CN112291191A - Lightweight privacy protection multidimensional data aggregation method based on edge calculation - Google Patents

Lightweight privacy protection multidimensional data aggregation method based on edge calculation Download PDF

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CN112291191A
CN112291191A CN202010881463.9A CN202010881463A CN112291191A CN 112291191 A CN112291191 A CN 112291191A CN 202010881463 A CN202010881463 A CN 202010881463A CN 112291191 A CN112291191 A CN 112291191A
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kdc
service center
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郭松涛
康宇昊
刘贵燕
程俊华
王曲苑
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Chongqing University
Southwest University
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Southwest University
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    • 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
    • H04L67/12—Protocols specially adapted for proprietary or special-purpose networking environments, e.g. medical networks, sensor networks, networks in vehicles or remote metering networks
    • 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
    • H04L63/06—Network architectures or network communication protocols for network security for supporting key management in a packet data network
    • 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
    • H04L63/06—Network architectures or network communication protocols for network security for supporting key management in a packet data network
    • H04L63/062—Network architectures or network communication protocols for network security for supporting key management in a packet data network for key distribution, e.g. centrally by trusted party
    • 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
    • H04L63/08—Network architectures or network communication protocols for network security for authentication of entities
    • 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
    • H04L63/12—Applying verification of the received information
    • H04L63/123—Applying verification of the received information received data contents, e.g. message integrity

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Abstract

The invention constructs an Internet of things model based on an edge computing framework, and provides an efficient and privacy-protecting multidimensional data aggregation scheme on the basis. The scheme adopts an identity-based lightweight signature algorithm and a Paillier encryption system to protect the privacy of the user from being invaded. In addition, the proposed scheme enables the IOT sensing device to report various types of data in one report message by using a super-increment sequence, so that the service provider can analyze the data. Theoretical security analysis shows that the scheme can effectively protect the personal data privacy of the user. Finally, experimental analysis shows that the scheme has lower calculation amount and communication overhead, and realizes lightweight communication to a certain extent.

