CN113691380B - Multidimensional private data aggregation method in smart power grid - Google Patents

Multidimensional private data aggregation method in smart power grid Download PDF

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CN113691380B
CN113691380B CN202111244046.4A CN202111244046A CN113691380B CN 113691380 B CN113691380 B CN 113691380B CN 202111244046 A CN202111244046 A CN 202111244046A CN 113691380 B CN113691380 B CN 113691380B
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data
fog
ciphertext
control center
fog node
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CN113691380A (en
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张晓均
唐伟
王鑫
王文琛
薛婧婷
刘庆
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Southwest Petroleum University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J13/00—Circuit arrangements for providing remote indication of network conditions, e.g. an instantaneous record of the open or closed condition of each circuitbreaker in the network; Circuit arrangements for providing remote control of switching means in a power distribution network, e.g. switching in and out of current consumers by using a pulse code signal carried by the network
    • H02J13/00006—Circuit arrangements for providing remote indication of network conditions, e.g. an instantaneous record of the open or closed condition of each circuitbreaker in the network; Circuit arrangements for providing remote control of switching means in a power distribution network, e.g. switching in and out of current consumers by using a pulse code signal carried by the network characterised by information or instructions transport means between the monitoring, controlling or managing units and monitored, controlled or operated power network element or electrical equipment
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • H04L63/0435—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload wherein the sending and receiving network entities apply symmetric encryption, i.e. same key used for encryption and decryption
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00—Network arrangements or protocols for supporting network services or applications
    • H04L67/01—Protocols
    • H04L67/10—Protocols in which an application is distributed across nodes in the network
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3236—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using cryptographic hash functions
    • H04L9/3242—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using cryptographic hash functions involving keyed hash functions, e.g. message authentication codes [MACs], CBC-MAC or HMAC
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
    • Y04S40/12—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them characterised by data transport means between the monitoring, controlling or managing units and monitored, controlled or operated electrical equipment
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
    • Y04S40/20—Information technology specific aspects, e.g. CAD, simulation, modelling, system security

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Power Engineering (AREA)
  • Computer Hardware Design (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Remote Monitoring And Control Of Power-Distribution Networks (AREA)

Abstract

The invention discloses a multidimensional private data aggregation method in a smart grid, which comprises the following steps: s1, a trusted center sets a security password component, a signature private key and a secret share parameter of each communication entity, and publishes a system public password parameter; s2, the intelligent electric meter performs binary preprocessing and encryption on the data of each dimension, generates a corresponding digital signature and uploads verifiable ciphertext data; s3, the fog node performs batch verification on verifiable ciphertext data, calculates an aggregation ciphertext to generate a first session key, calculates a second message authentication code, and uploads the verifiable fog level aggregation ciphertext to a power grid control center; and S4, the power grid control center generates a second session key, calculates a third message authentication code, checks the third message authentication code with the received second message authentication code, decrypts the verifiable fog-level aggregation ciphertext, and recovers the aggregated multiple dimension data values. The method can prevent an attacker from analyzing the user data and does not influence the statistical analysis of the power grid system.

Description

Multidimensional private data aggregation method in smart power grid
Technical Field
The invention belongs to the field of big data analysis and processing in a smart power grid, and particularly relates to a multidimensional privacy data aggregation method in the smart power grid.
Background
With the increasingly wide application of electric energy, the production mode and the management mode of the traditional power grid cannot meet the basic requirements of people. The appearance of the smart grid provides a more convenient, more reasonable and more economical mode for people. The smart meter is widely installed in each household and is responsible for collecting power data of the user and uploading the data to a corresponding edge computing server, such as a fog node server. And after collecting the data reported by the intelligent electric meters in the jurisdiction areas of the intelligent electric meters, the fog nodes carry out aggregation processing and then send the data to the power grid control center. The power grid control center analyzes the power consumption data, makes decisions such as power supply according to needs and the like, and saves power resources in three stages of power production, transmission and use.
However, since the power data generally reflects private information such as living habits of the user, it is necessary to encrypt the sensitive power data to ensure privacy of the user. However, the smart meter is usually a small-sized computing unit, cannot perform complicated encryption operations, and the transmitted data may depend on a home network or a private small-sized network. Too long ciphertext length of communication may also cause transmission congestion. In addition, in order to solve the data island problem, the homomorphic encryption technology can enable the fog nodes to carry out linear aggregation on ciphertext data transmitted by the plurality of terminal electric meters, and data analysis convenience of privacy protection is provided for a power grid control center. The existing encryption and polymerization technology is mostly based on classical Paillier and BGN homomorphic encryption algorithms which both need to use modular exponentiation calculation, so that the calculation cost of the terminal intelligent electric meter is extremely high, and the terminal intelligent electric meter is not suitable for small metering equipment.
During the transmission process, the grid users may try to tamper with the power data in the smart meter to avoid the subsequent electricity charging. Meanwhile, an internal adversary may exist in the power grid system, a private key of the smart meter or the control center is stolen, and the data confidentiality and the user privacy security are destroyed by decrypting a single ciphertext. Besides, the failure damage of the smart meter cannot be avoided in practice, so the encryption system should be provided with a fault tolerance mechanism. Therefore, designing a lightweight encryption and aggregation technology supporting transmission fault tolerance and verification functions is an important guarantee for realizing safe and wide deployment of the smart grid.
Disclosure of Invention
The invention aims to overcome one or more defects in the prior art and provides a multidimensional private data aggregation method in a smart grid.
