Unmanned aerial vehicle group distributed management method based on mobile active secret sharing technology

Abstract

The invention discloses an unmanned aerial vehicle group distributed management method based on a mobile active secret sharing technology, which supports off-line of a trusted institution and comprises the following steps: the trusted institution TA generates public parameters; a mobile base station MS and an unmanned aerial vehicle UAV participating in communication respectively register with a trusted mechanism in a registration stage, and acquire information such as a secret key and a certificate; the UAV joins the MS and is administered by the MS, and after mutual identity authentication, the MS distributes secret shares to the UAV; performing identity authentication on the unmanned aerial vehicle group; the unmanned aerial vehicles of the two groups share the share, group fusion is achieved, and after a new share is obtained, each unmanned aerial vehicle updates the certificate of the unmanned aerial vehicle. According to the method, the sub-secrets of the unmanned aerial vehicles are autonomously updated through a mobile active secret sharing technology, and fusion of completely decentralized unmanned aerial vehicle groups is realized. Secondly, an efficient certificate self-updating method is designed. The unmanned aerial vehicle can update the certificate only by calculating a threshold signature. Detailed safety certification and comprehensive experiments show that dynamic autonomous management of the distributed unmanned aerial vehicle group can be realized, and the method has good safety characteristics and relatively low calculation overhead.

Description

Technical Field

[0001] The present invention relates to mobile active secret sharing (MPSS) and threshold signature technology, and in particular to a distributed management method for a drone group based on mobile active secret sharing technology. Background Art

[0002] Secret sharing technology is a technology that divides secret information into multiple shares and distributes them to different participants for safekeeping. Only when a sufficient number of participants cooperate can the original secret be recovered, and any participant with less than the specified number cannot obtain the complete secret information. However, traditional secret sharing technology has certain security risks. If some participants are controlled by the adversary or the share storage device is attacked, the secret may be leaked. David Schultz, Barbara Liskov and Moses Liskov first proposed mobile active secret sharing technology in 2010. Mobile active secret sharing provides mobility on the basis of active secret sharing, that is, the node group holding the secret share can be changed. This scheme combines share update and share recovery into one step, allowing group members to change. Nodes periodically execute a switching protocol so that different node groups generate a new set of shares without changing the secret, and share the new shares with new node groups that may be different from the original share holding group. (t,n) threshold signature refers to a signature group composed of t members. A group of legal members greater than or equal to t in the group can sign on behalf of the group using the group's private key, and anyone can use the group's public key to verify the signature. Here t is the threshold value. Any t-1 or fewer members in the group cannot sign on behalf of the group, and no member can impersonate other members to sign. Threshold signature is a distributed multi-party signature protocol that includes three algorithms: distributed key generation, signature generation, and signature verification.

[0003] Although the existing centralized group management solutions are relatively mature, most solutions require trusted institutions to remain online, which has a single point of failure problem. In terms of group integration, some solutions require applying for certificates from trusted institutions before new members join, and mutual authentication with group members. In blockchain-based solutions, when new members join the group, the trusted institution needs to store their public key information on the blockchain. Group members obtain the new member's public key from the blockchain and verify whether the member is legitimate.

[0004] However, the maintenance cost of blockchain is very high, and the identity of members is still managed by trusted institutions. In the multi-center scheme, the trusted institution divides the entire system into multiple subgroups at the beginning and selects a cluster head for each subgroup. These cluster heads are responsible for managing the identity information of the members of the group and assisting in authentication. Before a new member joins the group, the cluster head in the group needs to distribute keys, certificates, etc. to it. However, once a single point of failure occurs in the cluster head, it is impossible to provide effective proof for the new member. In terms of certificate update, most schemes implement the update of public certificates or pseudonymous certificates through trusted institutions. When a member joins the group, the trusted institution needs to calculate and update the domain key parameters. All members in the group calculate the domain key based on the domain key parameters to ensure the security of subsequent communication within the group. Alternatively, when a new member joins, the trusted institution needs to distribute a pseudonymous certificate to it. At the same time, in order to ensure the long-term communication security of the entire group, the trusted institution needs to update the pseudonymous certificates of the original group members and upload these certificates to the blockchain.

[0005] However, the above solutions are not applicable to the integration of drone groups and the continuous availability of certificates of the integrated members in the scenario where the trusted institution is offline. Therefore, it is necessary to design a group management solution that supports group integration and certificate self-update for the scenario where the trusted institution is offline. Summary of the invention

[0006] Purpose of the invention: The purpose of the present invention is to solve the deficiencies in the prior art and to provide a distributed management method for drone groups based on mobile active secret sharing technology, which solves the problem of dynamic fusion of drone groups in distributed scenarios and update of member certificates after fusion.

[0007] Mobile active secret sharing technology can be applied in distributed scenarios to achieve the integration of drone groups by autonomously updating the sub-secrets of drones. Considering that the certificates of new group members after integration can be continuously available without the assistance of trusted institutions, an efficient certificate self-update method is designed so that drones only need to calculate a threshold signature to update the certificate. The principle of trust transfer in the certificate chain ensures the legitimacy of the source of the drone group. In addition, in order to ensure the communication security of the group during integration, threshold signatures are used to batch authenticate the legitimacy of the identities of drones before integration. Distributed authentication can be achieved based on the concept of threshold signatures, thereby avoiding single point failure problems.

