A multi-dimensional aggregate privacy protection system based on symmetric homomorphic encryption

Abstract

The present invention discloses a multi-dimensional aggregation privacy protection system of symmetric homomorphic encryption, which includes the following steps: initialization phase, system entity registration, blind factor generation, data reporting phase, data aggregation phase, data decryption phase, and dynamic user processing. The technical solution is compatible with dual CRT encoding, maximizes the amount of information of the aggregation result, improves data transmission efficiency and ciphertext space utilization, and takes into account the needs of smart meters with weak computing power, reduces system complexity, and improves data aggregation efficiency. At the same time, an efficient signature method that supports batch verification is introduced to effectively reduce the computational burden of signatures and improve the overall performance of the system. In order to deal with internal attacks, the technical solution not only strengthens the security of the blind factor in design, enables it to be frequently updated, provides forward and backward security, but also adds a fault-tolerant mechanism to the system architecture to improve the stability and reliability of the system.

Description

Technical Field

[0001] The present invention relates to the field of smart grid information security technology, and in particular to a multi-dimensional aggregate privacy protection system with symmetric homomorphic encryption. Background Art

[0002] The aggregation process is generally that the smart meter encrypts the data, then sends it to the aggregator for aggregation, and then submits the aggregation result to the control center for decryption. It is necessary to resist internal and external attacks. Among them, the most commonly used encryption technology is Paillier encryption, which has high security but long keys and high complexity. To resist external attacks, the ciphertext needs to be signed. Many signature technologies are constructed by scholars themselves using cryptographic primitives. Although they are innovative, they ignore the computational cost. Therefore, signatures with high computational costs such as bilinear mapping should be avoided.

[0003] In terms of defending against internal attacks, most existing technologies or solutions introduce a trusted third party to distribute keys and blinding factors. However, this method also makes the trusted third party a central node, whose security and stability must be very high and must be trustworthy, but this is too idealistic.

[0004] In addition, the fault tolerance of the solution must be high. When the smart meter is damaged, the system should be able to decrypt the aggregated data normally. The common solution is to let the normal smart meter delete the associated collaborative key and resend the data, or use a threshold solution, but this method also hides the forward and backward security issues of damaging the smart meter. For multi-dimensional aggregation, the technologies used include super-incremental sequence or slot construction, but both face the problem of long encoded data length. The solution also needs to meet the dynamic addition or exit of users.

[0005] The existing solutions have problems such as high complexity of asymmetric homomorphic cryptographic systems, large signature complexity, reliance on an idealized trusted third party for defense against internal attacks, insufficient security of blind factors, and lack of support for fault tolerance. Summary of the invention

[0006] The purpose of the present invention is to provide a multi-dimensional aggregate privacy protection system of symmetric homomorphic encryption to solve the problems raised in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical solution: a multi-dimensional aggregate privacy protection system for symmetric homomorphic encryption, comprising the following steps:

[0008] Step 1, initialization phase: including smart meters, fog nodes, and control centers;

[0009] System parameter initialization: Based on the secure elliptic curve, the control center selects CRT1 parameters according to the definition of the Chinese Remainder Theorem (CRT). The control center generates the parameters required for the extended Shamir threshold scheme: First, the control center selects a large prime number P s , GF(P s ) as its finite field, and then choose (P s -1) two large prime factors p s ,q s , set an N s =p s q s , in GF(P s ) Set g s is a generator and has order N s The control center takes the parameters of the elliptic curve and the hash function H and K pub =(P s , N s , g s ) broadcast it;

[0010] System entity registration: The control center generates public and private keys based on the entities that join, and sends the public and private keys corresponding to the entities to the fog nodes for storage;

[0011] Blind factor generation: Each smart meter and control center generates a blind factor through a secure communication channel. The smart meter and control center each randomly select a private key and calculate the corresponding public key. The smart meter uses the collaborative key set to calculate the root blind factor and updates the blind factor through the update rule. The blind factor is used to mask the electricity consumption data reported by the smart meter to protect the privacy of the smart meter.

