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

Abstract

The application discloses a kind of unmanned aerial vehicle group distribution management method based on mobile initiative secret sharing technology, support trusted agency offline, including trusted agency TA generates public parameter;Mobile base station MS and unmanned aerial vehicle UAV participating in communication are registered to trusted agency respectively in registration stage, and obtain key, certificate and the like information;UAV joins MS and is governed by MS, after mutual authentication identity, MS distributes secret share to UAV;Unmanned aerial vehicle group line identity authentication;Two groups of unmanned aerial vehicles realize the fusion of group by sharing share, obtain new share after each unmanned aerial vehicle updates own certificate.The sub-secret of unmanned aerial vehicle is updated autonomously by mobile initiative secret sharing technology in the application, and the fusion of completely decentralized unmanned aerial vehicle group is realized.Secondly, an efficient certificate self-update method is designed.Unmanned aerial vehicle only needs to calculate a threshold signature to update certificate.Detailed security proof and comprehensive experiment show that the application can realize the dynamic autonomous management of distributed unmanned aerial vehicle group, with good security characteristics and low computational overhead.

Description

TECHNICAL FIELD

[0001] The present application relates to mobile proactive secret sharing (MPSS) and threshold signature technology, and in particular to a method for distributed management of a UAV group based on mobile proactive secret sharing technology. BACKGROUND

[0002] Secret sharing is a technique that divides a secret into multiple shares and distributes them to different participants for storage. Only when a sufficient number of participants cooperate can the original secret be recovered, while any fewer than the specified number of participants cannot obtain the complete secret information. However, the traditional secret sharing technology has certain security risks. If some participants are controlled by an adversary or the share storage device is attacked, the secret may be leaked. David Schultz, Barbara Liskov and Moses Liskov first proposed mobile proactive secret sharing technology in 2010. Mobile proactive secret sharing provides mobility on the basis of proactive secret sharing, that is, the node group holding the secret shares can change. This scheme combines share update and share recovery into one step, allowing the group members to change. Nodes periodically perform a switching protocol so that, with the secret unchanged, a different node group generates a new set of shares and shares the new shares with a new node group that may be different from the original share holding group. (t, n) threshold signature means that a signature group is composed of t members, and a combination of more than or equal to t legitimate members in the group can represent the group to use the private key of the group to sign, and anyone can use the public key of the group to verify the signature. Here t is the threshold value, and any t-1 or fewer members in the group cannot represent the group to sign, and any member cannot impersonate other members to sign. Threshold signature is a distributed multi-party signature protocol, including distributed key generation, signature generation, and signature verification algorithms.

[0003] Although the existing centralized group management scheme is relatively mature, most of the schemes require a trusted agency to remain online, which has a single point of failure problem. In terms of group fusion, some schemes require a trusted agency to apply for a certificate before a new member joins, and to authenticate each other with the members in the group. In the scheme based on blockchain, when a new member joins the group, a trusted agency needs to store the public key information of the new member on the blockchain. The members in the group obtain the public key of the new member from the blockchain and verify whether the member is legitimate.

[0004] However, the maintenance cost of the blockchain is high, and the identity of the member is still managed by a trusted authority. In a multi-center scheme, the trusted authority divides the entire system into multiple subgroups at the initial time, and selects a cluster head for each subgroup. These cluster heads are responsible for managing the identity information of the members in the group, and assisting in authentication. When a new member joins the group, the cluster head in the group needs to distribute keys, certificates, etc. to the new member. However, once the cluster head has a single point of failure, it cannot provide effective proof for the new member. In terms of certificate update, most schemes update the public certificate or pseudonym certificate through the trusted authority. When a member joins the group, the trusted authority needs to calculate and update the domain key parameter. All members in the group calculate the domain key based on the domain key parameter to ensure the security of subsequent communication in the group. Alternatively, the trusted authority needs to distribute pseudonym certificates to the new member when the new member joins. At the same time, in order to ensure the long-term communication security of the entire group, the trusted authority needs to update the pseudonym certificates of the original group members, and upload these certificates to the blockchain.

[0005] However, the above schemes cannot be applied to the scene where the trusted authority is offline, the fusion of the unmanned aerial vehicle group, and the continuous availability of the certificates of the members after fusion. Therefore, it is necessary to design a group management scheme that supports group fusion and certificate self-update for the scene where the trusted authority is offline. SUMMARY

[0006] The purpose of the present application is to solve the problems in the prior art and provide a method for distributing management of an unmanned aerial vehicle group based on mobile proactive secret sharing technology, which solves the problems of dynamic fusion of the unmanned aerial vehicle group and update of the certificates of the members after fusion in a distributed scenario.