[0008] Technical solution: The distributed management method of drone groups based on mobile active secret sharing technology of the present invention comprises the following steps:

[0009] Step (1), system initialization phase, that is, the trusted organization TA generates and publishes the system's public parameters Para = {G, P, q, h1, h2, h3, TPK};

[0010] Among them, G is an additive group of order q, P is the generator of group G, h1, h2, h3, are three hash functions, and TPK is the public key of the trusted organization TA;

[0011] Step (2), registration phase, i.e. the mobile base station MS and the unmanned aerial vehicle UAV participating in the communication respectively request registration from the trusted authority TA in the registration phase and obtain corresponding key, certificate and other information;

[0012] Among them, for the i-th UAV i , obtain the unique real identity UID through the trusted institution TA i 、Private key upk i 、public key upk i , Certificate UCert i ; For the jth mobile base station MS j , obtain the unique real identity MID through the trusted institution TA j 、Private key msk j 、Public key mpk j 、Group Secret mk j , the public key MK corresponding to the group secret j , Certificate MCert j ;

[0013] Step (3), U2M initialization authentication, that is, the UAV first joins the mobile base station MS and is governed by the mobile base station MS; after mutual identity authentication, the mobile base station MS distributes secret shares to the UAV;

[0014] Specifically, when the intra-group session key negotiation is to be performed, the UAV i Send your own information to the mobile base station MS you want to join j , mobile base station MS j After receiving it, it is verified. If the verification is successful, the session key sk is calculated. j,i , and send its own message to the UAV i , UAV i After receiving, verify it, and if the verification is successful, calculate the session key sk i,j , so far the relevant identity authentication is completed; mobile base station MS j Distribute share x to all drones in its domain i When using the group key zsk j Unicast encrypted information To the corresponding UAV i ;

[0015] Step (4), group authentication, i.e., the drones authenticate the identities of the drones in another group as a group; assuming that the two drone groups from the mobile base station MS1 ​​and the mobile base station MS2 are group1 and group2 respectively, the two drone groups authenticate each other at the same time, which includes the two drone groups establishing intra-group session keys, the two drone groups establishing cross-group session keys, and verifying the certificate chain, until the two drone groups complete mutual authentication and the identities of all drones are legal;

[0016] Step (5), group management, including group integration and certificate update, that is, when there is no trusted agency TA involved, the drones in the two drone groups achieve group integration by sharing shares. After obtaining new shares, each drone updates its own certificate; specifically, it includes:

[0017] Step (5.1), group fusion;

[0018] Assume that the verified drones in drone groups group1 and group2 want to share shares with each other, UID i 、UID j The UID is the ID of the corresponding drone in the old group. k is the identity of the UAV in the new group; taking one of the parties as an example, at this time, the UAV in group2 shares the quota with the UAV in group1, group2 is equivalent to the old group, group1 and group2 are equivalent to the new group, and the process is: the UAV in the old group i Calculate Q i (x), and for each UAV in the new group k Polynomial R i,k (x), UAV in the old group i Also for UAV j Calculate the vector V i,j , and broadcast the encrypted information First, UAV j Decryption V i,j Get all legal shares and broadcast encrypted messages UAV in the new group k Decrypted to get v j,k , the share after sharing Similarly, after the UAVs in group1 share their shares with the UAVs in group2, each UAV k The share is Get the last new share Forming a fused group 1,2 ;

[0019] Step (5.2), certificate update, that is, the merged group 1，2 Each UAV in i Calculate new message mess new and certificates inew .

[0020] Furthermore, in step 1, the trusted institution TA selects three hash functions h1, h2, and h3, as follows:

[0021]

[0022] n1 represents the number of drones participating in the certification in the drone group;

[0023] Then the trusted authority TA generates a private key tsk, a public key TPK=tsk·P, and a system master key (tsk, TPK).

[0024] Furthermore, the detailed process of the registration in step (2) is as follows:

[0025] Step (2.1), the UAV registers with TA. The specific process is as follows:

[0026] The trusted authority TA is the i-th UAV i Choose a unique real identity UID i , and select a random number a for it i and a random private key usk i ;TA calculates A i =a i P, public key upk i =usk i P, corresponding to the UCert certificate i =a i +h1(UID i ||upk i ||A i )·tsk; TA sends the message Send to UAV via secure channel i ;

[0027] Step (2.2), MS registers with TA, the specific process is as follows:

[0028] The trusted authority TA is the jth MS j Choose a unique real identity MID j , and select two random numbers for it and random private key msk j ;TA calculation group secret The public key corresponding to the group secret Public key mpk j=msk j P, corresponding certificate

[0029] Finally, TA sent the message Sent to the mobile base station MS via a secure channel j .

[0030] Furthermore, the detailed process of step (3) is as follows:

[0031] Step (3.1), intra-group session key negotiation, the specific process is as follows:

[0032] UAV i Send the message Sent to mobile base station MS j ;MS j After receiving, first judge UCert i P = A i +h1(UID i ||upk i ||A i ) Whether TPK is established, if so, calculate MS j With UAV i The session key sk j,i =msk j ·upk i , the message Send to UAV i ; If not established, terminate the session;

[0033] UAV i After receiving, first judge Is it true? If true, store MCert j , and calculate UAV i With MS j The session key sk i,j =usk i ·mpk j ; If not established, terminate the session;

[0034] Step (3.2), distribution of secret shares, the specific process is:

[0035] Mobile Base Station MS j Select t-1 random numbers a1, a2, ..., a t-1 , generating polynomial P j (x) = mk j +a1x+a2x 2 +...+a t-1 x t-1 ;MS jEach UAV in the computational domain i The secret share x i and public key X i :

[0036] x i =P j (UID i ), X i =x i ·P;

[0037] MS j Select random number zsk j As the group key, unicast encrypted information For UAV i ; Each UAV i Received from MS j After the information is i,j Decrypt to get the group key zsk j and share x i .