[0012] The smart meter will update the blinding factor using the update rule at each reporting stage, and calculate the threshold parameters for fault tolerance and send them to the fog node to prevent accidental damage to the smart meter;

[0013] The smart meter uses the secret share and blinding factor to update its own mask value and sends the updated mask value to the control center for storage. The control center collects the mask values ​​of all smart meters for subsequent data aggregation and privacy protection processing;

[0014] Step 2, data reporting stage: the smart meter calculates the power consumption data of the appliance based on the data of each dimension and the power consumption interval to which it belongs, encrypts and blinds the data, and then sends all the data to the fog node;

[0015] Step 3, data aggregation phase: The fog node searches and verifies in the database based on the data of the smart meter. If it passes, it performs signature verification;

[0016] Step 4, data decryption phase: The control center first checks the timestamp and whether the public key of the fog node exists, and then performs signature verification. According to the properties of the Chinese remainder theorem, the total power consumption of a certain electrical appliance in the community can be extracted;

[0017] Step 5, dynamic smart meter processing: The control center generates public keys and private keys for newly registered smart meters, registers by issuing digital certificates, and then passes security protocols to ensure the security of system parameters released to newly registered smart meters.

[0018] Furthermore, smart meters collect multi-dimensional data, where each dimension represents the power consumption of a type of electrical appliance. The fog node aggregates the data of several smart meters in a community and submits it to the control center. The control center decrypts the data submitted by the fog node and extracts the aggregate value of each dimension and the total number of different power consumption intervals of electrical appliances in each dimension.

[0019] Furthermore, suppose there are n smart meters in the system, w is the electrical appliance, and the control center selects k continuous power consumption ranges [R 1 , R 2 ), [R 2 , R 3 ),…,[R k , E), and l continuous power consumption range [R′ 1 , R′ 2 ), [R′ 2 , R′ 3 ), ..., [R′ l , E′);

[0020] Among them, R 1 =R′ 1 = 0, E and E′ are the maximum power consumption of two continuous power consumption ranges, m i represents the total power consumption of the i-th smart meter, and m i ∈[R j , R j+1 ) represents m i Belong to [R 1 , R 2 ), [R 2 , R 3 ),…,[R k , E) in the first gear power consumption, m ij ∈[R′ x , R′ x+1 ) indicates that the jth electrical appliance of the ith smart meter belongs to [R′ 1 , R′ 2 ), [R 2 ′,R′ 3 ), ..., [R′ l , E′) in the xth gear power consumption;

[0021] Generate CRT2 parameters according to the Chinese remainder theorem: The same generation parameters q 2j , j∈[1,w+k], where q 21 ,q 22 …, q 2w >nQ 1 , and q 2(w+1) ,q 2(w+2) …, q 2(w+k) >n, similarly, they are all relatively prime numbers, and the same basis is used to generate Q 2 =q 21 q 22 …q 2(k+w) , E 2j =Q 2 / q 2j and E′ 2j , the control center selects a random number r and a small random number d, and then selects a p that satisfies |r|+|n|+|Q 2 |<|p|;

[0022] Then in Next, we select a random number s, so we have the encryption key K sm =s d r mod p, decryption key SK = (s, d, r).

[0023] Furthermore, on the initialized elliptic curve, the newly added SM i Randomly select an integer x i As the private key, corresponding to the generated X i =x i G is used as the public key and the public key is sent to the control center for registration. The control center registers each SM i Each is assigned an ID i , ID i ∈[1, n], the control center defines U for the n registered smart meters, and stipulates The fog node randomly selects x FN As the private key, corresponding to the generated X PN =x FN G is used as the public key and the public key is sent to the control center, which also generates a private key x cc and public key X cc , private key SM i Self storage.

[0024] The control center will Sent to registered SMs, each SM i according to Parameters, randomly selected from U The smart meters are used to share the Shamir secret, and the IDs of the selected smart meters are all loaded into O i , and broadcast O i , the control center will U||X sm ||X cc Sent to the registered fog nodes for storage, where X sm It contains the public keys of all smart meter registrations;

[0025] SM i Randomly select a private key κ i , and calculate the public key K t =κ i G, SM i Send K i ||ID i Give SM z , S.M. z After receiving, generate K in the same way z , K z =K z G, K z ||ID z Send to SM i .

[0026] Furthermore, each smart meter uses u i and key K sm Encrypt and blind your own datam i，CRT , c i =K sm (m i，CRT +u i )mod p=s d r(m i，CRT +u i )mod p, update its own u according to the update rules in the system entity registration i Used as the blinding factor for the next time, and calculate The smart meter randomly selects a number f according to the elliptic curve defined by the control center initialization i , and the corresponding F i =f i G, then calculate Then calculate the signature σ i =ex i +f i ,Will Sent to FN, where T i It is the current timestamp, indicating the time when the message is actually sent.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) The technical solution provided by the present invention is compatible with dual CRT encoding, maximizes the amount of information in the aggregation results, improves data transmission efficiency and ciphertext space utilization, and takes into account the needs of smart meters with weak computing power, reduces system complexity, and improves data aggregation efficiency. At the same time, an efficient signature method that supports batch verification is introduced to effectively reduce the computational burden of signatures and improve the overall performance of the system. In order to deal with internal attacks, this technical solution not only strengthens the security of the blind factor in design, enables it to be updated frequently, and provides forward and backward security, but also adds a fault-tolerant mechanism to the system architecture to improve the stability and reliability of the system.