Description

Lightweight privacy protection multidimensional data aggregation method based on edge calculation
Technical Field
The invention relates to the technical field of data privacy protection, in particular to a lightweight privacy protection multidimensional data aggregation method based on edge calculation.
Background
The development and widespread use of the internet of things (IoT) has greatly changed our lifestyle, providing great convenience and flexibility to our daily lives. In order to collect real-time data of users, internet of things devices are deployed close to consumers, and the internet of things devices record and report usage data of the consumers to a control center in real time. However, directly delivering the user usage data to the control center would result in the control center having to process a large amount of fine-grained usage data in a short time, thereby placing severe stress on the communication channel. In addition, the data directly reported by the internet of things equipment can expose the real-time use condition of the data of the consumer, so that the privacy of the user is damaged. Because the real-time consumption data can reflect the user's current behavior, such as whether the user is at home, taking a bath, watching television, and even what appliances are in use at home. Therefore, the temperature of the molten metal is controlled,
therefore, in order to fully utilize the advantages brought by the internet of things, some challenges of the internet of things must be solved, and therefore, a data aggregation method capable of conveniently using data and protecting real-time use data of a user from being leaked is urgently needed.
Disclosure of Invention
In view of this, the invention provides a lightweight privacy protection multidimensional data aggregation method based on edge calculation.
The invention provides a lightweight privacy protection multidimensional data polymerization method based on edge calculation, which is characterized by comprising the following steps: the system framework implemented by the method comprises the Internet of things equipment, the edge node, the service center SC and the key distribution center KDC, and the data aggregation method specifically comprises the following steps: system initialization, a registration phase, a usage data report generation phase, data aggregation, verification and decryption of aggregated data, data reading and analysis;
the system initialization comprises initialization of a signature scheme and initialization of a secure data aggregation scheme;
the initialization of the signature scheme comprises the following steps:
setting the safety parameter as K, KDC selecting two multiplication circulation groups G1，G2P is a group G1Generation of (e: G)1×G1→G2；
KDC selects three secure hash functions H1，H3：{0，1}*→G1，
Figure BDA0002654251570000021
Wherein
Figure BDA0002654251570000022
A multiplicative group representing q;
KDC selects a random number
Figure BDA0002654251570000023
As a private key, and the computing system public key is PpubsP; wherein, PpubPublic key representing system, s random number, P G1A generator of (2);
KDC release system parameters:<k，e,G1,G2,P,Ppub,H1,H2，H3>and keeping s secret;
the initialization of the secure data aggregation scheme comprises the steps of:
the KDC generates the following parameters for the Paillier cryptosystem: KDC randomly selects two independent large prime numbers P1And q, and determining a public key (N, g) and a private key (lambda, mu) of the Paillier cryptosystem:
the public key (N, g) is determined by the following method:
N＝p1q
where N denotes an element of the public key, p1Representing a random large prime number, q representing a random large prime number, p1And q represents that the KDC randomly selects two independent large prime numbers;
the private key (λ, μ) is determined using the following method:
λ＝lcm(p1-1,q-1)；
wherein λ represents the private keyElement 1, p of1Representing random big prime numbers, q representing random big prime numbers, and p and q representing that the KDC randomly selects two independent big prime numbers;
μ＝(L(gλmodN2))-1，
where μ denotes element 2 of the private key, L is defined as L (x) x-1/N, g denotes a random integer chosen by KDC, and g satisfies
Figure BDA0002654251570000024
λ represents an element of the private key, N represents an element of the public key;
the registration stage comprises the registration of the Internet of things equipment to the KDC, the registration of the edge node to the KDC and the registration of the service center to the KDC;
in the use data report generation stage, the Internet of things equipment collects use data from a user and reports the use data to the edge node periodically;
the specific steps of the generation phase of the usage data report comprise:
the service center generates a group of super increasing sequences according to self requirements
Figure BDA0002654251570000031
Wherein
Figure BDA0002654251570000032
And i is less than or equal to w, w represents the data type needed to be known by the service center, ujRepresenting the upper limit of the jth data, and n representing the number of users;
the service center generates a group of generating elements G ═ G (G)1，g2,…,gl) Wherein
Figure BDA0002654251570000033
w represents the data type needed to be known by the service center, G represents the generator, G represents a random integer selected by KDC, and G satisfies
Figure BDA0002654251570000034
The service center sends the generated element G to the SM through a secure channeli，SMiRepresenting Internet of things equipment i, SMiW data can be reported according to the requirements of the service center;
the data aggregation stage receives { c) from the Internet of things equipmenti，σi,Ti，IDiAfter the data is processed, the edge node judges whether the time stamp obtained after the Hash operation is consistent with the time stamp received by the edge node, if not, the encrypted data is maliciously tampered and is not accepted, and if so, an aggregate signature sigma is calculatedjAnd sending the aggregated data information to a service center;
the verification and decryption of the aggregated data comprises obtaining { c } at the service center SCj，σj，Tj,IDjAfter that, the current timestamp T is checkedjJudging whether the time stamp obtained after the Hash operation is consistent with the time stamp received by the service center, if not, indicating that the encrypted data is maliciously tampered and does not accept the data, and if so, executing the following steps to verify and recover the aggregated data
Service center calculation hi＝H2(cj，IDj) And T ═ H3(Ppub) Wherein h isiRepresenting an intermediate variable, cjIndicating ciphertext data, ID, generated by an edge nodejRepresenting the identity of the edge node, PpubRepresenting the public key of the system, T represents an intermediate variable,