The purpose of the invention is realized by the following technical scheme: a multidimensional private data aggregation method in a smart grid is applied to a smart grid system, the smart grid comprises a grid control center, a fog node, a smart meter and a trusted center, the grid control center is in communication connection with the fog node, the fog node is in communication connection with the smart meter, the grid control center, the fog node and the smart meter are all in communication connection with the trusted center, and the multidimensional private data aggregation method in the smart grid comprises the following steps:
s1, a trusted center sets a security password component, a signature private key of each communication entity and a secret share parameter of a threshold secret sharing technology, wherein the security password component comprises a symmetric homomorphic encryption algorithm, a symmetric key of the symmetric homomorphic encryption algorithm, bilinear pairwise mapping, a security hash function and a first message authentication code, and the communication entities comprise a power grid control center, an intelligent ammeter and a fog node; the trusted center publishes system public password parameters, generates secret parameters of each communication entity according to the symmetric key, the signature private key and the secret share parameters, and sends the secret parameters to each communication entity through a secure channel;
s2, the intelligent electric meter performs binary preprocessing on data of each dimension of a user, encrypts the binary preprocessed data by adopting a homomorphic symmetric encryption algorithm to obtain ciphertext data, and generates a digital signature corresponding to the ciphertext data by using a signature private key; the intelligent electric meter uploads verifiable ciphertext data to a corresponding fog node in a time period, wherein the verifiable ciphertext data comprise the ciphertext data, a digital signature, the time period and the identity of the intelligent electric meter;
s3, judging whether the number of normally working intelligent electric meters which upload verifiable ciphertext data in a responsible area of each fog node in a time period is larger than a preset threshold value or not, and if so, verifying the verifiable ciphertext data in batches by the fog nodes; after the verification is passed, the fog node calculates an aggregation ciphertext, generates a first session key temporarily negotiated with a power grid control center, calculates a second message authentication code, and uploads a verifiable fog-level aggregation ciphertext to the power grid control center, wherein the verifiable fog-level aggregation ciphertext comprises the aggregation ciphertext, the second message authentication code, a time period and the identity of the fog node;
and S4, after receiving the verifiable fog-level aggregation ciphertext of the fog node, the power grid control center generates a second session key temporarily negotiated with the fog node, calculates a third message authentication code, and checks the third session key with the received second message authentication code, if the third session key passes the checking, the power grid control center decrypts the verifiable fog-level aggregation ciphertext and recovers a plurality of dimension data values after aggregation.
Preferably, the S1 includes the following steps:
s101, the trusted center generates a symmetric key of a symmetric homomorphic encryption algorithm
Figure 484280DEST_PATH_IMAGE001
Where u and v are both large prime numbers, and the bit length of u is greater than or equal to 2 times the bit length of v, and s is a u-order finite field
Figure 807945DEST_PATH_IMAGE002
D is the number of times of the ciphertext, and the trusted center is represented by TTP;
s102, the credible center sets a bilinear mapping
Figure 853261DEST_PATH_IMAGE003
Wherein, in the step (A),
Figure 654995DEST_PATH_IMAGE004
is a p-order addition cycle group,
Figure 526DEST_PATH_IMAGE005
is a P-factorial cyclic group, P is an additive cyclic group
Figure 229513DEST_PATH_IMAGE006
A generator of (2);
s103, the credible center sets the number of the fog nodes as
Figure 27705DEST_PATH_IMAGE007
And setting the maximum intelligent electric meter number of a fog node responsible area to be N, wherein the fog node is used
Figure 633130DEST_PATH_IMAGE008
To said smart meter
Figure 833167DEST_PATH_IMAGE009
Represents;
s104, the credible center sets a fixed positive integer
Figure 233055DEST_PATH_IMAGE010
Wherein
Figure 190647DEST_PATH_IMAGE011
Represents an upward integer, DRepresenting supremum boundaries of the data of each dimension;
s105, the credible center sets an anti-collision Hash function
Figure 458817DEST_PATH_IMAGE012
Wherein, in the step (A),
Figure 388727DEST_PATH_IMAGE013
representing a bit string with any length, and setting a first message authentication code HMAC;
s106, the credible center is in a limited domain of order p
Figure 349730DEST_PATH_IMAGE014
Mist node signature private key selected for mist nodes
Figure 997880DEST_PATH_IMAGE015
And calculates its public key of the fog node
Figure 804162DEST_PATH_IMAGE016
The identity of the fog node is
Figure 854158DEST_PATH_IMAGE017
；
S107, the trusted center slave finite field
Figure 720482DEST_PATH_IMAGE018
Electric meter signature private key selection method for intelligent electric meter
Figure 855929DEST_PATH_IMAGE019
And calculate the public key of the electric meter
Figure 200322DEST_PATH_IMAGE020
The identity of the intelligent electric meter is
Figure 104824DEST_PATH_IMAGE021
；
S108, the trusted center slave finite field
Figure 407630DEST_PATH_IMAGE022
Selecting a control center signature private key x for a power grid control center, and calculating a control center public key of the control center signature private key x
Figure 764793DEST_PATH_IMAGE023
The grid control center is denoted by CC;
s109, the credible center determines two parameters
Figure 850561DEST_PATH_IMAGE024
And is and
Figure 734203DEST_PATH_IMAGE025
；
s110, the credible center selects a t-1 degree polynomial
Figure 411172DEST_PATH_IMAGE026
And is and
Figure 888306DEST_PATH_IMAGE027
wherein y is a variable;
s111, the credible center selects a positive integer
Figure 43344DEST_PATH_IMAGE028
And calculating a secret share parameter one
Figure 922439DEST_PATH_IMAGE029
Secret share parameter two
Figure 239150DEST_PATH_IMAGE030
Secret share parameter three
Figure 695540DEST_PATH_IMAGE031
Secret share parameter four
Figure 326372DEST_PATH_IMAGE032
And secret share parameter five
Figure 919028DEST_PATH_IMAGE033
Wherein is a positive integer
Figure 344324DEST_PATH_IMAGE034
The bit length of (f) is less than or equal to 20 bits, and (f) (j) represents the value of a t-1 degree polynomial corresponding to the jth intelligent electric meter;
s112, the trusted center issues system public parameters
Figure 288009DEST_PATH_IMAGE035
；
S113, the trusted center controls the secret parameters of the center
Figure 722533DEST_PATH_IMAGE036
Sending the parameters to a power grid control center to obtain the secret parameters of the electric meter
Figure 435274DEST_PATH_IMAGE037
Sending the parameters to each intelligent ammeter, and carrying out secret parameter of the fog node
Figure 31471DEST_PATH_IMAGE038
To each of the fog nodes.