[0038] Furthermore, before the group merges, all drones need to authenticate the identity of the group to be joined. After the authentication is passed, each two drones can negotiate the session key to encrypt the shared share of the next stage. In step (4), the two drone groups respectively establish the U2U group session key to achieve authentication as follows:

[0039] To avoid redundant description, this section takes group1 authentication and group2 authentication of group1 as examples.

[0040] UAV in UAV group group1 i Choose a random number k i , calculate the random number k i The corresponding public key K i =k i P, broadcast message

[0041] UAV in group 1 i After receiving the message from group2, calculate the hash code HMAC j ′((UID j ||K j ),zsk1), determine HMAC′ j ((UID j ||K j ),zsk1)=HMAC j ((UID j ||K j ),zsk1) is true; if not, terminate the session;

[0042] If established, UAV i Computing and UAVs j The session key key i,j =k i ·K j ;

[0043] Among them, K j It is UAV j The random number k is chosen j The corresponding public key.

[0044] Furthermore, after completing the U2U intra-group session key, the U2U cross-group session key between different drone groups is established. The process is as follows;

[0045] Step 1), generate individual signature;

[0046] UAV in group1 i Calculate Lagrange interpolation coefficients Order part of the message Partial message Combined message mess = {mess1, mess2};

[0047] Calculate individual signature s i =k i +h3(mess)·x i ·L i (modq);

[0048] Next, broadcast the message n1 and n2 are the numbers of drones in the two drone groups respectively;

[0049] Step 2), certificate aggregation and verification;

[0050] After receiving the n1 individual signatures from group1, the drone in group2 calculates the aggregated certificate Aggregated public key Verify whether s·P=K+h4(mess)·MK1 holds. If so, threshold authentication is successful. If not, the equation s i ·PK i =h4(mess)·L i ·X i Verify UAV by checking if both sides are equal i Individual signatures i , thereby finding illegal drones;

[0051] This completes the verification of the legitimacy of group1.

[0052] Step 3) The drone in group2 uses TA's public key TPK to verify the source of group1, that is, the legitimacy of MS1. The process is as follows:

[0053] First determine the equation Is it true? If both sides of the equation are equal, it means that MS1 is a legitimate base station authenticated by TA and is authenticated by UAV in group1. i and UAV in group2 k Calculate the session key i,k =usk i ·upk k ; If not established, terminate the session;

[0054] Next, the drone in group1 verifies the legitimacy of the drone in group2 through the above method and establishes a session key;

[0055] At this point, the two drone groups have completed mutual authentication and the identities of all drones are legal.

[0056] Furthermore, the detailed process of group fusion in step (5) is as follows:

[0057] Step 1) UAV in the old group i Select t-1 random numbers q i,1 ,q i,2 ,...,q i,t-1 , generating polynomial Q i (x) = q i,1 x+...+q i,t-1 x t-1 Obviously, Q i (0) = 0;

[0058] Step 2) UAV in the old group i For each UAV in the new group k Select t-1 random numbers r i,k,1 ,r i,k,2 ,...,r i,k,t-1 , generating polynomial R i,k (x) = r i,k,1 x+r i,k,2 x 2 ...+r i,k,t-1 x t-1 , satisfying R i,k (k) = 0;

[0059] Step 3) UAV in the old group i For UAV j Calculate the vector V i,j = {Q i (j)+Ri,1 (j),Q i (j)+R i,2 (j),...,Q i (j)+R i,k (j)}, broadcast the encrypted information

[0060] Improved efficiency: Calculation and communication between old group members can be completed in advance, and the addition of new members does not affect the share sharing process of the old group;

[0061] Step 4) For the UAV in the new group k , UAV j Decrypt V i,j Get all legal shares: Q i (j)+R i,1 (j),Q i (j)+R i,2 (j),...,Q i (j)+R i,k (j), then calculate Broadcasting encrypted messages

[0062] Step 5) UAV k Decrypted to get v j,k , when at least t legal shares are obtained, the interpolation recovery polynomial Calculate the share after sharing

[0063]

[0064] Step 6) Similarly, after the drones in group 1 share their shares with the drones in group 2, each UAV k The share is

[0065] Calculate the final new share Due to the homomorphism of Shamir's secret sharing, the point formed by each drone All satisfy the polynomial P(x)=mk1+mk2+e1x+e2x 2 +...+e t-1 x t-1 ; where mk1 and mk2 are the original secrets of group1 and group2 respectively, e1, e2, ..., e t-1 is a random number;

[0066] At this point, the fused group is formed 1,2 .

[0067] Furthermore, the specific process of updating the certificate in step (5) is as follows:

[0068] The merged group 1，2 In each UAV i calculate:

[0069] in,

[0070]

[0071] Each UAV i Renewing Certificates

[0072] Furthermore, the method of continuous integration of drone groups is:

[0073] Assume that the fused group 1,2 Plan to join group3. The drones in group3 only need to verify the group through the public key MK=(mk1+mk2)·P=MK1+MK2 1，2 The threshold signature is sufficient.

[0074] Beneficial effects: The present invention realizes the dynamic fusion of drone groups by autonomously updating the sub-secrets of drones without the participation of trusted institutions. The scheme supports dynamic self-update of certificates of members of the original group, and realizes secure communication of the new group after fusion and continuous and reliable use of certificates.

