Figure BDA0003720789640000057
and k =1,2, ·, m-1, j =1,2, ·, n.
In this embodiment, the third party terminal P 0 Corresponding value A 0 ＝C 0 ＝00…0
As can be seen from the above description, a method and a specific embodiment of calculating a secret string are given.
Further, in step S3, in the two ordered particle sequences, the initial state of each two quantum pairs is:
Figure BDA0003720789640000058
from the above description, constraints are given for the generation of two particle sequences.
Further, in the step S4, each participant P i According to its character string A i [l]、B i [l]And C i [l]The encoding operation is performed on the sequence
Figure BDA0003720789640000059
The j (th) particle of
Figure BDA00037207896400000510
Performing local unitary operation to obtain new
Figure BDA00037207896400000511
As can be seen from the above description, an encoding operation is achieved.
Further, the pair of jth particles
Figure BDA00037207896400000512
Executing a local unitary operation, specifically:
performing unitary operations
Figure BDA0003720789640000061
Wherein:
U 0,0 ＝I＝|0><0|+|1><1|,U 0,1 ＝X＝|0><1|+|1><0|；
U 1,0 ＝Z＝|0><0|-|1><1|,U 1,1 ＝iY＝|0><1|-|1><0|；
Figure BDA0003720789640000062
as can be seen from the above description, a specific embodiment of unitary operation is given.
Further, the step S5 specifically includes:
each participant terminal P i For two particle sequences
Figure BDA0003720789640000063
And R i The Bell state measurement was performed for each two particle pair to obtain the results:
Figure BDA0003720789640000064
deriving from the n measurements
Figure BDA0003720789640000065
Wherein
Figure BDA0003720789640000066
From the above description, specific embodiments of Bell state measurements and Si are given.
Further, the step S6 specifically includes:
third party terminal P 0 According to B 0 A bit sequence of length n is calculated, i.e.
Figure BDA0003720789640000067
All take part inA terminal P i According to bit sequence D
Figure BDA0003720789640000068
Dividing into sample sequences
Figure BDA0003720789640000069
And information sequence
Figure BDA00037207896400000610
Each participant terminal P i Calculating δ = (D) from D 1 ×2 n-1 +d 2 ×2 n-2 +…+d n ×2 0 ) Modulo n 1 And disclose T i '，
Figure BDA00037207896400000611
Each participant terminal P i M strings of T i ' New n of composition 1 Bit sequence T' and its own T i Making a comparison if all T i All equal T', then all participants accept K = K 0 ＝K 1 ＝…＝K m-1 As the original negotiated key, otherwise the protocol is aborted.
As can be seen from the above description, a specific method of eavesdropping detection is given.
Further, the sequence is determined according to the bit sequence D
Figure BDA00037207896400000612
Dividing into sample sequences
Figure BDA00037207896400000613
And information sequence
Figure BDA00037207896400000614
The method comprises the following steps:
if d is j Is equal to 0, the corresponding bit is selected
Figure BDA00037207896400000615
Composing a sample sequence as a sample
Figure BDA00037207896400000616
Figure BDA00037207896400000619
The remaining bits constitute the information sequence
Figure BDA00037207896400000617
As can be seen from the above description, it is achieved that the sequence is formed from the bit sequence D
Figure BDA00037207896400000618
Dividing into sample sequences
Figure BDA0003720789640000071
And information sequence
Figure BDA0003720789640000072
An authenticatable multi-party quantum key agreement system based on Bell state comprises a third party terminal and at least two participant terminals, wherein the third party terminal and the participant terminals respectively comprise a memory, a processor and a computer program which is stored on the memory and can run on the processor, and the processor realizes the method when executing the computer program.
The invention is applied to information transmission with a plurality of participants to avoid collusion attack.
Referring to fig. 1 to fig. 2, a first embodiment of the present invention is:
an authenticatable multi-party quantum key agreement method based on Bell state includes the following steps:
s1, third party terminal P 0 Obtaining participant terminal P i (i =1,2, \ 8230;, m-1) number (m-1), authentication information B of each participant terminal is calculated i Obtaining the hash value of the third party terminal
Figure BDA0003720789640000073
In particular, the third party terminal P 0 Obtaining participant terminal P i (i =1,2, \ 8230;, m-1) number (m-1), generating a random number r 0 And is disclosed to all participant terminals and acquires the random numbers r generated by all participant terminals i Selecting a hash function h:2 from the hash family * →2 (m-1)n And discloses to all participant terminals, calculates authentication information of each participant terminal
Figure BDA0003720789640000074
To obtain the hash value of the third party terminal
Figure BDA0003720789640000075
Where | | | represents string concatenation, ID i Representing the ith participant terminal P i Identity information of r i A random number generated for participant i.