Preferably, the S2 includes the following steps:
s201, enabling the intelligent electric meter to obtain data of each dimension of a user
Figure 462452DEST_PATH_IMAGE039
Encoding into binary bit strings
Figure 435088DEST_PATH_IMAGE040
Wherein the encoded data of each dimension is,
Figure 267914DEST_PATH_IMAGE041
representing data
Figure 831751DEST_PATH_IMAGE042
In the form of a binary code of (a),
Figure 625395DEST_PATH_IMAGE043
is expressed as length of
Figure 526355DEST_PATH_IMAGE044
Padding all-zero bit strings of (1);
s202, the intelligent electric meter sets the electricity utilization data to be
Figure 823475DEST_PATH_IMAGE045
；
S203, the intelligent electric meter selects a positive random number
Figure 151688DEST_PATH_IMAGE046
And is and
Figure 901469DEST_PATH_IMAGE047
wherein, the symbols
Figure 278224DEST_PATH_IMAGE048
Which represents the length of the bit string and,
Figure 898692DEST_PATH_IMAGE049
has a bit length of
Figure 601069DEST_PATH_IMAGE050
；
S204, using the electric meter secret parameter by the intelligent electric meter
Figure 838147DEST_PATH_IMAGE051
The electricity data are compared in the following way
Figure 80909DEST_PATH_IMAGE052
And (3) encryption:
Figure 352621DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure 22637DEST_PATH_IMAGE054
is power consumption data
Figure 12590DEST_PATH_IMAGE055
The ciphertext of (a) may be encrypted,
Figure 793464DEST_PATH_IMAGE056
is a random number;
s205. the smart electric meter uses the private key of electric meter signature
Figure 185262DEST_PATH_IMAGE057
Generating
Figure 26179DEST_PATH_IMAGE058
Is signed
Figure 503428DEST_PATH_IMAGE059
：
Figure 87993DEST_PATH_IMAGE060
；
S206. the intelligent electric meter verifies the ciphertext data
Figure 131036DEST_PATH_IMAGE061
And sending the information to the corresponding fog node.
Preferably, the S3 includes the following steps:
s301, judging the number of intelligent electric meters which are in charge of normal work of regional uploading verifiable ciphertext data by the fog nodes in the time period T
Figure 18220DEST_PATH_IMAGE062
If the threshold value is larger than the preset threshold value t, if yes, S302 is executed, wherein,
Figure 841820DEST_PATH_IMAGE063
a subscript set of the smart meter which works normally is represented;
s302, carrying out batch verification on the fog nodes according to the following equation:
Figure 105442DEST_PATH_IMAGE064
if the equation is established, the verification is passed;
s303, calculating Lagrange coefficient in polymerization process by using fog node
Figure 330887DEST_PATH_IMAGE065
Wherein, in the step (A),
Figure 388973DEST_PATH_IMAGE066
is a sequence value managed by the user at the fog node,
Figure 699869DEST_PATH_IMAGE067
indicated as the location of one user,
Figure 501602DEST_PATH_IMAGE068
representing a pointer in the traversal process, and calculating all user subscripts received by the fog nodes;
s304, the fog node calculates an aggregation ciphertext:
Figure 581554DEST_PATH_IMAGE069
；
s305, the fog node calculates a first session key temporarily negotiated with a power grid control center
Figure 341699DEST_PATH_IMAGE070
；
S306, the fog node calculates a second message authentication code
Figure 874312DEST_PATH_IMAGE071
Wherein
Figure 479737DEST_PATH_IMAGE072
Representing points on an elliptic curve
Figure 414195DEST_PATH_IMAGE073
The ordinate of (a);
s307, the fog node sends a verifiable fog level aggregation ciphertext to a power grid control center
Figure 79662DEST_PATH_IMAGE074
。
Preferably, the S4 includes the following steps:
s401, the power grid control center receives verifiable fog-level aggregation ciphertext from a fog node
Figure 365150DEST_PATH_IMAGE075
Then, a second session key temporarily negotiated with the fog node is calculated
Figure 508687DEST_PATH_IMAGE076
；
S402, the power grid control center calculates a third message authentication code
Figure 235334DEST_PATH_IMAGE077
Wherein
Figure 196337DEST_PATH_IMAGE078
Representing points on an elliptic curve
Figure 578908DEST_PATH_IMAGE079
On the ordinate, if
Figure 650769DEST_PATH_IMAGE080
Then, S403 is executed;
s403, the power grid control center utilizes secret parameters of the control center
Figure 435186DEST_PATH_IMAGE081
Decrypting the verifiable fog level aggregation ciphertext of the fog node:
Figure 301510DEST_PATH_IMAGE082
in the formula (I), the compound is shown in the specification,
Figure 436957DEST_PATH_IMAGE083
the decrypted aggregated data of the intelligent electric meter are represented;
s404, the power grid control center recovers the aggregated data of each dimension, wherein the eta isAggregated data of dimensions
Figure 46930DEST_PATH_IMAGE084
As a bit string
Figure 951432DEST_PATH_IMAGE085
To middle
Figure 988658DEST_PATH_IMAGE086
Bit to bit
Figure 611400DEST_PATH_IMAGE087
The data in the bit positions of the data,
Figure 25064DEST_PATH_IMAGE088
and l denotes how many data dimensions are present in total.