[0075] (1) Considering the lack of offline assistance from a trusted institution, it is difficult to achieve group fusion. Therefore, a distributed management solution for drone groups that does not require the full participation of a trusted institution is proposed. The sub-secrets of drones are updated based on mobile active secret sharing technology, and the fusion of drone groups is achieved by utilizing the homomorphism of secret sharing. In addition, in order to ensure communication security during fusion, threshold signatures are used to batch authenticate the legitimacy of the identities of drones before fusion.

[0076] (2) Aiming at the problem of continued validity of certificates of new group members after fusion, the present invention designs an efficient certificate self-update method. Each drone only needs to calculate a small amount of lightweight operations to update the certificate. The principle of certificate chain is used to ensure the legitimacy of the source of the drone group through trust transfer.

[0077] (3) The present invention uses the ROR model to perform formal security proof and informal security analysis to verify the correctness and security of the proposed scheme. Experimental results show that compared with other schemes, this scheme has a smaller computational overhead and can achieve more security functions. At the same time, this invention is the first to use mobile active secret sharing technology to solve the security management solution of drone groups when the trusted organization is offline.

[0078] (3) The present invention uses detailed analysis to evaluate the performance of the scheme, such as the computational and communication overhead of each stage. In addition, the security of the cryptographic protocol has been proven through formal security proofs and informal security analysis, and can resist multiple types of attacks. Compared with other related schemes, this scheme has a smaller computational overhead and can achieve more security functions. At the same time, the present invention is the first to use mobile active secret sharing technology to solve the security management solution of drone groups when the trusted organization is offline. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a system model diagram of the present invention;

[0080] Figure 2 Result diagram of calculation cost of each stage in one embodiment of the present invention;

[0081] Figure 3 It is a result diagram of communication overhead at each stage in an embodiment of the present invention;

[0082] Figure 4 This is a result diagram showing how the computational overhead of the fusion process varies with the number of groups in one embodiment of the present invention;

[0083] Figure 5 This is a result diagram of how the computational overhead of the update process varies with the number of groups in one embodiment of the present invention. DETAILED DESCRIPTION

[0084] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0085] In order to solve the problem that the existing technology lacks the assistance of a trusted institution and is difficult to achieve group fusion, the present invention proposes a safe and efficient drone group autonomous management solution suitable for offline scenarios of trusted institutions. Specifically, this solution autonomously updates the sub-secrets of drones through mobile active secret sharing technology to achieve the fusion of drone groups. Considering that the certificates of new group members after fusion can be continuously available without the assistance of a trusted institution, an efficient certificate self-update method is designed. The drone only needs to calculate a threshold signature to update the certificate. The principle of trust transfer in the certificate chain ensures the legitimacy of the source of the drone group. In addition, in order to ensure the communication security of the group during fusion, the threshold signature is used to batch authenticate the legitimacy of the identity of the drones before fusion. Experimental results show that this solution has good system performance and is suitable for large-scale distributed scenarios.

[0086] like Figure 1 As shown, the distributed management scheme of the drone group based on the mobile active secret sharing technology of this embodiment mainly includes the following participating entities, namely, a trusted authority (TA), a mobile base station (MS), and an unmanned aerial vehicle (UAV). TA is a trusted authority, and all participating entities must first register with TA. TA is responsible for generating the public parameters of the system, generating public and private key pairs for each participating entity and issuing certificates. In this scheme, TA only participates in the initialization stage and the registration stage, and the subsequent process is offline. MS is a mobile base station, which has sufficient computing and storage resources. When the UAV is successfully deployed to an area managed by the MS, the MS is responsible for verifying the identity of the drone and distributing the secret shares of the legitimate drones joining the area. Similar to TA, MS only participates in the initialization authentication stage. When the drone receives the share, the MS is offline and no longer participates in the subsequent process. UAV is the main communication entity and has limited computing and storage resources. The drones in each group have the same status, and there is no cluster head node. Considering the loss during the flight, some drones in the group may be physically damaged. The authentication, fusion, and certificate update of the group are all completed autonomously by the drone without the participation of TA and MS.

[0087] In order to facilitate understanding of the technical solution of this embodiment, the meanings of the relevant variables are first explained, and the specific contents are shown in Table 1.

[0088] Table 1

[0089]

[0090]

[0091] The distributed management method of drone groups based on mobile active secret sharing technology in this embodiment includes the following steps:

[0092] Step (1), system initialization phase, that is, the trusted organization TA generates and publishes the system's public parameters Para = {G, P, q, h1, h2, h3, TPK};

[0093] Among them, G is an additive group of order q, P is the generator of group G, h1, h2, h3, are three hash functions, and TPK is the public key of the trusted organization TA;

[0094] Step (2), registration phase, i.e. the mobile base station MS and the unmanned aerial vehicle UAV participating in the communication respectively request registration from the trusted authority TA in the registration phase and obtain corresponding key, certificate and other information;

[0095] Among them, for the i-th UAV i , obtain the unique real identity UID through the trusted institution TA i 、Private key usk i 、public key upk i , Certificate UCert i ; For the jth mobile base station MS j , obtain the unique real identity MID through the trusted institution TA j 、Private key msk j 、Public key mpk j 、Group Secret mk j , the public key MK corresponding to the group secret j 、Certificate MCert j ;

[0096] Step (3), U2M initialization authentication, that is, the UAV first joins the mobile base station MS and is governed by the mobile base station MS; after mutual identity authentication, the mobile base station MS distributes secret shares to the UAV;