Specifically, it is calculated according to the following formula:
Figure BDA0003720789640000076
here, function
Figure BDA0003720789640000077
Firstly, the
Figure BDA0003720789640000078
Extending to a bit string with the same length as IDi ri r0, and then carrying out bit-by-bit XOR operation on the two bit strings to obtain the bit string
Figure BDA0003720789640000079
Finally, the bit string is subjected to hash operation to obtain a corresponding hash value B i
S2, each participant terminal P i Generating a set of random bit strings A i Then according to A i And holding secret character strings
Figure BDA00037207896400000710
Calculating to obtain a bit string C i ；
In particular, each participant terminal P i Each generates a random string of (m-1) n bits long:
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}}；
in the formula, A i Is the ith participant terminal P i A generated random string;
each participant terminal P i According to its own random string A i And held n-bit secret string
Figure BDA0003720789640000081
Calculating to obtain a string of m-1 n long bit strings:
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}}；
wherein the content of the first and second substances,
Figure BDA0003720789640000082
and k =1,2, ·, m-1, j =1,2, ·, n.
S3, each participant terminal P i N Bell states were prepared, resulting in two ordered particle sequences:
Figure BDA0003720789640000083
R i ＝{r i 1 ,r i 2 ,...,r i n }；
each participant terminal P i All will
Figure BDA0003720789640000084
To the next participant terminal
Figure BDA0003720789640000085
Wherein the last participant terminal P m-1 Will Q m-1→0 To the first participant terminal P 0 。
Specifically, in the two ordered particle sequences, the initial state of each two-quantum pair is:
Figure BDA0003720789640000086
s4, setting l =1, repeatedly executing the following contents m-1 times:
from the received signal particle sequence
Figure BDA0003720789640000087
Each participant P i (i = 1...., m-1) according to its character string a i [l]、B i [l]And C i [l]Performing coding operations to obtain
Figure BDA0003720789640000088
Each participant terminal P i All will be new
Figure BDA0003720789640000089
To the next participant terminal
Figure BDA00037207896400000810
Wherein the last participant terminal P m-1 Will be provided with
Figure BDA00037207896400000811
To the first participant terminal P 1 Let l = l +1.
In particular, each participant P i According to its character string A i [l]、B i [l]And C i [l]The encoding operation is performed on the sequence
Figure BDA00037207896400000812
The jth particle of (1)
Figure BDA00037207896400000813
Performing local unitary operation to obtain new
Figure BDA00037207896400000814
Figure BDA00037207896400000815
Wherein:
U 0,0 ＝I＝|0><0|+|1><1|,U 0,1 ＝X＝|0><1|+|1><0|；
U 1,0 ＝Z＝|0><0|-|1><1|,U 1,1 ＝iY＝|0><1|-|1><0|；
Figure BDA0003720789640000091
s5, each participant terminal P i For two particle sequences
Figure BDA0003720789640000092
And R i Each two-particle pair is subjected to Bell state measurement, and the Bell state measurement is obtained according to the measurement result
Figure BDA0003720789640000093
In particular, each participant terminal P i For two particle sequences
Figure BDA0003720789640000094
And R i The Bell state measurement was performed for each two particle pair, resulting in:
Figure BDA0003720789640000095
deriving from the n measurements
Figure BDA0003720789640000096
Wherein
Figure BDA0003720789640000097
S6, all participant terminals P i According to
Figure BDA0003720789640000098
Performing eavesdropping detection, if passing, all participant terminals P i And eavesdropping the key generated in the detection process, and abandoning the protocol if the key does not pass the detection process.
In particular, the third party terminal P 0 According to B 0 A bit sequence of length n is calculated, i.e.