[0029] (2) This technical solution overcomes many shortcomings of current smart meter data aggregation solutions. Its purpose is to provide an efficient and secure method for data aggregation and signing processes that takes into account constraints such as smart meter computing power, security requirements, and communication efficiency, and takes user privacy and data security as a prerequisite. This method can be used in communities or large parks equipped with smart meters. It can protect personal data privacy during the multi-dimensional data aggregation process and provide valuable data for smart grids to make decisions such as pricing or power distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a system model diagram of the present invention. DETAILED DESCRIPTION

[0031] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0032] Example:

[0033] See also Figure 1 The present invention provides a technical solution: a multi-dimensional aggregate privacy protection system with symmetric homomorphic encryption, comprising the following steps:

[0034] Step 1: Initialization phase

[0035] 1.1 System Model

[0036] The system model includes three entities, namely, smart meter (SM), fog node (FN), and control center (CC). Figure 1 shown.

[0037] SM: It can collect multi-dimensional data. Each dimension of data represents the power consumption of a type of electrical appliance, and the data will be reported every 15 minutes.

[0038] FN: It is used to aggregate the data of n smart meters in a community and submit it to CC.

[0039] CC: Decrypts the ciphertext submitted by FN and extracts the aggregate value of each dimension.

[0040] 1.2 System parameter initialization

[0041] Assume that there are n smart meters in the system, w is the electrical appliance, CC selects k continuous power consumption ranges [R 1 , R 2 ), [R 2 , R 3 ),…,[R k , E), and l continuous power consumption range [R′ 1 , R′ 2 ), [R′ 2 , R′ 3 ), ..., [R′ l , E′).

[0042] Where R 1 =R′ 1 =0, E and E′ are the maximum power consumptions of two continuous power consumption ranges. i represents the total power consumption of the i-th user (the user is equivalent to a smart meter), and m i ∈[R j , R j+1 ) represents m i Belong to [R 1 , R 2 ), [R 2 , R 3 ),…,[R k , E) is the power consumption of the jth gear.

[0043] Similarly, m ij ∈[R′ x , R′ x+1 ) indicates that the jth electrical appliance of the ith user belongs to [R′ 1 , R′ 2 ), [R′ 2 , R′ 3 ), ..., [R′ l , E′) in the xth gear power consumption.

[0044] CC selects a sufficiently secure elliptic curve and selects a group G of order h on the elliptic curve 1 , and G is its generator. And define a one-way hash function H.

[0045] CC generates the parameters required for the extended Shamir threshold scheme: First, CC selects a large prime number Ps , GF(P s ) is its finite field. Then choose (P s -1) two large prime factors p s ,q s , set an N s =p s q s , in GF(P s ) Set g s is a generator and has order N s CC selects a random number r and a small random number d, and then selects a p that satisfies |r|+|n|+|Q 2 |<|p|, where Indicates the maximum value of the smart meter data after encryption and other operations.

[0046] Then in Next, select a random number s. So there is an encryption key K sm =s d r mod p, decryption key SK = (s, d, r), and select CRT1 parameters according to the definition of Chinese Remainder Theorem (CRT): select mutually prime q 1x , x∈[1,l+1], among which only q 11 >nE′, the remaining q 12 ,q 13 ..., q 1(x+1) >n,q 1x , x∈[1, l+1] are mutually prime. Then calculate Q 1 =q 11 q 12 …q 1(l+1) , and calculate E 1x =Q 1 / q 1x , and calculate E′ 1x Make E 1x E′ 1x ≡1 mod q 1x .

[0047] Same generation parameters for CRT2: Same generation parameters for q 2j , j∈[1,w+k], where q 21 ,q 22 ..., q 2w >nQ 1 , and q 2(w+1) ,q 2(w+2) …, q 2(w+k) >n, and similarly, they are all relatively prime numbers. 2 =q 21 q22 …q 2(k+w) , E 2j =Q 2 / q 2j and E′ 2j .