[0097] Specifically, when the intra-group session key negotiation is to be performed, the UAV i Send your own information to the mobile base station MS you want to join j , mobile base station MS j After receiving it, it is verified. If the verification is successful, the session key sk is calculated. j,i , and send its own message to the UAV i , UAV i After receiving, verify it, and if the verification is successful, calculate the session key sk i,j , so far the relevant identity authentication is completed; mobile base station MS j Distribute share x to all drones in its domain i When using the group key zsk j Unicast encrypted information To the corresponding UAV i ;

[0098] Step (4), group authentication, i.e., the drones authenticate the identities of the drones in another group as a group; assuming that the two drone groups from the mobile base station MS1 ​​and the mobile base station MS2 are group1 and group2 respectively, the two drone groups authenticate each other at the same time, which includes the two drone groups establishing intra-group session keys, the two drone groups establishing cross-group session keys, and verifying the certificate chain, until the two drone groups complete mutual authentication and the identities of all drones are legal;

[0099] Step (5), group management, including group integration and certificate update, that is, when there is no trusted agency TA involved, the drones in the two drone groups achieve group integration by sharing shares. After obtaining new shares, each drone updates its own certificate; specifically, it includes:

[0100] Step (5.1), group fusion;

[0101] Assume that the verified drones in drone groups group1 and group2 want to share shares with each other, UID i 、UID j The UID is the ID of the corresponding drone in the old group. k is the identity of the UAV in the new group; taking one of the parties as an example, at this time, the UAV in group2 shares the quota with the UAV in group1, group2 is equivalent to the old group, group1 and group2 are equivalent to the new group, and the process is: the UAV in the old group i Calculate Q i (x), and for each UAV in the new group k Polynomial R i,k (x), UAV in the old group i Also for UAV j Calculate the vector V i,j , and broadcast the encrypted information First, UAV j Decrypt V i,j Get all legal shares and broadcast encrypted messages UAV in the new group k Decrypted to get v j,k , the share after sharing Similarly, after the UAVs in group1 share their shares with the UAVs in group2, each UAV k The share is Get the last new share Forming a fused group1,2 ;

[0102] Step (5.2), certificate update, that is, the merged group 1，2 Each UAV in i Calculate new message mess new and certificates inew .

[0103] In step 1 of this embodiment, the trusted institution TA selects three hash functions h1, h2, and h3, as follows:

[0104]

[0105] n1 represents the number of drones participating in the certification in the drone group;

[0106] Then the trusted authority TA generates a private key tsk, a public key TPK=tsk·P, and a system master key (tsk, TPK).

[0107] The detailed process of registration in step (2) of this embodiment is as follows:

[0108] Step (2.1), the UAV registers with TA. The specific process is as follows:

[0109] The trusted authority TA is the i-th UAV i Choose a unique real identity UID i , and select a random number a for it i and a random private key usk i ;TA calculates A i =a i P, public key upk i =usk i P, corresponding to the UCert certificate i =a i +h1(UID i ||upk i ||A i )·tsk; TA sends the message Send to UAV via secure channel i ;

[0110] Step (2.2), MS registers with TA, the specific process is as follows:

[0111] The trusted authority TA is the jth MS j Choose a unique real identity MID j , and select two random numbers for it and random private key msk j ;TA calculation group secret The public key corresponding to the group secret Public key mpk j =msk j P, corresponding certificate

[0112] Finally, TA sent the message Sent to the mobile base station MS via a secure channel j .

[0113] The detailed process of step (3) in this embodiment is as follows:

[0114] Step (3.1), intra-group session key negotiation, the specific process is as follows:

[0115] UAV i Send the message Sent to mobile base station MS j ;MS j After receiving, first judge UCert i P = A i +h1(UID i ||upk i ||A i ) Whether TPK is established, if so, calculate MS j With UAV i The session key sk j,i =msk j ·upk i , the message Send to UAV i ;

[0116] UAV i After receiving, first judge Is it true? If true, store MCert j , and calculate UAV i With MS j The session key sk i,j =usk i ·mpk j ;

[0117] Step (3.2), distribution of secret shares, the specific process is:

[0118] Mobile Base Station MS j Select t-1 random numbers a1, a2, ..., a t-1 , generating polynomial P j (x) = mk j +a1x+a2x 2 +...+a t-1 x t-1 ;MSj Each UAV in the computational domain i The secret share x i and public key X t :

[0119] x t =P j (UID i ), X i =x i ·P;

[0120] MS j Select random number zsk j As the group key, unicast encrypted information For UAV i ; Each UAV i Received from MS j After the information is i,j Decrypt to get the group key zsk j and share x i .

[0121] In this embodiment, before the group merges, all drones need to authenticate the identity of the group to be joined. After the authentication is passed, every two drones can negotiate the session key to encrypt the shared share in the next stage. In step (4), the two drone groups respectively establish the U2U group session key to achieve the authentication process as follows:

[0122] To avoid redundant description, this section takes group1 authentication and group2 authentication of group1 as examples.

[0123] UAV in UAV group group1 i Choose a random number k i , calculate the random number k i The corresponding public key K i =k i P, broadcast message

[0124] UAV in group 1 i After receiving the message from group2, calculate the hash code HMAC′ j ((UID j ||K j ),zsk1), determine HMAC′ j ((UID j ||K j ),zsk1)=HMAC j ((UID j ||K j ),zsk1) is true;

[0125] If established, UAV i Computing and UAVs j The session key key i,j =k i ·K j ;

[0126] Among them, K j It is UAV j The random number k is chosen j The corresponding public key.