Figure BDA0003720789640000099
All participant terminals P i Sequencing according to bit sequence D
Figure BDA00037207896400000910
Dividing into sample sequences
Figure BDA00037207896400000911
And information sequence
Figure BDA00037207896400000912
Specifically, if d j Is equal to 0, the corresponding bit is selected
Figure BDA00037207896400000913
Composing a sample sequence as a sample
Figure BDA00037207896400000914
The remaining bits constitute the information sequence
Figure BDA00037207896400000915
Each participant terminal P i Calculating δ = (D) from D 1 ×2 n-1 +d 2 ×2 n-2 +…+d n ×2 0 ) Modulo n of 1 And disclose T i '，
Figure BDA00037207896400000916
Each participant terminal P i M strings of T i ' novel n of composition 1 Bit sequence T' and its own T i Making a comparison if all T i All equal T', then all participants accept K = K 0 ＝K 1 ＝…＝K m-1 As the original negotiated key, otherwise the protocol is aborted.
Referring to fig. 3-5, the second embodiment of the present invention is:
an authenticatable multi-party quantum key agreement system 1 based on the Bell state includes a third party terminal 2 and at least two participant terminals 3, where the third party terminal and the participant terminals each include a memory, a processor, and a computer program stored in the memory and capable of running on the processor, and is characterized in that the processor implements the steps of the first embodiment when executing the computer program.
In summary, the present invention provides a method and a terminal,
the above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all equivalent changes made by using the contents of the present specification and the drawings, or applied directly or indirectly to the related technical fields, are included in the scope of the present invention.

Claims (10)

1. An authenticatable multi-party quantum key agreement method based on Bell state is characterized by comprising the following steps:
s1, third party terminal P 0 Obtaining participant terminal P i (i =1, 2.., m-1), the authentication information B of each participant terminal is calculated i Obtaining the hash value of the third party terminal
Figure FDA0003720789630000011
S2, each participant terminal P i Generating a set of random bit strings A i Then according to A i And holding secret character strings
Figure FDA0003720789630000012
Calculating to obtain a bit string C i ；
S3, each participant terminal P i N Bell states were randomly generated, resulting in two ordered particle sequences:
Figure FDA0003720789630000013
R i ＝{r i 1 ,r i 2 ,...,r i n }；
each participant terminal P i All will
Figure FDA0003720789630000014
To the next participant terminal
Figure FDA0003720789630000015
Wherein the last participant terminal P m-1 Will Q m-1→0 To the first participant terminal P 0 ；
S4, setting l =1, repeatedly executing the following contents m-1 times:
according to the received signal particle sequence
Figure FDA0003720789630000016
Each participant P i (i = 1.., m-1) according to its character string a i [l]、B i [l]And C i [l]Performing coding operations to obtain
Figure FDA0003720789630000017
Each participant terminal P i All will be new
Figure FDA0003720789630000018
Is sent toThe next participant terminal
Figure FDA0003720789630000019
Wherein the last participant terminal P m-1 Will Q m-1→0 To a first participant terminal P 0 Let l = l +1;
s5, each participant terminal P i For two particle sequences
Figure FDA00037207896300000110
And R i Each two-particle pair is subjected to Bell state measurement, and the Bell state measurement is obtained according to the measurement result
Figure FDA00037207896300000111
S6, all participant terminals P i According to
Figure FDA00037207896300000112
Performing eavesdropping detection, if passing, all participant terminals P i And eavesdropping the key generated in the detection process, and abandoning the protocol if the key does not pass the detection process.
2. The method as claimed in claim 1, wherein the step S1 specifically includes:
s1, third party terminal P 0 Obtaining participant terminal P i (i =1, 2.., m-1), generating a random number r 0 And is disclosed to all participant terminals and acquires random numbers r generated by all participant terminals i Selecting a hash function h from the hash family: 2 * →2 (m-1)n And discloses to all participant terminals, calculates authentication information of each participant terminal
Figure FDA00037207896300000113
To obtain the hash value of the third party terminal
Figure FDA00037207896300000114
Where, | | represents a string connection, ID i Representing the ith participant terminal P i Identity information of r i A random number generated for participant i;
the calculation of authentication information B for each participant terminal i Specifically, the calculation is performed according to the following formula:
Figure FDA0003720789630000021
wherein the function
Figure FDA0003720789630000022
Is to be
Figure FDA0003720789630000023
Extending to a bit string with the same length as IDi ri r0, and then carrying out bit-by-bit XOR operation on the two bit strings to obtain the bit string
Figure FDA0003720789630000024
Performing hash operation on the bit string to obtain a corresponding hash value Bi, wherein
Figure FDA0003720789630000025
As participant P i The held private key.