[0048] CC combines the parameters of the elliptic curve with the hash function H and K pub =(P s , N s , g s ) broadcast it out.

[0049] 1.3 System Entity Registration

[0050] It is assumed that the registration phase communicates over a secure channel and that all entities perform the relevant steps honestly.

[0051] On the initialized elliptic curve, the SM you want to join i Randomly select an integer x i As the private key, corresponding to the generated X i =x i G is used as the public key and the public key is sent to CC for registration. CC registers each SM i Each is assigned an ID i , ID i ∈[1, n], in addition, CC for n registered users is defined as U, which contains all the user IDs i . And stipulate Parameters. FN randomly selects x FN As the private key, corresponding to the generated X PN =x FN G is used as the public key and the public key is sent to CC. CC also generates a corresponding private key x cc and public key X cc , the private key is stored by yourself.

[0052] CC will Sent to registered SMs. Each SM i according to Parameters, randomly selected from U The user is used to share the Shamir secret, and all the selected user IDs are loaded into O i , and broadcast O i . CC will U||X sm ||X cc Sent to the registered FN for storage, where X sm Contains the public keys of all smart meters registered.

[0053] 1.4 Blind Factor Generation

[0054] The system has not yet been officially put into operation during the blind factor generation phase. Assuming that its communication is a secure channel, each smart meter SM i and CC generate the root blinding factor u according to the following rules i and u cc :

[0055] SM i and SM z For example (assuming ID i >ID z ), on the initialized elliptic curve, SM i Randomly select a private key κ i , and calculate the public key K i =κ i G. SM i Send K t ||ID i Give SM z .

[0056] SM z After receiving, the same κ is generated z , K z =K z G, K z ||ID z Send to SM i . Then calculate:

[0057] V zi =-H(κ z K t )=-H(κ z κ i G) (1)

[0058] (Here we take κ z κ i The x-axis hash of G is used as the collaborative key, the same below), and V zi Put your own collaborative key set V z .

[0059] SM i Receive K z ||ID z Then, the same calculation is obtained:

[0060] V iz =H(κ i K z )=H(κ i κ z G) (2)

[0061] V iz Put your own collaborative key set V i .

[0062] When n smart meters and CC complete the collaborative smart meter selection, each smart meter and CC will obtain a collaborative key set V. Obviously, every collaborative key must have an opposite number, so the sum of the collaborative keys of n+1 entities must be 0.

[0063] SM i Take the blinding factor as an example:

[0064]

[0065] Where V i (·) indicates V i The collaborative key V of a collaborative key set of an entity in xy , sign(x) is the sign function, x>0 returns 1, x<0 returns -1. i0 It is expressed as the root blinding factor and is not used to mask the data. The masked data uses the updated blinding factor u i Update blinding factor: Update the collaborative key. i Each collaborative key in must be updated, and the update rule is:

[0066] V i (·)=sign(V i (·))H(|V i (·)|) (4)

[0067] So update the blinding factor accordingly:

[0068]

[0069] In addition, let the blinding factor of CC be u cc ,(u cc =u 0 ), obviously The same is still true, because the update of the mutually opposite collaborative keys is the same every time the data is reported. The recommended number of collaborative keys selected by each smart meter is no less than 3, so as to provide sufficient blind factor security.

[0070] Each SM i Randomly select an integer s i As the derived key of Shamir's threshold scheme, a binary polynomial f with k random numbers is selected i (x), let f i (0) = s i , and calculate the set O i All f ij (ID j ), j∈[O i ]where i≠j, fij (ID j ) indicates SM i According to O i The ID of each smart meter in the collection j To calculate the secret share and distribute it to the corresponding SM j .

[0071] So for each smart meter SM in a community that is selected as a secret share holder j There will be a collection And store it locally, where x≠j, the secret share is simply referred to as f ij , indicating SM i About SM j The secret share to send.

[0072] Then each smart meter u i0 They will first update their mask value to u i , and calculate:

[0073]

[0074] where r s =H(T k ), T k It indicates the current time of reporting data. Obviously, each smart meter should report data at the same time T k , which is also specified in advance. For example, it is sent every 15 minutes starting from 10 o'clock. k That is 10:00, 10:15, 10:30... Each smart meter will Sent to FN for storage, so FN will have a collection

[0075] Step 2: Data reporting stage

[0076] SM i According to the data of each dimension (m i1 , m i2 ,…,m iw ), the total amount m can be calculated i =m i1 +m i2 +…+m iw , and according to [R 1 , R 2 ), [R 2 , R 3 ),…,[R k , E) can know the power consumption gear. Similarly, according to (m i1 , m i2 ,…,miw ) in each dimension and its corresponding power consumption interval [R′ 1 , R′ 2 ), [R′ 2 , R′ 3 ), ..., [R′ l , E′), we can calculate:

[0077] m i，CRT =CRT2(CRT1(m i ))=(m i1 E 11 E′ 11 +|S 11 |E 12 E′ 12 +…+|S 1l |E 1(l+1 )E′ 1(l+1) mod Q 1 )E 21 E′ 21 +(m i2 E 11 E′ 11 +|S 21 |E 12 E′ 12 +…+|S 2l |E 1(l+1) E′ 1(l+1) mod Q 1 )E 22 E′ 22 +…+(m iw E 11 E′ 11 +|S w1 |E 12 E′ 12 +…+|S wl |E 1(l+1) E′ 1(l+1) mod Q 1 )E 2w E′ 2w +|S m1 |E 2(w+1) E′ 2(w+1) +|S m2 |E 2(w+2) E′ 2(w+2) +…+|S mk |E 2(w+k) E′ 2(w+k) mod Q 2 (7)

[0078] Where |S wl | indicates that when the power consumption data of the wth electrical appliance is in the lth level, |S wl | is 1. |Smk |Indicates that the smart meter is in the kth gear|S mk | is 1, each smart meter uses u i and key K sm To encrypt and blind your data i，CRT :

[0079] c i =K sm (m i，CRT +u i )mod p=s d r(m i，CRT +u i )mod p (8)

[0080] Then update your own u according to the update rules in the system entity registration i Used as the blinding factor for the next time,

[0081] And calculate:

[0082] The smart meter randomly selects a number f according to the elliptic curve defined by CC initialization i , the corresponding production:

[0083] F i =f i G (10)

[0084] Then calculate:

[0085]

[0086] Calculate the signature:

[0087] σ i =ex i +f i (12)

[0088] Will Sent to FN. Where T i It is the current timestamp, indicating the actual time when the data is sent. It is used to verify whether the interval between sending and receiving data is within a reasonable interval.

[0089] Step 3: Data Aggregation

[0090] FN received Then, in the database according to ID i Find the corresponding X i . Check timestamp T i and whether the database contains X i If it passes, the signature verification is performed. FN is first calculated locally based on the received data:

[0091]

[0092] Then verify:

[0093]

[0094] If they are equal, the verification is successful. i '" indicates the actual value received. Batch verification:

[0095]

[0096] If the verification passes, the message integrity is proven.

[0097] FN first checks the missed smart meter based on U and the received smart meter ID, assuming that the missed smart meter is ID j , the missing ID j and the corresponding Put into a set BRK, then Assume that FN collects The power data sent by the smart meter is aggregated in the following format:

[0098]

[0099] At this time, |S wl | represents the number of users when the wth appliance's electricity consumption data is in the lth level, |S wl |∈[0,n], and |S mk | represents the number of users whose total electricity consumption is in the kth level, |S mk |∈[0,n],

[0100] Similarly, FN randomly selects a number f on the elliptic curve FN , which produces:

[0101] F FN =f FN G (17)

[0102] calculate:

[0103] e FN =H(F FN , X FN , c FN , T FN , BRK) (18)

[0104] Calculate the signature:

[0105] σ FN =e FN xFN +f FN (19)

[0106] Then c FN ||F FN ||X FN ||σ FN ||T FN ||BRK is sent to CC, where T FN Indicates the current timestamp.

[0107] Step 4: Data decryption phase

[0108] CC first checks the timestamp and whether FN's public key exists, and then performs signature verification. The verification method is similar and will not be repeated here.

[0109] First check if BRK is empty:

[0110] (1) If BRK is not empty, the ID in BRK j Broadcast to O j In the smart meter, if there is an element ID in BRK j , then O j Smart Meter SM i Receive ID j After that, to SM j Send a message similar to a request response to confirm whether it is damaged or offline. If so, SM i Just local Find f in ji , and according to f ji calculate Sent to CC. In the end, CC will receive at most shares, randomly select k or more Y i , and according to To calculate u j :

[0111]

[0112] in According to the initialization of the extended threshold scheme parameters, Fermat's little theorem is satisfied, and we have:

[0113]

[0114] Finally, CC restored the SM of the damaged smart meter. j The updated mask value u j After calculating c cc

[0115] c cc =s dr(u cc +u j )mod p (22)

[0116] Then calculate:

[0117] c=c FN +c cc (twenty three)

[0118] Finally, c is decrypted, but the faulty smart meter SM may be missing j If the faulty smart meter still exists when the next data is reported, then j The coordinated smart meter autonomously deletes the key coordinated with it to ensure the correctness of future aggregation. If there is no faulty smart meter, the coordinated key can continue to be used to update the blind factor for reuse.