[0007] The mobile proactive secret sharing technology can be applied in a distributed scenario, and the fusion of the unmanned aerial vehicle group can be realized by autonomously updating the sub-secrets of the unmanned aerial vehicles. Considering that the certificates of the members of the new group after fusion can be continuously available without the assistance of the trusted authority, an efficient certificate self-update method is designed, and the unmanned aerial vehicle only needs to calculate a threshold signature to update the certificate. The principle of trust transfer in the certificate chain ensures the legality of the source of the unmanned aerial vehicle group. In addition, in order to ensure the communication security of the group during fusion, the identity legality of the unmanned aerial vehicles is batch-authenticated using a threshold signature before fusion. Based on the concept of threshold signature, distributed authentication can be realized, thereby avoiding the single point of failure problem.

[0008] Technical scheme: The method for distributing management of an unmanned aerial vehicle group based on mobile proactive secret sharing technology comprises the following steps:

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

[0010] 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 authority TA;

[0011] Step (2), the 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 the corresponding key and certificate 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 UCert Certificate 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 it, it is verified and the session key sk is calculated if the verification is successful 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, that is, the drones authenticate the identities of the drones in another group as a group; assuming that the two different 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, specifically including 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, includes group integration and certificate update. That is, when there is no trusted authority TA involved, the drones in the two drone groups achieve group integration by sharing the quota. After obtaining the new quota, 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 quotas with each other, UID i 、UID j The UID is the ID of the corresponding drone in the old group. k The UAV in the new group is identified; taking one of the parties as an example, the UAV in group2 shares the quota with the UAV in group1. Group2 is equivalent to the old group, and group1 and group2 are equivalent to the new group. 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 vector V i,j , and broadcast the encrypted information First by UAV j Decrypt V i,j Get all legal shares and broadcast encrypted messages UAVs in the new group k Decrypted to get v j,k , the share after sharing Similarly, after the UAVs in group 1 share their shares with the UAVs in group 2, each UAV k The share of 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 authority TA selects three hash functions h1, h2, and h3, as follows:

[0021]

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

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

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

[0025] Step (2.1), the UAV is registered 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 will send the message Send to UAV via secure channel i ;

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

[0028] Trusted institution 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 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 The message Sent to mobile base station MS j ;MS j After receiving it, 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, terminate the session;

[0033] UAV i After receiving, first judge Is it true? If so, store MCert j , and calculate the UAV i With MS j The session key sk i,j =usk i ·mpk j ; If not, 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 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 Decryption to obtain the group key zsk j and share x i .

[0038] Furthermore, before group fusion, 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 in the next stage. The process of establishing the U2U intra-group session key for authentication in step (4) is as follows:

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

[0040] UAV in drone 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] UAVs in group 1 i After receiving the message from group2, calculate the hash code HMAC j ′((UID j ||K j ),zsk1), judge 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 Session key key i,j =k i ·K j ;

[0043] Among them, K j It's a UAV j The random number k selected 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 group 1 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 number of drones in the two drone groups respectively;

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

[0050] After receiving n1 individual signatures from group1, the drone in group2 calculates the aggregated certificate Aggregated public key Verify whether s·P=K+h4(mess)·MK1 is true. If so, it means that the threshold authentication is passed; if not, through equation s i ·PK i =h4(mess)·L i ·X i Verify UAV by checking whether 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 its public key TPK to verify the source of group1, i.e. 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 controlled by UAV in group1. i and the UAV in group2 k Calculate the session key i,k =usk i ·upk k ; If not, terminate the session;

[0054] Next, the drone in group 1 verifies the legitimacy of the drone in group 2 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 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] Efficiency improvement: the computation and communication among the old group members can be done in advance, and the joining of new members does not affect the share sharing process of the old group;

[0061] Step 4), for the UAVs in the new group k , the UAVs j decrypt V i,j get all the legal share: Q i (j) + R i,1 (j), Q i (j) + R i,2 (j),..., Q i (j) + R i,k (j), and then calculate Broadcast the encrypted message

[0062] Step 5), the UAVs k decrypt to get v j,k When at least t legal shares are obtained, interpolate to recover the polynomial Calculate the shared share

[0063]

[0064] Step 6), similarly, after the UAVs in group1 share the shares with the UAVs in group2, the share of each UAV k is

[0065] Calculate the final new share Due to the homomorphism of Shamir secret sharing, the point formed by each UAV satisfies 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 are random numbers;

[0066] So far, the fused group group 1,2 is formed.