[0127] After completing the U2U intra-group session key in this embodiment, the U2U cross-group session key between different drone groups is established. The process is as follows:

[0128] Step 1), generate individual signature;

[0129] UAV in group1 i Calculate Lagrange interpolation coefficients Order part of the message Partial message Combined message mess = {mess1, mess2};

[0130] Calculate individual signature s i =k i +h3(mess)·x i ·L i (mod q);

[0131] Next, broadcast the message n1 and n2 are the numbers of drones in the two drone groups respectively;

[0132] Step 2), certificate aggregation and verification;

[0133] After receiving the n1 individual signatures from group1, the drone in group2 calculates the aggregated certificate Aggregated public key Verify whether s·P=K+h4(mess)·MK1 holds. If so, threshold authentication is successful. If not, the equation s i ·PK i =h4(mess)·L i ·X i Verify UAV by checking if both sides are equal i Individual signatures i , thereby finding illegal drones;

[0134] This completes the verification of the legitimacy of group1.

[0135] Step 3) The drone in group2 uses TA's public key TPK to verify the source of group1, that is, the legitimacy of MS1. The process is as follows:

[0136] First determine the equation Is it true? If both sides of the equation are equal, it means that MS1 is a legitimate base station authenticated by TA and is authenticated by UAV in group1. i and UAV in group2 k Calculate the session key i,k =usk i ·upk k ;

[0137] Next, the drone in group1 verifies the legitimacy of the drone in group2 through the above method and establishes a session key;

[0138] At this point, the two drone groups have completed mutual authentication and the identities of all drones are legal.

[0139] The detailed process of group fusion in step (5) of this embodiment is as follows:

[0140] Step 1) UAV in the old group i Select t-1 random numbers q i,1 ,q i,2 ,...,q i,t-1 , generating polynomial Q i (x) = q i,1 x+...+q i,t-1 x t-1 Obviously, Q i (0) = 0;

[0141] Step 2) UAV in the old group i For each UAV in the new group k Select t-1 random numbers r i,k,1 ,r i,k,2 ,...,x i,k,t-1 , generating polynomial R i,k (x) = r i,k,1 x+r i,k,2 x 2 ...+r i,k,t-1 x t-1 , satisfying R i,k (k) = 0;

[0142] Step 3) UAV in the old group i For UAV j Calculate the vector V i,j = {Q i (j)+R i,1 (j),Qi (j)+R i,2 (j),...,Q i (j)+R i,k (j)}, broadcast the encrypted information (Efficiency improvement: calculations and communications between old group members can be completed in advance, and the addition of new members does not affect the share sharing process of the old group)

[0143] Step 4) For the UAV in the new group k , UAV j Decryption V i,j Get all legal shares: Q i (j)+R i,1 (j),Q i (j)+R i,2 (j),...,Q i (j)+R i,k (j), then calculate Broadcasting encrypted messages

[0144] Step 5) UAV k Decrypted to get v j,k , when at least t legal shares are obtained, the interpolation recovery polynomial Calculate the share after sharing

[0145]

[0146] Step 6) Similarly, after the drones in group 1 share their shares with the drones in group 2, each UAV k The share is

[0147] Calculate the final new share Due to the homomorphism of Shamir's secret sharing, the point formed by each drone All satisfy the polynomial P(x)=mk1+mk2+e1x+e2x 2 +...+e t-1 x t-1 ; where mk1 and mk2 are the original secrets of group1 and group2 respectively, e1, e2, ..., e t-1 is a random number;

[0148] At this point, the fused group is formed 1,2 .

[0149] The specific process of certificate update in step (5) of this embodiment is as follows:

[0150] The merged group 1，2 In each UAV i calculate:

[0151] in,

[0152] Each UAV i Renewing Certificates

[0153] The present invention can also realize the continuous integration of drone groups, and the specific method is as follows:

[0154] Assume that the fused group 1,2 Plan to join group3. The drones in group3 only need to verify the group through the public key MK=(mk1+mk2)·P=MK1+MK2 1，2 The threshold signature is sufficient.

[0155] Example:

[0156] This embodiment runs on the drone AmovLab Prometheus 600 provided by AmovLab and a PC. The drone has a six-core NVIDIA Carmel ARM 64-bit processor with a main frequency of 1.8 GHz and an operating system of Ubuntu 18.04. The PC host is used to simulate a trusted organization and is equipped with an Intel(R) Core(TM) i7-11700@2.50GHz2.50GHz processor and 16GB memory, and the operating system is Windows 10.

[0157] The computational overhead of each operation of the technical solution of this embodiment is shown in Table 2_1 and Table 2_2:

[0158] Table 2_1

[0159] OP T1(ms) T2(ms) <![CDATA[T pm ]]> 0.670 0.197 <![CDATA[T pa ]]> 0.005 0.001 <![CDATA[T h ]]> 0.007 0.002 <![CDATA[T hm ]]> 0.014 0.004 <![CDATA[T enc ]]> 0.016 0.009 <![CDATA[T dec ]]> 0.013 0.009 <![CDATA[T che ]]> 5.837 0.869 <![CDATA[T sm ]]> 0.011 0.004 <![CDATA[T sa ]]> 0.001 0.0002

[0160] Table 2_2

[0161] t <![CDATA[T sha (ms)]]> <![CDATA[T pr (ms)]]> 10 0.570 8.661 20 1.067 25.101 30 1.635 51.067 40 1.802 85.174 50 2.153 128.135 60 2.546 183.038

[0162] In Table 2_1, OP represents operation, T1 represents the running time on the drone, and T2 represents the running time on the trusted institution. pm : The execution time of the point multiplication operation on the elliptic curve; T pa : execution time of point addition operation on elliptic curve; T h : execution time of a single hash operation; T hm : Execution time for calculating hash verification code; Tenc : Execution time of AES encryption 48 bytes operation; T dec : Execution time of AES decryption 48 bytes operation; T che : Execution time for calculating Chebyshev polynomials; T sm : Execution time of large number multiplication operation; T sa : Execution time of large number addition operation. Table 2_2 shows the execution time T of calculating Shamir polynomial on the drone corresponding to different thresholds t sha and the execution time T of recovering the Shamir polynomial pr .