The invention has the beneficial effects that:
(1) the method can prevent an attacker from analyzing the user data and does not influence the statistical analysis of the power grid system;
(2) the method reduces the calculation complexity and the calculation requirement of the intelligent ammeter while not affecting the safety, and can effectively improve the system efficiency, reduce the time delay and the like;
(3) the method has the fault-tolerant function of the intelligent electric meter, and even if the damaged intelligent electric meter exists or part of data of the intelligent electric meter is not received due to network blockage, the control center can still analyze correct results from most of data of the intelligent electric meter;
(4) the method has the function of resisting the key leakage, and the control center or the intelligent electric meter can perform timely remediation after the symmetric key is lost, so that a large amount of loss is avoided.
Drawings
FIG. 1 is a schematic diagram of a smart grid system;
FIG. 2 is a flowchart of a method for aggregating multidimensional private data in a smart grid;
fig. 3 is a schematic diagram of an aggregated plaintext data form.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the following embodiments, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
Referring to fig. 1 to fig. 3, the embodiment provides a multidimensional private data aggregation method in a smart grid:
as shown in fig. 1, a multidimensional private data aggregation method in a smart grid is applied to a smart grid system, the smart grid comprises a grid control center, a fog node, a smart meter and a trusted center, the grid control center is in communication connection with the fog node, the fog node is in communication connection with the smart meter, and the grid control center, the fog node and the smart meter are in communication connection with the trusted center.
As shown in fig. 2, a method for aggregating multidimensional private data in a smart grid includes the following steps:
s1, a trusted center sets a security password component, a signature private key of each communication entity and a secret share parameter of a threshold secret sharing technology, wherein the security password component comprises a symmetric homomorphic encryption algorithm, a symmetric key of the symmetric homomorphic encryption algorithm, bilinear pairwise mapping, a security hash function and a first message authentication code, and the communication entities comprise a power grid control center, an intelligent ammeter and a fog node; the trusted center publishes the system public password parameters, generates the secret parameters of each communication entity according to the symmetric key, the signature private key and the secret share parameters, and sends the secret parameters to each communication entity through a secure channel.
Specifically, the S1 includes the following steps:
s101, the trusted center generates a symmetric key of a symmetric homomorphic encryption algorithm
Figure 784073DEST_PATH_IMAGE001
Where u and v are both large prime numbers and the bit length of u2 times the bit length of v or more, s being a finite field of order u
Figure 257779DEST_PATH_IMAGE002
D is the number of times of the ciphertext, and the trusted center is represented by TTP.
S102, the credible center sets a bilinear mapping
Figure 102238DEST_PATH_IMAGE003
Wherein, in the step (A),
Figure 54014DEST_PATH_IMAGE004
is a p-order addition cycle group,
Figure 933108DEST_PATH_IMAGE005
is a P-factorial cyclic group, P is an additive cyclic group
Figure 312137DEST_PATH_IMAGE006
The generator of (1).
S103, the credible center sets the number of the fog nodes as
Figure 643892DEST_PATH_IMAGE007
And setting the maximum intelligent electric meter number of a fog node responsible area to be N, wherein the fog node is used
Figure 71463DEST_PATH_IMAGE008
To said smart meter
Figure 929697DEST_PATH_IMAGE009
And (4) showing.
S104, the credible center sets a fixed positive integer
Figure 620573DEST_PATH_IMAGE010
Wherein
Figure 564258DEST_PATH_IMAGE011
Represents taking an integer upward, and D represents the supremum of each dimension data.
S105, the credible center is provided withPlacing an anti-collision hash function
Figure 733202DEST_PATH_IMAGE012
Wherein, in the step (A),
Figure 445943DEST_PATH_IMAGE013
representing a bit string of arbitrary length and setting a first message authentication code HMAC.
S106, the credible center is in a limited domain of order p
Figure 307720DEST_PATH_IMAGE014
Mist node signature private key selected for mist nodes
Figure 473122DEST_PATH_IMAGE015
And calculates its public key of the fog node
Figure 711337DEST_PATH_IMAGE016
The identity of the fog node is
Figure 278584DEST_PATH_IMAGE017
。
S107, the trusted center slave finite field
Figure 311262DEST_PATH_IMAGE018
Electric meter signature private key selection method for intelligent electric meter
Figure 229540DEST_PATH_IMAGE019
And calculate the public key of the electric meter
Figure 740287DEST_PATH_IMAGE020
The identity of the intelligent electric meter is
Figure 427620DEST_PATH_IMAGE021
。
S108, the trusted center slave finite field
Figure 631199DEST_PATH_IMAGE022
Control center signature private key x selected for power grid control centerAnd calculating its control center public key
Figure 771194DEST_PATH_IMAGE023
The grid control center is denoted CC.
S109, the credible center determines two parameters
Figure 351211DEST_PATH_IMAGE024
And is and
Figure 893050DEST_PATH_IMAGE025
。
s110, the credible center selects a t-1 degree polynomial
Figure 595427DEST_PATH_IMAGE026
And is and
Figure 98084DEST_PATH_IMAGE027
wherein y is a variable.