[0119] (2) If BRK is empty, it means that there is no smart meter that cannot send data due to disconnection or damage.

[0120] For the received c FN , CC first converts its blinding factor u cc Substitute into the symmetric homomorphic key calculation:

[0121] c cc =s d ru cc mod p (24)

[0122] Then calculate the final ciphertext as follows:

[0123] c=c FN +c cc (25)

[0124] At this point the blinding factor has been eliminated.

[0125] The aggregate plaintext obtained by decrypting the ciphertext c is as follows:

[0126]

[0127]

[0128] According to the properties of the Chinese remainder theorem, the following information can be extracted:

[0129] Total power consumption of the xth electrical appliance in the community:

[0130] M x =(M mod q 2x )mod q 11 (27)

[0131] The distribution of the power consumption value of the xth electrical appliance in the community in l gears, that is, |S x1 |,|S x2 |, ..., |S xl |The following algorithms can be executed:

[0132] Algorithm 1:

[0133] Input M, CRT1 and CRT2 parameters, output |S x1 |,|S x2 |, ..., |S xl |.

[0134] for i=1;i<l+1;l++:

[0135] {|S xi |=(M mod q 2k )mod q 1i ;}

[0136] The k-level distribution of the total power consumption of each user in the community is obtained, that is, |S m1 |,|S m2 |, ..., |S mk |

[0137] Algorithm 2:

[0138] Input M, CRT1 and CRT2 parameters, output |S m1 |,|S m2 |, ..., |S mk |.

[0139] for i=1;i<k+1;i++:

[0140] {|S mi |=M mod q 2(w+i) ;}.

[0141] Step 5: Processing of dynamic users

[0142] Smart grids often require the addition, deletion, and fault handling of dynamic users. This solution supports the setting of privacy protection based on dynamic users. The specific process is as follows:

[0143] 5.1 User Dynamic Joining

[0144] If there is an honest SM new Need new members to join the community, SM new First, obtain a series of necessary parameters as in the registration process. Since it is the first communication, issue a certificate and then use the TLS security protocol to ensure that it is published to the SM. new Security of system parameters.

[0145] CC:SM new The coordinated user that needs to generate the blinding factor is randomly selected and reported to the CC. The CC sends the coordinated user ID to the selected user and the GW. new ||X new .

[0146] SM new :Diffie-Hellman key negotiation based on elliptic curve generates a collaborative key, which needs to be accompanied by a Schnorr signature to ensure authentication and integrity. And the blinding factor u in stage 3 i The generation process is the same, and the process for selecting and distributing threshold keys is also the same.

[0147] The user SM who is randomly selected to generate the collaborative key i : and SM new The collaborative key is generated through the corresponding protocol above, and the generated collaborative key is added to V i , and use it to update the blinding factor u i , updated Sent to FN in advance for storage to prevent next communication loss.

[0148] FN: Update SM in set Δ new Sent

[0149] For the user SM who is randomly selected to distribute the threshold key j :You need to update the F that stores the threshold key share j ={(ID 1 , f 1j (ID 1 ))(ID 2 , f 2j (ID 2 )),...,(ID new , f new，j (ID x ))), the rest are the same.

[0150] 5.2 User dynamic deletion

[0151] When a user SM out When it is necessary to exit the community, it will send a withdrawal notification to CC and send it to CC with a schnorr signature. After receiving it, CC verifies the signature to ensure authentication and integrity, and then broadcasts the exit ID to all SMs. out , the smart meter that cooperates with it needs to delete the corresponding cooperative key to ensure that the blind factor generated is still 0, and the smart meter successfully exits.

[0152] 5.3 User Fault Tolerance

[0153] When the smart meter is unable to send messages due to damage, power outage or other reasons, the solution needs to have a certain fault tolerance. The specific process has been given in the "data decryption stage".