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

[0068] The fused group 1，2 Each UAV i Calculate:

[0069] Wherein,

[0070]

[0071] Each UAV i Update the certificate

[0072] Further, the method for continuously fusing the UAV group is:

[0073] Suppose the fused group 1,2 Plan to join group 3, and the UAV in group 3 only needs to verify the threshold signature of group 1，2 By public key MK=(mk1+mk2)·P=MK1+MK2.

[0074] Beneficial effects: the UAV sub-secret of the application is updated autonomously, the dynamic fusion of the UAV group is realized, the participation of the trusted agency is not needed, the scheme supports the dynamic self-update of the original group member certificate, the secure communication of the new group after fusion and the continuous and reliable use of the certificate are realized.

[0075] (1), the application considers that it is difficult to realize group fusion due to the lack of offline assistance of the trusted agency, and proposes a UAV group distributed management scheme without the whole participation of the trusted agency. Based on the mobile active secret sharing technology, the sub-secret of the UAV is updated, and the homomorphism of secret sharing is used to realize the fusion of the UAV group. In addition, in order to ensure the communication security during fusion, the identity legitimacy of the UAV is authenticated in batches by using threshold signature before fusion.

[0076] (2), the application designs an efficient certificate self-update method for the continuous validity of the certificate of the new group member after fusion. Each UAV only needs to calculate a small amount of lightweight operation to update the certificate. By using the principle of certificate chain, the source legitimacy of the UAV group is ensured through trust transmission.

[0077] (3) The present application uses ROR model to perform formal security proof and non-formal security analysis, and verifies the correctness and security of the proposed scheme. Experimental results show that, compared with other schemes, the present application has smaller calculation overhead and can realize more security functions. Meanwhile, the present application is the first to use mobile proactive secret sharing technology to solve the security management scheme of the UAV group when the trusted agency is offline.

[0078] (3) The present application uses ROR model to perform formal security proof and non-formal security analysis, and verifies the correctness and security of the proposed scheme. Experimental results show that, compared with other schemes, the present application has smaller calculation overhead and can realize more security functions. Meanwhile, the present application is the first to use mobile proactive secret sharing technology to solve the security management scheme of the UAV group when the trusted agency is offline. BRIEF DESCRIPTION OF DRAWINGS

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

[0080] Figure 2 is a calculation overhead result diagram of each stage in an embodiment of the present application;

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

[0082] Figure 4 is a calculation overhead result diagram of the fusion process in an embodiment of the present application;

[0083] Figure 5 is a calculation overhead result diagram of the update process in an embodiment of the present application. DETAILED DESCRIPTION

[0084] The technical scheme of the present application will be described in detail below, but the protection scope of the present application is not limited to the described embodiments.

[0085] In order to solve the problem that the group fusion is difficult to realize due to the lack of assistance of a trusted agency in the prior art, the present application proposes a safe and efficient unmanned aerial vehicle group autonomous management scheme suitable for the offline scene of a trusted agency. Specifically, the present scheme realizes the fusion of the unmanned aerial vehicle group by autonomously updating the sub-secret of the unmanned aerial vehicle through mobile proactive secret sharing technology. Considering that the certificate of the new group member after fusion can be continuously available without the assistance of a trusted agency, an efficient certificate self-update method is designed. The unmanned aerial vehicle only needs to calculate a threshold signature to update the certificate. The principle of trust transmission in the certificate chain guarantees the legitimacy of the source of the unmanned aerial vehicle group. In addition, in order to guarantee the communication security of the group during fusion, the identity legitimacy of the unmanned aerial vehicle is batch authenticated using a threshold signature before fusion. The experimental results show that the present scheme has good system performance and is suitable for large-scale distributed scenes.