S111, the credible center selects a positive integer
Figure 747371DEST_PATH_IMAGE028
And calculating a secret share parameter one
Figure 409296DEST_PATH_IMAGE029
Secret share parameter two
Figure 954678DEST_PATH_IMAGE030
Secret share parameter three
Figure 69265DEST_PATH_IMAGE031
Secret share parameter four
Figure 725505DEST_PATH_IMAGE032
And secret share parameter five
Figure 241937DEST_PATH_IMAGE033
Wherein is a positive integer
Figure 958221DEST_PATH_IMAGE034
The bit length of (f) is less than or equal to 20 bits, and (f) and (j) represent the value of the t-1 degree polynomial corresponding to the jth intelligent electric meter.
S112, the trusted center issues system public parameters
Figure 560103DEST_PATH_IMAGE035
。
S113, the trusted center controls the secret parameters of the center
Figure 20035DEST_PATH_IMAGE036
Sending the parameters to a power grid control center to obtain the secret parameters of the electric meter
Figure 390973DEST_PATH_IMAGE037
Sending the parameters to each intelligent ammeter, and carrying out secret parameter of the fog node
Figure 278158DEST_PATH_IMAGE038
To each of the fog nodes.
S2, the intelligent electric meter performs binary preprocessing on data of each dimension of a user, encrypts the binary preprocessed data by adopting a homomorphic symmetric encryption algorithm to obtain ciphertext data, and generates a digital signature corresponding to the ciphertext data by using a signature private key; the intelligent electric meter uploads verifiable ciphertext data to the corresponding fog node in a time period, wherein the verifiable ciphertext data comprise the ciphertext data, the digital signature, the time period and the identity of the intelligent electric meter.
Generally, a time period defaults to 15 minutes, and can be changed according to network conditions, calculation conditions of each device and statistical requirements of a control center.
Specifically, the S2 includes the following steps:
s201, enabling the intelligent electric meter to obtain data of each dimension of a user
Figure 305019DEST_PATH_IMAGE039
Encoding into binary bit strings
Figure 693275DEST_PATH_IMAGE040
Wherein the encoded data of each dimension is,
Figure 794087DEST_PATH_IMAGE041
representing data
Figure 976806DEST_PATH_IMAGE042
In the form of a binary code of (a),
Figure 428647DEST_PATH_IMAGE043
is expressed as length of
Figure 620594DEST_PATH_IMAGE044
Is filled with all-zero bit strings.
S202, the intelligent electric meter sets the electricity utilization data to be
Figure 575912DEST_PATH_IMAGE045
。
S203, the intelligent electric meter selects a positive random number
Figure 195112DEST_PATH_IMAGE046
And is and
Figure 868670DEST_PATH_IMAGE047
wherein, the symbols
Figure 333149DEST_PATH_IMAGE048
Which represents the length of the bit string and,
Figure 408553DEST_PATH_IMAGE049
has a bit length of
Figure 401917DEST_PATH_IMAGE050
。
S204, using the electric meter secret parameter by the intelligent electric meter
Figure 421825DEST_PATH_IMAGE051
The electricity data are compared in the following way
Figure 830941DEST_PATH_IMAGE052
And (3) encryption:
Figure 151064DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure 721854DEST_PATH_IMAGE054
is power consumption data
Figure 494638DEST_PATH_IMAGE055
The ciphertext of (a) may be encrypted,
Figure 441865DEST_PATH_IMAGE056
is a random number, and the main function of the random number is to ensure the randomness of the ciphertext to prevent differential attack.
S205. the smart electric meter uses the private key of electric meter signature
Figure 350915DEST_PATH_IMAGE057
Generating
Figure 334748DEST_PATH_IMAGE058
Is signed
Figure 329249DEST_PATH_IMAGE059
：
Figure 80167DEST_PATH_IMAGE060
。
S206. the intelligent electric meter verifies the ciphertext data
Figure 109303DEST_PATH_IMAGE061
And sending the information to the corresponding fog node.
S3, judging whether the number of normally working intelligent electric meters which upload verifiable ciphertext data in a responsible area of each fog node in a time period is larger than a preset threshold value or not, and if so, verifying the verifiable ciphertext data in batches by the fog nodes; and after the verification is passed, the fog node calculates an aggregation ciphertext, simultaneously generates a first session key temporarily negotiated with the power grid control center, calculates a second message authentication code, and uploads a verifiable fog-level aggregation ciphertext to the power grid control center, wherein the verifiable fog-level aggregation ciphertext comprises the aggregation ciphertext, the second message authentication code, a time period and the identity of the fog node.
Specifically, the S3 includes the following steps:
s301, judging the number of intelligent electric meters which are in charge of normal work of regional uploading verifiable ciphertext data by the fog nodes in the time period T
Figure 21895DEST_PATH_IMAGE062
If the threshold value is larger than the preset threshold value t, if yes, S302 is executed, wherein,
Figure 972534DEST_PATH_IMAGE063
and indicating a subscript set of the smart meter which normally works.
S302, carrying out batch verification on the fog nodes according to the following equation:
Figure 386198DEST_PATH_IMAGE064
if the equation is true, the verification passes. If all data sources are legal users, the verification can be successfully passed, and the derivation process is in a correctness formula (2).
S303, calculating Lagrange coefficient in polymerization process by using fog node
Figure 145206DEST_PATH_IMAGE065
Wherein, in the step (A),
Figure 353334DEST_PATH_IMAGE066
is a sequence value managed by the user at the fog node,
Figure 197793DEST_PATH_IMAGE067
indicated as the location of one user,
Figure 680727DEST_PATH_IMAGE068
and (4) representing a pointer of the traversal process, and calculating all the user subscripts received by the fog nodes.