3. The method as claimed in claim 2, wherein the step S2 specifically includes:
each participant terminal P i Each generates a random string of (m-1) n bits long:
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}}；
in the formula, A i Is the ith participantTerminal P i A generated random string;
each participant terminal P i According to its own random string A i And held n-bit secret string
Figure FDA0003720789630000026
A string of m-1 n long bit strings is obtained by calculation:
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}}；
wherein the content of the first and second substances,
Figure FDA0003720789630000027
and k =1,2, ·, m-1, j =1,2, ·, n.
4. The method as claimed in claim 3, wherein in step S3, in the two ordered particle sequences, the initial state of each two quantum pairs is:
Figure FDA0003720789630000028
5. the Bell-state-based authenticatable multi-party quantum key agreement method as claimed in claim 4, wherein in the step S4, each participant P i According to its character string A i [l]、B i [l]And C i [l]The encoding operation is performed on the sequence
Figure FDA0003720789630000029
The jth particle of (1)
Figure FDA00037207896300000210
Performing local unitary operation to obtain new
Figure FDA00037207896300000211
6. The Bell-state-based authenticatable multi-party quantum key agreement method as claimed in claim 5, wherein the jth particle pair
Figure FDA0003720789630000031
Executing a local unitary operation, specifically:
performing unitary operations
Figure FDA0003720789630000032
Wherein:
U 0,0 ＝I＝|0><0|+|1><1|,U 0,1 ＝X＝|0><1|+|1><0|；
U 1,0 ＝Z＝|0><0|-|1><1|,U 1,1 ＝iY＝|0><1|-|1><0|；
Figure FDA0003720789630000033
7. the method as claimed in claim 6, wherein the step S5 specifically includes:
each participant terminal P i For two particle sequences
Figure FDA0003720789630000034
And R i The Bell state measurement was performed for each two particle pair to obtain the results:
Figure FDA0003720789630000035
deriving from the n measurements
Figure FDA0003720789630000036
Wherein
Figure FDA0003720789630000037
8. The method as claimed in claim 7, wherein the step S6 specifically includes:
third party terminal P 0 According to B 0 A bit sequence of length n is calculated, i.e.
Figure FDA0003720789630000038
All participant terminals P i According to bit sequence D
Figure FDA0003720789630000039
Dividing into sample sequences
Figure FDA00037207896300000310
And information sequence
Figure FDA00037207896300000311
Each participant terminal P i Calculating δ = (D) from D 1 ×2 n-1 +d 2 ×2 n-2 +…+d n ×2 0 ) Modulo n of 1 And disclose T i '，
Figure FDA00037207896300000312
Each participant terminal P i Will m strings T i ' novel n of composition 1 Bit sequence T' and its own T i Making a comparison if all T i All equal T', then all participants accept K = K 0 ＝K 1 ＝…＝K m-1 As the original negotiated key, otherwise the protocol is aborted.
9. The method as claimed in claim 8, wherein the sequence is determined according to a bit sequence D
Figure FDA00037207896300000313
Dividing into sample sequences
Figure FDA00037207896300000314
And information sequence
Figure FDA00037207896300000315
The method comprises the following steps:
if d is j Is equal to 0, the corresponding bit is selected
Figure FDA00037207896300000316
Composing a sample sequence as a sample
Figure FDA00037207896300000317
Figure FDA00037207896300000318
The remaining bits constitute the information sequence
Figure FDA00037207896300000319
10. An authenticatable multi-party quantum key agreement system based on Bell states, comprising a third party terminal and at least two participant terminals, wherein each of the third party terminal and the participant terminals comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the method of any one of claims 1 to 9 when executing the computer program.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116961883A (en) * 2023-09-21 2023-10-27 山东高速建设管理集团有限公司 Quantum privacy comparison method based on three-particle GHZ-like state

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116961883A (en) * 2023-09-21 2023-10-27 山东高速建设管理集团有限公司 Quantum privacy comparison method based on three-particle GHZ-like state
CN116961883B (en) * 2023-09-21 2023-11-21 山东高速建设管理集团有限公司 Quantum privacy comparison method based on three-particle GHZ-like state

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