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

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

[0088] Table 1

[0089]

[0090]

[0091] The unmanned aerial vehicle group distributed management method based on mobile proactive secret sharing technology of the present 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] 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 authority TA;

[0094] Step (2), the 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 the corresponding key and certificate 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 UCert Certificate 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 it, it is verified and the session key sk is calculated if the verification is successful 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, that is, the drones authenticate the identities of the drones in another group as a group; assuming that the two different drone groups from mobile base station MS1 ​​and mobile base station MS2 are group1 and group2 respectively, these two drone groups authenticate each other at the same time, specifically including 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, includes group integration and certificate update. That is, when there is no trusted authority TA involved, the drones in the two drone groups achieve group integration by sharing the quota. After obtaining the new quota, 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 quotas with each other, UID i 、UID j The UID is the ID of the corresponding drone in the old group. k The UAV in the new group is identified; taking one of the parties as an example, the UAV in group2 shares the quota with the UAV in group1. Group2 is equivalent to the old group, and group1 and group2 are equivalent to the new group. 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 vector V i,j , and broadcast the encrypted information First, UAV j Decrypt V i,j Get all legal shares and broadcast encrypted messages UAVs in the new group k Decrypted to get v j,k , the share after sharing Similarly, after the UAVs in group 1 share their shares with the UAVs in group 2, each UAV k The share of Get the last new share Forming a fused group1,2 ;

[0102] Step (5.2), certificate update, i.e. the fused group group 1，2 of each UAV i calculates a new message mess new and a certificate s inew .

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

[0104]

[0105] n1 represents the number of UAVs participating in authentication in the UAV 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 step (2) registration described in the embodiment is as follows:

[0108] Step (2.1), registration of the UAV UAV at the TA, and the specific process is as follows:

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

[0110] Step (2.2), registration of the MS at the TA, and the specific process is as follows:

[0111] The trusted authority TA selects a unique real identity MID j for the j-th MS j , and selects two random numbers and a random private key msk j for it; the TA calculates a group secret A public key 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 The message Sent to mobile base station MS j ;MS j After receiving it, 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 so, store MCert j , and calculate the 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 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 Decryption to obtain the group key zsk j and share x i .

[0121] In this embodiment, before group fusion, all drones need to authenticate their identities to join the group. After authentication, each two drones can negotiate a session key to encrypt the shared share in the next phase. In step (4), the two drone groups establish U2U intra-group session keys to implement authentication as follows:

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

[0123] UAV in drone 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] UAVs in group 1 i After receiving the message from group2, calculate the hash code HMAC′ j ((UID j ||K j ),zsk1), judge 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 Session key key i,j =k i ·K j ;

[0126] Among them, K j It's a UAV j The random number k selected j The corresponding public key.

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

[0128] Step 1) Generate individual signature;

[0129] UAV in group 1 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 number of drones in the two drone groups respectively;

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

[0133] After receiving n1 individual signatures from group1, the drone in group2 calculates the aggregated certificate Aggregated public key Verify whether s·P=K+h4(mess)·MK1 is true. If so, it means that the threshold authentication is passed; if not, through equation s i ·PK i =h4(mess)·L i ·X i Verify UAV by checking whether 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 its public key TPK to verify the source of group1, i.e. 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 controlled by UAV in group1. i and the UAV in group2 k Calculate the session key i,k =usk i ·upk k ;

[0137] Next, the drone in group 1 verifies the legitimacy of the drone in group 2 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 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: the calculation and communication between the old group members can be done in advance, and the joining of new members does not affect the share sharing process of the old group)

[0143] Step 4), for the UAVs in the new group k , the UAVs 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), and then calculate broadcast the encrypted message

[0144] Step 5), the UAVs k decrypt to get v j,k , when at least t legal shares are obtained, interpolate to recover the polynomial calculate the shared shares

[0145]

[0146] Step 6), similarly, after the UAVs in group1 share the shares with the UAVs in group2, the share of each UAV k is

[0147] calculate the final new shares Due to the homomorphism of Shamir secret sharing, the point formed by each UAV satisfies the polynomial P(x) = mk1+mk2+e1x+e2x 2 +...+e t-1 x t-1 ; where mk1and mk2are the original secrets of group1 and group2 respectively, e1, e2,..., e t-1 are random numbers;

[0148] So far, the fused group group 1,2 is formed.

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

[0150] The fused group 1，2 Each UAV i Computing:

[0151] Wherein,

[0152] Each UAV i Update the certificate

[0153] The present application can also realize the continuous fusion of the UAV group, and the specific method is:

[0154] Suppose the fused group 1,2 Plan to join group 3, and the UAVs in group 3 only need to verify the threshold signature of group 1，2 Through the public key MK=(mk1+mk2)·P=MK1+MK2.