S304, the fog node calculates an aggregation ciphertext:
Figure 294242DEST_PATH_IMAGE069
。
s305, the fog node calculates a first session key temporarily negotiated with a power grid control center
Figure 673271DEST_PATH_IMAGE070
。
S306, the fog node calculates a second message authentication code
Figure 270605DEST_PATH_IMAGE071
Wherein
Figure 26072DEST_PATH_IMAGE072
Representing points on an elliptic curve
Figure 759672DEST_PATH_IMAGE073
The ordinate of (c).
S307, the fog node sends a verifiable fog level aggregation ciphertext to a power grid control center
Figure 575182DEST_PATH_IMAGE074
。
And S4, after receiving the verifiable fog-level aggregation ciphertext of the fog node, the power grid control center generates a second session key temporarily negotiated with the fog node, calculates a third message authentication code, and checks the third session key with the received second message authentication code, if the third session key passes the checking, the power grid control center decrypts the verifiable fog-level aggregation ciphertext and recovers a plurality of dimension data values after aggregation.
Specifically, the S4 includes the following steps:
s401, the power grid control center receives verifiable fog-level aggregation ciphertext from a fog node
Figure 456550DEST_PATH_IMAGE075
Then, a second session key temporarily negotiated with the fog node is calculated
Figure 891073DEST_PATH_IMAGE076
。
S402, the power grid control center calculates a third message authentication code
Figure 603815DEST_PATH_IMAGE077
Wherein
Figure 465591DEST_PATH_IMAGE078
Representing points on an elliptic curve
Figure 162152DEST_PATH_IMAGE079
On the ordinate, if
Figure 134787DEST_PATH_IMAGE080
Then S403 is executed.
S403, the power grid control center utilizes secret parameters of the control center
Figure 702035DEST_PATH_IMAGE081
Decrypting the verifiable fog level aggregation ciphertext of the fog node:
Figure 734713DEST_PATH_IMAGE082
in the formula (I), the compound is shown in the specification,
Figure 121832DEST_PATH_IMAGE083
and the decrypted aggregate data of the intelligent electric meter is represented.
S404, the power grid control center recovers the aggregated data of each dimension, wherein the aggregated data of the eta dimension
Figure 163737DEST_PATH_IMAGE084
As a bit string
Figure 851070DEST_PATH_IMAGE085
To middle
Figure 54650DEST_PATH_IMAGE086
Bit to bit
Figure 538852DEST_PATH_IMAGE087
The data in the bit positions of the data,
Figure 977923DEST_PATH_IMAGE088
and l denotes how many data dimensions are present in total.
Since it is known that data of each dimension after aggregation should be less than or equal to ND in the initial stage of the system, the data bit length of each dimension should be less than or equal to ND
Figure 723026DEST_PATH_IMAGE089
. Therefore, for each
Figure 894244DEST_PATH_IMAGE088
Aggregated data in the eta dimension
Figure 724797DEST_PATH_IMAGE084
Should be a bit string
Figure 842925DEST_PATH_IMAGE090
To middle
Figure 504851DEST_PATH_IMAGE086
Bit to bit
Figure 315812DEST_PATH_IMAGE087
Data in bits. The power grid control center can quickly recover the aggregated data of each dimension according to the rule.
The correctness of the method of the invention proves as follows:
(1) user computing
Figure 164819DEST_PATH_IMAGE091
The ciphertext of (a):
Figure 86639DEST_PATH_IMAGE092
(2) after receiving the user valid data, the fog node verifies the information in batches, and the integrity is correctly deduced as follows:
Figure 603071DEST_PATH_IMAGE093
(3) if the fog node receives a plurality of pieces of user valid data, and the user data volume is greater than or equal to the threshold value t, the fog node executes aggregation operation and generates a fog level aggregation ciphertext:
Figure 319354DEST_PATH_IMAGE094
(4) due to the fact that
Figure DEST_PATH_IMAGE095
The power grid control center can calculate the same temporary session key as the fog node
Figure 390078DEST_PATH_IMAGE096
=
Figure 850010DEST_PATH_IMAGE097
Thereby calculating the correct second message authentication code
Figure 220948DEST_PATH_IMAGE098
。
(5) After the power grid control center receives the verifiable fog level aggregation ciphertext of the fog nodes, the power grid control center distributes the ciphertext by using the credible center
Figure 108133DEST_PATH_IMAGE099
Figure 197311DEST_PATH_IMAGE100
To decrypt the fog-level aggregate ciphertext:
Figure 195354DEST_PATH_IMAGE101
(6) and after recovering the fog-level aggregation ciphertext, the power grid control center recovers the aggregation data of each dimension in a character string segmentation mode. Because in the system initialization phase, the maximum value of each dimension is set to be D, and the number of the smart meters to which each fog node belongs is N. Therefore, at the fog node, the aggregated binary length of each dimension data should be less than or equal to
Figure 951958DEST_PATH_IMAGE102
The aggregated plaintext data form is shown in fig. 3. Therefore, the power grid control center can restore the aggregation data of the specified dimensionality only by intercepting the corresponding bit string.