[0154] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A multi-dimensional aggregate privacy protection system based on symmetric homomorphic encryption, characterized in that: Including smart meter SM, fog node FN, control center CC, perform the following steps: Step 1, initialization phase; System parameter initialization: Based on the secure elliptic curve and according to the definition of the Chinese remainder theorem, the control center selects the CRT1 parameters and generates the parameters required for the extended Shamir threshold scheme: First, the control center selects a large prime number P s， GF(P s ) as its finite field, and then choose (P s -1) s ,q s , set an N s =p s q s , in GF(P s ) Set g s is a generator and has order N s The control center takes the parameters of the elliptic curve and the hash function H and K pub =(P s , N s , g s ) broadcast it; System entity registration: The control center generates public and private keys based on the entities that join, and sends the public and private keys corresponding to the entities to the fog nodes for storage; Blind factor generation: Each smart meter and control center generate blind factors through a secure communication channel. The smart meter and control center each randomly select a private key and calculate the corresponding public key. The smart meter uses the collaborative key set to calculate the root blind factor and updates the blind factor through the update rule. The blind factor is used to mask the electricity consumption data reported by the smart meter. The smart meter will update the blinding factor using the update rule at each reporting stage, and calculate the threshold parameters for fault tolerance and send them to the fog node to prevent accidental damage to the smart meter; The smart meter uses the secret share and blinding factor to update its own mask value and sends the updated mask value to the control center for storage. The control center collects the mask values ​​of all smart meters for subsequent data aggregation and privacy protection processing; Step 2, data reporting stage: the smart meter calculates the power consumption data of the appliance based on the data of each dimension and the power consumption interval to which it belongs, encrypts and blinds the data, and then sends all the data to the fog node; Step 3, data aggregation phase: The fog node searches and verifies in the database based on the data of the smart meter. If it passes, it performs signature verification; Step 4, data decryption phase: The control center first checks the timestamp and whether the public key of the fog node exists, and then performs signature verification. According to the properties of the Chinese remainder theorem, the total power consumption of a certain electrical appliance in the community can be extracted; Step 5, dynamic smart meter processing: the control center generates public and private keys for newly registered smart meters, registers by issuing digital certificates, and then passes security protocols to ensure the security of system parameters released to newly registered smart meters; Assume that there are n smart meters in the system, w is the electrical appliance, and the control center selects k continuous power consumption ranges [R1, R2), [R2, R3), …, [R k , E), and l continuous power consumption ranges [R′1, R′2), [R′2, R′3), …, [R′ l , E′); Among them, R1=R′1=0, E and E′ are the maximum power consumption of two continuous power consumption ranges, m i represents the total power consumption of the i-th smart meter, and m i ∈[R j , R j+1 ) represents m i belongs to [R1, R2), [R2, R3), …, [R k , E) in the j-th gear power consumption, m ij ∈[R′ x , R′ x+1 ) indicates that the jth electrical appliance of the ith smart meter belongs to [R′1, R′2), [R′2, R′3), …, [R′ l , E′) in the xth gear power consumption; According to the definition of the Chinese remainder theorem, the CRT1 parameters are selected: select q 1x , x∈[1,l+1], among which only q 11 >nE′, the remaining q 12 ,q 13 …, q 1(x+1) >n,q 1x , x∈[1, l+1] are mutually prime, and then Q1=q is calculated 11 q 12 …q 1(l+1) , and calculate E 1x =Q1 / q 1x , and calculate E′ 1x Make E 1x E′ 1x ≡1mod q 1x ; Generate CRT2 parameters according to the Chinese remainder theorem: The same generation parameters q 2j , j∈[1,w+k], where q 21 ,q 22 …, q 2w >nQ1, and q 2(w+1) ,q 2(w+2) ..., q 2(w+k) >n, according to the Chinese remainder theorem, Q2=q 21 q 22 …q 2(k+w) , E 2j =Q2 / q 2j and E′ 2j , the control center selects a random number r and a random number d, and then selects a p that satisfies |r|+|n|+|Q2|<|p|; Then in Next, we select a random number s, so we have the encryption key K sm =s d r mod p, decryption key SK = (s, d, r); SM i According to the data of each dimension (m i1 , m i2 ,…,m iw ), the total amount m can be calculated i =m i1 +m i2 +…+m iw , and according to [R1, R2), [R2, R3), …, [R k , E) can know the power consumption gear, according to (m i1 , m i2 ,…,m iw ) and the corresponding power consumption interval [R′1, R′2), [R′2, R′3), …, [R′ l , E′), calculate: m i,CRT =CRT2(CRT1(m i ))=(m i1 HAVE BEEN 11 HAVE BEEN' 11 +|S 11 E 12 HAVE BEEN' 12 +…+|S 1l E 1(l+1) HAVE BEEN' 1(l+1) mode Q1)E 21 HAVE BEEN' 21 +(m i2 HAVE BEEN 11 HAVE BEEN' 11 +|S 21 E 12 HAVE BEEN' 12 +…+|S 2l E 1(l+1) HAVE BEEN' 1(l+1) modQ1)E 22 HAVE BEEN' 22 +…+(m iw HAVE BEEN 11 HAVE BEEN' 11 +|S w1 E 12 HAVE BEEN' 12 +…+|S wl E 1(l+1) HAVE BEEN' 1(l+1) modQ1)E 2w HAVE BEEN' 2w +|S m1 E 2(w+1) HAVE BEEN' 2(w+1) +|S m2 E 2(w+2) HAVE BEEN' 2(w+2) +…+|S mk E 2(w+k) HAVE BEEN' 2(w+k) mode Q2; Where |S wl | indicates that when the power consumption data of the wth electrical appliance is in the lth level, |S wl | is 1, |S mk | indicates that the total power consumption of the smart meter is in the kth level |S mk | is 1, and each smart meter uses a blinding factor u i and key K sm To encrypt and blind your data i，CRT .