[0163] Table 3

[0164]

[0165]

[0166] Table 4

[0167]

[0168] According to the above operations, the computational overhead and communication overhead of the technical solution of the present invention in each stage are shown in Table 3, and the overhead of group fusion and certificate update is shown in Table 4. This result clearly shows that the computational overhead of the technical method of the present invention is very lightweight and has obvious advantages over existing methods.

Claims

1. A distributed management method for drone groups based on mobile active secret sharing technology, characterized in that: The following steps are involved: Step (1), system initialization phase, that is, the trusted organization TA generates and publishes the system's public parameters Para = {G, P, q, h1, h2, h3, TPK}; Where G is an additive group of order q, P is the generator of group G, h1, h2, h3 are three hash functions, and TPK is the public key of the trusted organization TA; Step (2), registration phase, i.e. the mobile base station MS and the unmanned aerial vehicle UAV participating in the communication respectively request registration from the trusted authority TA in the registration phase and obtain corresponding key, certificate and other information; Among them, for the i-th UAV i , obtain the unique real identity UID through the trusted institution TA i 、Private key usk i 、public key upk i , Certificate UCert i ; For the jth mobile base station MS j , obtain the unique real identity MID through the trusted institution TA j 、Private key msk j 、Public key mpk j 、Group Secret mk j , the public key MK corresponding to the group secret j 、Certificate MCert j ; Step (3), U2M initialization authentication, that is, the UAV first joins the mobile base station MS and is governed by the mobile base station MS; after mutual identity authentication, the mobile base station MS distributes secret shares to the UAV; Specifically, when the intra-group session key negotiation is to be performed, the UAV i Send your own information to the mobile base station MS you want to join j , mobile base station MS j After receiving it, it is verified. If the verification is successful, the session key sk is calculated. j,i , and send its own message to the UAV i , UAV i After receiving it, it is verified. If the verification is successful, the session key sk is calculated. i,j , so far the relevant identity authentication is completed; mobile base station MS j Distribute share x to all drones in its domain i When using the group key zsk j Unicast encrypted information To the corresponding UAV i ; Step (4), group authentication, i.e., the drones authenticate the identities of the drones in another group as a group; assuming that the two drone groups from the mobile base station MS1 ​​and the mobile base station MS2 are group1 and group2 respectively, the two drone groups authenticate each other at the same time, which includes the two drone groups establishing intra-group session keys, the two drone groups establishing cross-group session keys, and verifying the certificate chain, until the two drone groups complete mutual authentication and the identities of all drones are legal; Step (5), group management, including group integration and certificate update, that is, when there is no trusted agency TA involved, the drones in the two drone groups achieve group integration by sharing shares. After obtaining new shares, each drone updates its own certificate; specifically, it includes: Step (5.1), group fusion; Assume that the verified drones in drone groups group1 and group2 want to share shares with each other, UID i 、UID j The UID is the ID of the corresponding drone in the old group. k is the identity of the UAV in the new group; taking one of the parties as an example, at this time, the UAV in group2 shares the quota with the UAV in group1, group2 is equivalent to the old group, group1 and group2 are equivalent to the new group, and the process is: the UAV in the old group i Calculate Q i (x), and for each UAV in the new group k Polynomial R i,k (x), UAV in the old group i Also for UAV j Calculate the vector V i,j , and broadcast the encrypted information First, UAV j Decryption V i,j Get all legal shares and broadcast encrypted messages UAV in the new group k Decrypted to get v j,k , the share after sharing Similarly, after the UAVs in group1 share their shares with the UAVs in group2, each UAV k The share is Get the last new share Forming a fused group 1,2 ; Step (5.2), certificate update, that is, the merged group 1，2 Each UAV in i Calculate new message mess new and Certificate 2. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1 is characterized in that: In step 1, the trusted institution TA selects three hash functions h1, h2, and h3, as follows: n1 represents the number of drones participating in the certification in the drone group; Then the trusted authority TA generates a private key tsk, a public key TPK=tsk·P, and a system master key (tsk, TPK).

3. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1 is characterized in that: The detailed process of registration in step (2) is as follows: Step (2.1), the UAV registers with TA. The specific process is as follows: The trusted authority TA is the i-th UAV i Choose a unique real identity UID i , and select a random number a for it i and a random private key usk i ;TA calculates A i =a i P, public key upk i =usk i P, corresponding certificate UCert i =a i +h1(UID i ||upk i ||A i )·tsk; TA sends the message Send to UAV via secure channel i ; Step (2.2), MS registers with TA, the specific process is as follows: The trusted authority TA is the jth MS j Choose a unique real identity MID j , and select two random numbers for it and random private key msk j ;TA calculation group secret The public key MK corresponding to the group secret j =mk j ·P, Public key mpk j =msk j P, corresponding certificate Finally, TA sent the message Sent to the mobile base station MS via a secure channel j .

4. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1 or 3, characterized in that: The detailed process of step (3) is as follows: Step (3.1), intra-group session key negotiation, the specific process is as follows: UAV i Send the message Sent to mobile base station MS j ;MS j After receiving, first judge UCert i P = A i +h1(UID i ||upk i ||A i )·Whether TPK is established, if established, calculate MS j With UAV i The session key sk j,i =msk j ·upk i , the message Send to UAV i ; If not established, terminate the session; UAV i After receiving, first judge Is it true? If true, store MCert j , and calculate the UAV i With MS j The session key sk i,j =usk i ·mpk j ; If not established, terminate the session; Step (3.2), distribution of secret shares, the specific process is: Mobile Base Station MS j Select t-1 random numbers a1, a2, ..., a t-1 , generating polynomial P j (x) = mk j +a1x+a2x 2 +...+a t-1 x t-1 ; MS j Each UAV in the computational domain i The secret share x i and public key X i : x i =P j (ID i ),X i =x i ·P; MS j Select random number zsk j As the group key, unicast encrypted information For UAV i ; Each UAV i Received from MS j After the information is i,j Decrypt to get the group key zsk j and share x i .

5. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1 is characterized in that: Before group fusion, all drones need to authenticate the identity of the group to be joined. After the authentication is passed, every two drones can negotiate the session key to encrypt the shared share in the next stage. The process of establishing the U2U intra-group session key for authentication between the two drone groups in step (4) is as follows: Assume that group1 authenticates within the group and group2 authenticates group1; UAV in UAV group group1 i Choose a random number k i , calculate the random number k i The corresponding public key K i =k i P, broadcast message UAV in group 1 i After receiving the message from group2, calculate the hash code HMAC′ j ((UID j ||K j ),zsk1), determine HMAC′ j ((UID j ||K j ),zsk1)=HMAC j ((UID j ||K j ),zsk1) is true, if not, terminate the session; If established, UAV i Computing and UAVs j The session key key i,j =k i ·K j ; Among them, K j It is UAV j The random number k is chosen j The corresponding public key.

6. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1 or 5, characterized in that: After completing the U2U intra-group session key, establish the U2U cross-group session key between different drone groups. The process is as follows; Step 1), generate individual signature; UAV in group1 i Calculate Lagrange interpolation coefficients Order part of the message Partial message Combined message mess = {mess1, mess2}; Calculate individual signature s i =k i +h3(mess)·x i ·L i (mod q); Next, broadcast the message n1 and n2 are the numbers of drones in the two drone groups respectively; Step 2), certificate aggregation and verification; After receiving the n1 individual signatures from group1, the drone in group2 calculates the aggregated certificate Aggregated public key Verify whether s·P=K+h4(mess)·MK1 holds. If so, threshold authentication is successful. If not, the equation s i ·PK i =h4(mess)·L i ·X i Verify UAV by checking if both sides are equal i Individual signatures i , thereby finding illegal drones; This completes the verification of the legitimacy of group1. Step 3) The drone in group2 uses TA's public key TPK to verify the source of group1, that is, the legitimacy of MS1. The process is as follows: First determine the equation Is it true? If both sides of the equation are equal, it means that MS1 is a legitimate base station authenticated by TA and is authenticated by UAV in group1. i and UAV in group2 k Calculate the session key i,k =usk i ·upk k , if not established, terminate the session; Next, the drone in group1 verifies the legitimacy of the drone in group2 through the above method and establishes a session key; At this point, the two drone groups have completed mutual authentication and the identities of all drones are legal.

7. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1 is characterized in that: The detailed process of group fusion in step (5) is as follows: Step 1) UAV in the old group i Select t-1 random numbers q i,1 ,q i,2 ,...,q i,t-1 , generating polynomial Q i (x) = q i,1 x+...+q i,t-1 x t-1 Obviously, Q i (0) = 0; Step 2) UAV in the old group i For each UAV in the new group k Select t-1 random numbers r i,k,1 ,r i,k,2 ,...,r i,k,t-1 , generating polynomial R i,k (x) = r i,k,1 x+r i,k,2 x 2 ...+r i,k,t-1 x t-1 , satisfying R i,k (k) = 0; Step 3) UAV in the old group i For UAV j Calculate the vector V i,j = {Q i (j)+R i,1 (j),Q i (j)+R i,2 (j),...,Q i (j)+R i,k (j)}, broadcast the encrypted information Step 4) For the UAV in the new group k , UAV j Decryption V i,j Get all legal shares: Q i (j)+R i,1 (j),Q i (j)+R i,2 (j),...,Q i (j)+R i,k (j), then calculate Broadcasting encrypted messages Step 5) UAV k Decrypted to get v j,k , when at least t legal shares are obtained, the interpolation recovery polynomial Calculate the share after sharing Step 6) Similarly, after the drones in group 1 share their shares with the drones in group 2, each UAV k The share is Calculate the final new share Due to the homomorphism of Shamir's secret sharing, the point formed by each drone All satisfy the polynomial P(x)=mk1+mk2+e1x+e2x 2 +...+e t-1 x t-1 ; where mk1 and mk2 are the original secrets of group1 and group2 respectively, e1, e2, ..., e t-1 is a random number; At this point, the fused group is formed 1,2 .

8. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1 or 7, characterized in that: The specific process of certificate update in step (5) is as follows: The merged group 1，2 In each UAV i calculate: in, Each UAV i Renewing Certificates 9. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1 or 7, characterized in that: The method of continuous integration of drone groups is: Assume that the fused group 1,2 Plan to join group3. The drones in group3 only need to verify the group through the public key MK=(mk1+mk2)·P=MK1+MK2 1，2 The threshold signature is sufficient.

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