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A multidimensional private data aggregation method in a smart grid is applied to a smart grid system, the smart grid comprises a grid control center, a fog node, a smart meter and a trusted center, the grid control center is in communication connection with the fog node, the fog node is in communication connection with the smart meter, and the grid control center, the fog node and the smart meter are all in communication connection with the trusted center, and is characterized in that the multidimensional private data aggregation method in the smart grid comprises the following steps:
s1, a trusted center sets a security password component, a signature private key of each communication entity and a secret share parameter of a threshold secret sharing technology, wherein the security password component comprises a symmetric homomorphic encryption algorithm, a symmetric key of the symmetric homomorphic encryption algorithm, bilinear pairwise mapping, a security hash function and a first message authentication code, and the communication entities comprise a power grid control center, an intelligent ammeter and a fog node; the trusted center publishes system public password parameters, generates secret parameters of each communication entity according to the symmetric key, the signature private key and the secret share parameters, and sends the secret parameters to each communication entity through a secure channel;
s2, the intelligent electric meter performs binary preprocessing on data of each dimension of a user, encrypts the binary preprocessed data by adopting a homomorphic symmetric encryption algorithm to obtain ciphertext data, and generates a digital signature corresponding to the ciphertext data by using a signature private key; the intelligent electric meter uploads verifiable ciphertext data to a corresponding fog node in a time period, wherein the verifiable ciphertext data comprise the ciphertext data, a digital signature, the time period and the identity of the intelligent electric meter;
s3, judging whether the number of normally working intelligent electric meters which upload verifiable ciphertext data in a responsible area of each fog node in a time period is larger than a preset threshold value or not, and if so, verifying the verifiable ciphertext data in batches by the fog nodes; after the verification is passed, the fog node calculates an aggregation ciphertext, generates a first session key temporarily negotiated with a power grid control center, calculates a second message authentication code, and uploads a verifiable fog-level aggregation ciphertext to the power grid control center, wherein the verifiable fog-level aggregation ciphertext comprises the aggregation ciphertext, the second message authentication code, a time period and the identity of the fog node;
s4, after receiving the verifiable fog-level aggregation ciphertext of the fog node, the power grid control center generates a second session key temporarily negotiated with the fog node, calculates a third message authentication code, and tests the third session key and the received second message authentication code, if the third session key passes the test, the power grid control center decrypts the verifiable fog-level aggregation ciphertext and recovers a plurality of dimension data values after aggregation; the S1 includes the steps of:
s101, the trusted center generates a symmetric key of a symmetric homomorphic encryption algorithm
Figure DEST_PATH_IMAGE001
Wherein u and v are bothIs a large prime number, and the bit length of u is greater than or equal to 2 times that of v, and s is a u-order finite field
Figure DEST_PATH_IMAGE002
D is the number of times of the ciphertext, and the trusted center is represented by TTP;
s102, the credible center sets a bilinear mapping
Figure DEST_PATH_IMAGE003
Wherein, in the step (A),
Figure DEST_PATH_IMAGE004
is a p-order addition cycle group,
Figure DEST_PATH_IMAGE005
is a P-factorial cyclic group, P is an additive cyclic group
Figure DEST_PATH_IMAGE006
A generator of (2);
s103, the credible center sets the number of the fog nodes as
Figure DEST_PATH_IMAGE007
And setting the maximum intelligent electric meter number of a fog node responsible area to be N, wherein the fog node is used
Figure DEST_PATH_IMAGE008
To said smart meter
Figure DEST_PATH_IMAGE009
It is shown that,
Figure DEST_PATH_IMAGE010
；
s104, the credible center sets a fixed positive integer
Figure DEST_PATH_IMAGE011
Wherein
Figure DEST_PATH_IMAGE012
Representing upward integer taking, D represents the supremum of each dimension data;
s105, the credible center sets an anti-collision Hash function
Figure DEST_PATH_IMAGE013
Wherein, in the step (A),
Figure DEST_PATH_IMAGE014
representing a bit string with any length, and setting a first message authentication code HMAC;
s106, the credible center is in a limited domain of order p
Figure DEST_PATH_IMAGE015
Mist node signature private key selected for mist nodes
Figure DEST_PATH_IMAGE016
And calculates its public key of the fog node
Figure DEST_PATH_IMAGE017
The identity of the fog node is
Figure DEST_PATH_IMAGE018
；
S107, the trusted center slave finite field
Figure DEST_PATH_IMAGE019
Electric meter signature private key selection method for intelligent electric meter
Figure DEST_PATH_IMAGE020
And calculate the public key of the electric meter
Figure DEST_PATH_IMAGE021
The identity of the intelligent electric meter is
Figure DEST_PATH_IMAGE022
；
S108, the trusted center slave finite field
Figure DEST_PATH_IMAGE023
Selecting a control center signature private key x for a power grid control center, and calculating a control center public key of the control center signature private key x
Figure DEST_PATH_IMAGE024
The grid control center is denoted by CC;
s109, the credible center determines two parameters
Figure DEST_PATH_IMAGE025
And is and
Figure DEST_PATH_IMAGE026
；
s110, the credible center selects a t-1 degree polynomial
Figure DEST_PATH_IMAGE027
And is and
Figure DEST_PATH_IMAGE028