2. According to claim 1, a multi-dimensional aggregate privacy protection system of symmetric homomorphic encryption is characterized by: Smart meters collect multi-dimensional data, each dimension of which represents the power consumption of a type of electrical appliance. Fog nodes aggregate the data of several smart meters in a community and submit them to the control center. The control center decrypts the data submitted by the fog nodes and extracts the aggregate value of each dimension and the total number of different power consumption intervals of electrical appliances in each dimension.

3. According to the multi-dimensional aggregate privacy protection system of symmetric homomorphic encryption of claim 1, it is characterized by: On the initialized elliptic curve, the newly added SM i Randomly select an integer x i As the private key, corresponding to the generated X i =x i G is used as the public key and the public key is sent to the control center for registration. The control center registers each SM i Each is assigned an ID i , ID i ∈[1, n], the control center defines U for the n registered smart meters, and stipulates The fog node randomly selects x FN As the private key, corresponding to the generated X FN =x FN G is used as the public key and the public key is sent to the control center, which also generates a private key x cc and public key X cc , private key SM i Self storage; The control center will Sent to registered SMs, each SM i according to Parameters, randomly selected from U Smart meters are used to share Shamir's secret, and all the selected smart meter IDs are loaded into And broadcast The control center will U||X sm ||X cc Sent to the registered fog nodes for storage, where X sm Contains the public keys of all smart meters registered.

4. According to claim 3, a multi-dimensional aggregate privacy protection system of symmetric homomorphic encryption is characterized in that: SM i Randomly select a private key κ i , and calculate the public key K i =κ i G, SM i Send K i ||ID i Give SM z , S.M. z After receiving, the same κ is generated z , K z =κ z G, K z ||ID z Send to SM i .

5. A multi-dimensional aggregate privacy protection system based on symmetric homomorphic encryption according to claim 4, characterized in that: Each smart meter uses u i and key K sm Encrypt and blind your own datam i，CRT , c i =K sm (m i，CRT +u i )mod p=s d r(m i，CRT +u i )mod p, update its own u according to the update rules in the system entity registration i Used as the blinding factor for the next time, and calculate r s =H(T k ), T k Indicates the current time for reporting data, s i is the derived key; The smart meter randomly selects a number f according to the elliptic curve defined by the control center initialization i , and the corresponding F i =f i G, then calculate Then calculate the signature σ i =ex i +f i ,Will Sent to FN, where T i It is the current timestamp, indicating the time when the message is actually sent.

6. A multi-dimensional aggregate privacy protection system based on symmetric homomorphic encryption according to claim 5, characterized in that: When a new smart meter is added to the control center, the new smart meter is recorded as SM new , S.M. new The coordinated smart meter that needs to generate the blinding factor is randomly selected and reported to the control center. The control center sends the ID of the coordinated smart meter to the selected smart meter and FN. new ||X new , S.M. new Diffie-Hellman key negotiation based on elliptic curve generates collaborative keys, SM new The generated collaborative key is added to V i , and use it to update the blinding factor u i , updated It is sent to fog nodes in advance for storage to prevent the next communication damage.

7. The multi-dimensional aggregate privacy protection system of symmetric homomorphic encryption according to claim 1 is characterized by: When the control center deletes a smart meter, the deleted smart meter is recorded as SM out , S.M. out Send an exit notification to the control center, which verifies the SM out Signed with SM out The coordinated smart meter deletes the corresponding coordinated key.

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