[0155] Embodiment:

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

[0157] The computing overheads of each operation of the technical solution of this embodiment are shown in Table 2_1 and Table 2_2:

[0158] Table 2_1

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

[0160] Table 2_2

[0161] t T sha (ms) 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 UAV, and T2 represents the running time on the trusted agency. pm : The execution time of the point multiplication operation on the elliptic curve; T pa : The execution time of the point addition operation on the elliptic curve; T h : The execution time of a single hash operation; T hm : The execution time of calculating the 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 of calculating Chebyshev polynomial; 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 UAV corresponding to different threshold values t sha and the execution time T of recovering Shamir polynomial pr .

[0163] Table 3

[0164]

[0165]

[0166] Table 4

[0167]

[0168] According to the above operation, the actual application of the technical scheme of the present application in each stage of the calculation overhead and the communication overhead result is shown in Table 3, and the overhead of group fusion and certificate update is shown in Table 4. This result obviously shows that the calculation overhead of the technical method of the present application is very light, and has obvious advantages compared with the existing method.

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 authority TA; Step (2), the 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 the corresponding key and certificate 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 UCert Certificate 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; When the intra-group session key negotiation is to be completed, 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 and the session key sk is calculated if the verification is successful 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, that is, the drones authenticate the identities of the drones in another group as a group; assuming that the two different 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, specifically including 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, includes group integration and certificate update. That is, when there is no trusted authority TA involved, the drones in the two drone groups achieve group integration by sharing the quota. After obtaining the new quota, 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 quotas with each other, UID i 、UID j The UID is the ID of the corresponding drone in the old group. k The drones in group 2 share the quota with the drones in group 1. Group 2 is equivalent to the old group. After group 1 and group 2 are merged, the group is equivalent to the new group. The process 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 , 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 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 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 Broadcast encrypted message 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) After the UAVs in group 1 share their shares with the UAVs 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 is 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 ; Step (5.2), certificate update, that is, the merged group 1，2 Each UAV in i Calculate new message mess new and certificates The specific method is: The merged group 1，2 In each UAV i calculate: in, Each UAV i Renewing a certificate 2. The method for distributed management of drone groups based on mobile active secret sharing technology according to claim 1, characterized in that: In step (1), the trusted authority TA selects three hash functions h1, h2, and h3, as follows: n1 represents the number of drones participating in the authentication in the drone group; Then the trusted authority TA generates a private key tsk, a public key TPK = tsk·P, and the system master key is (tsk, TPK).

3. The distributed management method for drone groups based on mobile active secret sharing technology according to claim 1 is characterized in that: The registration process of step (2) is as follows: Step (2.1), the UAV is registered 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 to the UCert certificate i =a i +h1(UID i ||upk i ||A i )·tsk;TA will send the message Send to UAV via secure channel i ; Step (2.2): MS registers with TA. The specific process is as follows: Trusted institution 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 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 process of step (3) is: Step (3.1), intra-group session key negotiation, the specific process is as follows: UAV i The message Sent to mobile base station MS j ;MS j After receiving it, 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, terminate the session; UAV i After receiving, first judge Is it true? If so, store MCert j , and calculate the UAV i With MS j The session key sk i,j =usk i ·mpk j ; If not, 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 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 Decryption to obtain 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, characterized in that: In step (4), the process of establishing U2U intra-group session keys for authentication between the two drone groups is as follows: assuming that group 1 authenticates within the group and group 2 authenticates group 1; UAV in drone 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 UAVs in group 1 i After receiving the message from group2, calculate the hash code HMAC′ j ((UID j ||K j ),zsk1), judge 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 Session key key i,j =k i ·K j ; Among them, K j It's a UAV j The random number k selected 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 group 1 i Calculate Lagrange interpolation coefficients Order message information 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 number of drones in the two drone groups respectively; Step 2), certificate aggregation and verification; After receiving n1 individual signatures from group1, the drone in group2 calculates the aggregated certificate Aggregated public key Verify whether s·P=K+h4(mess)·MK1 is true. If so, the threshold authentication is passed; if not, the equation s is passed. i ·PK i =h4(mess)·L i ·X i Verify UAV by checking whether 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 its public key TPK to verify the source of group1, i.e. 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 controlled by UAV in group1. i and the UAV in group2 k Calculate the session key i,k =usk i ·upk k , if not established, terminate the session; Next, the drone in group 1 verifies the legitimacy of the drone in group 2 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, characterized in that: The method of drone group fusion 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 Threshold signature.

Images