wherein y is a variable, and t is a preset threshold value;
s111, the credible center selects a positive integer
Figure DEST_PATH_IMAGE029
And calculating a secret share parameter one
Figure DEST_PATH_IMAGE030
Secret share parameter two
Figure DEST_PATH_IMAGE031
Secret share parameter three
Figure DEST_PATH_IMAGE032
Secret share parameterFourthly
Figure DEST_PATH_IMAGE033
And secret share parameter five
Figure DEST_PATH_IMAGE034
Wherein is a positive integer
Figure DEST_PATH_IMAGE035
The bit length of (d) is less than or equal to 20 bits, f (j) represents the value of a t-1 degree polynomial corresponding to the jth intelligent electric meter, and s is a u-order finite field
Figure 889538DEST_PATH_IMAGE002
D refers to the fourth component of the symmetric key of the symmetric homomorphic encryption algorithm;
s112, the trusted center issues system public parameters
Figure 541099DEST_PATH_IMAGE036
；
S113, the trusted center controls the secret parameters of the center
Figure DEST_PATH_IMAGE037
Sending the parameters to a power grid control center to obtain the secret parameters of the electric meter
Figure DEST_PATH_IMAGE038
Sending the parameters to each intelligent ammeter, and carrying out secret parameter of the fog node
Figure DEST_PATH_IMAGE039
Sending the data to each fog node; the S2 includes the steps of:
s201, enabling the intelligent electric meter to obtain data of each dimension of a user
Figure DEST_PATH_IMAGE040
Encoding into binary bit strings
Figure DEST_PATH_IMAGE041
Wherein the encoded data of each dimension is
Figure DEST_PATH_IMAGE042
Representing data
Figure DEST_PATH_IMAGE043
In the form of a binary code of (a),
Figure DEST_PATH_IMAGE044
is expressed as length of
Figure DEST_PATH_IMAGE045
Filling all-zero bit strings, wherein eta represents the dimension of the electric meter data, and l represents the total number of data dimensions;
s202, the intelligent electric meter sets the electricity utilization data to be
Figure DEST_PATH_IMAGE046
；
S203, the intelligent electric meter selects a positive random number
Figure DEST_PATH_IMAGE047
And is and
Figure DEST_PATH_IMAGE048
wherein, the symbols
Figure DEST_PATH_IMAGE049
Which represents the length of the bit string and,
Figure DEST_PATH_IMAGE050
has a bit length of
Figure DEST_PATH_IMAGE051
；
S204, using the electric meter secret parameter by the intelligent electric meter
Figure DEST_PATH_IMAGE052
The electricity data are compared in the following way
Figure DEST_PATH_IMAGE053
And (3) encryption:
Figure DEST_PATH_IMAGE054
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE055
is power consumption data
Figure DEST_PATH_IMAGE056
The ciphertext of (a) may be encrypted,
Figure DEST_PATH_IMAGE057
is a random number;
s205. Intelligent electric meter
Figure DEST_PATH_IMAGE058
Signing private key using electricity meter
Figure DEST_PATH_IMAGE059
Generating
Figure DEST_PATH_IMAGE060
Is signed
Figure DEST_PATH_IMAGE061
：
Figure DEST_PATH_IMAGE062
Wherein T is a time period;
s206. the intelligent electric meter verifies the ciphertext data
Figure DEST_PATH_IMAGE063
Sending the information to the corresponding fog node; the S3 includes the steps of:
s301, judging the number of intelligent electric meters which are in charge of normal work of regional uploading verifiable ciphertext data by the fog nodes in the time period T
Figure DEST_PATH_IMAGE064
If the threshold value is larger than the preset threshold value t, if yes, S302 is executed, wherein,
Figure DEST_PATH_IMAGE065
a subscript set of the smart meter which works normally is represented;
s302, carrying out batch verification on the fog nodes according to the following equation:
Figure DEST_PATH_IMAGE066
if the equation is established, the verification is passed;
s303, calculating Lagrange coefficient in polymerization process by using fog node
Figure DEST_PATH_IMAGE067
Wherein, in the step (A),
Figure DEST_PATH_IMAGE068
is a sequence value managed by the user at the fog node,
Figure DEST_PATH_IMAGE069
indicated as the location of one user,
Figure DEST_PATH_IMAGE070
representing a pointer in the traversal process, and calculating all user subscripts received by the fog nodes;
s304, the fog node calculates an aggregation ciphertext:
Figure DEST_PATH_IMAGE071
；
s305, the fog node calculates a first session key temporarily negotiated with a power grid control center
Figure DEST_PATH_IMAGE072
；
S306, the fog node calculates a second message authentication code
Figure DEST_PATH_IMAGE073
Wherein
Figure DEST_PATH_IMAGE074
Representing points on an elliptic curve
Figure DEST_PATH_IMAGE075
The ordinate of (a);
s307, the fog node sends a verifiable fog level aggregation ciphertext to a power grid control center
Figure DEST_PATH_IMAGE076
(ii) a The S4 includes the steps of:
s401, the power grid control center receives verifiable fog-level aggregation ciphertext from a fog node
Figure DEST_PATH_IMAGE077
Then, a second session key temporarily negotiated with the fog node is calculated
Figure DEST_PATH_IMAGE078
；
S402, the power grid control center calculates a third message authentication code
Figure DEST_PATH_IMAGE079
Wherein
Figure DEST_PATH_IMAGE080
Representing points on an elliptic curve
Figure DEST_PATH_IMAGE081
Ordinate ofIf, if
Figure DEST_PATH_IMAGE082
Then, S403 is executed;
s403, the power grid control center utilizes secret parameters of the control center
Figure DEST_PATH_IMAGE083
Decrypting the verifiable fog level aggregation ciphertext of the fog node:
Figure DEST_PATH_IMAGE084
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE085
the decrypted aggregated data of the intelligent electric meter are represented;
s404, the power grid control center recovers the aggregated data of each dimension, wherein the aggregated data of the eta dimension
Figure DEST_PATH_IMAGE086
As a bit string
Figure DEST_PATH_IMAGE087
To middle
Figure DEST_PATH_IMAGE088
Bit to bit
Figure DEST_PATH_IMAGE089
The data in the bit positions of the data,
Figure DEST_PATH_IMAGE090
and l denotes how many data dimensions are present in total.
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