when e (P, V)i)＝e(Ui,T)e(hiQi,Ppub) Time-accept message, where P denotes G1Is generated from the generator, ViPart yi, U representing a digital signatureiDenotes an intermediate variable, T denotes an intermediate variable, hiDenotes an intermediate variable, QiRepresenting a public key, PpubA public key representing the system is shown,
the service center SC may use its private key to recover the plaintext
Figure BDA0002654251570000041
Where M denotes a plaintext, L denotes L (u) (u-1) N, C denotes a ciphertext, λ denotes an element 1 of a private key, and N is a tableAn element of a public key;
the service centre SC then runs algorithm 1 to recover the aggregated data (D)1,D2,…,Dj)，D1Representing the sum of intermediate variables, in which
Figure BDA0002654251570000042
DlDenotes the sum of the l-th intermediate variable, n denotes the number of users, dilRepresents the ith intermediate variable of the user, and we can then get it separately
Figure BDA0002654251570000043
Where n denotes the number of users, mi1Represents the plaintext after polymerization.
Further, the registering of the internet of things device to the KDC comprises the following steps:
thing networking device SMiBased on IDiGenerating a hash function Hi＝H(IDi) And then SMiRequest to send { IDi,hiRegister to KDC, SMiRepresenting identity information as IDi(i is more than or equal to 1 and less than or equal to n), wherein n represents the number of users;
KDC received SMiAfter the registration request, h is judgediAnd h (ID)i) If not, then not registering, if yes, then KDC according to function
Figure BDA0002654251570000044
Qi＝H1(IDi) (ii) a Obtaining SMiPrivate key of
Figure BDA0002654251570000045
Wherein s is the private key of the system;
KDC sending private key
Figure BDA0002654251570000046
To the equipment SM of the Internet of thingsiThen, then
Figure BDA0002654251570000047
As SMiWith the public key being Qi；
The edge node registering to the service center comprises the following steps:
edge node ID basedjGenerating a hash function hj＝h(IDj) And sends a request { IDj,hjRegistering to KDC; IDjRepresenting the identity of the edge node;
after KDC receives the registration request, h is judgedjAnd h (ID)j) If not, then not registering, if yes, then KDC according to function
Figure BDA0002654251570000048
Obtaining a private key
Figure BDA0002654251570000049
Wherein s is the private key of the system;
KDC sending private key
Figure BDA00026542515700000410
To an edge node, then
Figure BDA00026542515700000411
As private key storage for edge nodes, while the public key is Qj，Qj＝H1(IDj)；
The registration of the service center with the KDC comprises the steps of:
service center ID-basedsGenerating a hash function hs＝h(IDs) And sends a request { IDs,hsRegistering to KDC; IDsAn identity representing a service center;
after KDC receives the registration request, h is judgedsAnd h (ID)s) If not, then not registering, if yes, then KDC according to function
Figure BDA0002654251570000051
Obtaining a private key
Figure BDA0002654251570000052
Wherein s is the private key of the system;
KDC sending private key
Figure BDA0002654251570000053
To a service center and then
Figure BDA0002654251570000054
As a private key store for the service center, while the public key is Qs，Qs＝H1(IDs)。
Further, the specific steps of generating the W data are as follows:
thing networking device SMiExtracting the collected data into M-M according to the requirements of the service centeri1,mi2…,miw}; m represents plaintext, Mi1Represents the plaintext after polymerization;
SMiselecting a random number
Figure BDA0002654251570000055
Determining a ciphertext, the ciphertext being represented as
Figure BDA0002654251570000056
Figure BDA0002654251570000057
Wherein, ciRepresentation SMiGenerated ciphertext, g1,g2,…,gwA group of generating elements generated by the service center are represented, and N represents one element of the public key;
determining SMiFor message miSignature σ ofi，σi＝(Ui，Vi)，
SMiRandom selection
Figure BDA0002654251570000058
Determining a signature Ui＝riP；
Calculate Hi＝H2(mi，IDi，Ti)
And T ═ H3(Ppub)
Calculating Vi＝riT+hidID
Wherein, TiIndicates the current timestamp, hiAnd T represents an intermediate variable, PpubA public key representing the system is shown,
SMiwill { c }i,σi,Ti,IDiIt is sent to the edge node.
Further, said verifying the validity of the n signatures is the validity of the n signatures if and only if the following n equations are true;
e(P,Vi)＝e(Ui,T)e(hiQi,Ppub) (1≤i≤n)
hi＝H2(mi,IDi)
T＝H3(Ppub)
wherein P is a group G1One generator of, ViRepresenting part of a digital signature, UiDenotes the intermediate variable, hiAnd T represents an intermediate variable, QiRepresenting a public key, PpubPublic key, m, representing the systemiRepresenting the plaintext, ID, after aggregationiRepresenting the identity of the internet of things device;
the aggregate signature σiThe method comprises the following steps:
Figure BDA0002654251570000061
get
Figure BDA0002654251570000062
And
Figure BDA0002654251570000063
wherein, cjRepresenting ciphertext generated by an edge node, ciRepresenting a ciphertext generated by the intelligent ammeter; g1，g2，…，gwRepresenting a set of generators generated by a service centre, N representing an element of a public key, a1,a2，…，awRepresenting a set of super-increment sequences.
Determining edge node aggregate signatures σj，
Figure BDA0002654251570000064
And
Figure BDA0002654251570000065
n represents the number of users, and the aggregation signature sigma of n users is obtainedj(U, V), the edge node will { c }j,σj,Tj,IDjIt is sent to the service center.
Further, the method further includes data reading and analysis, and when analyzing the data obtained by the service center, the service provider may perform one-way analysis of variance (ANOVA) on the usage data of the user, and check whether a change of a certain factor affects the data usage policy of the user:
the service center needs to regenerate a group of super-increment sequences
Figure BDA0002654251570000066
Wherein the content of the first and second substances,
Figure BDA0002654251570000067
representing a super-increasing sequence, a1,a2，…，a2wRepresenting elements in a set of super-increment sequences;
wherein a is1＝1i≤(w+1)，
Figure BDA0002654251570000068
When i is>When (l +1), there are
Figure BDA0002654251570000069
ujRepresenting the upper limit of the jth data, and n representing the number of users;
the service center generates a group of generating elements G ═ G (G)1,g2，…,g2w) Wherein
Figure BDA0002654251570000071
The specific steps are as follows;
the service center SC sends a request for carrying out one-way variance analysis on the user data, and then the Internet of things equipment extracts data mi1,mi2…miwAnd separately calculate
Figure BDA0002654251570000072
Then the Internet of things equipment generates ciphertext
Figure BDA0002654251570000073
Where i is 1,2 …, M, and sends these ciphertexts to the edge node
The edge node receives the ciphertexts, divides the M messages into s according to certain factors, each set has T messages, and then the ciphertexts aggregated by the edge node are expressed as OCj，OCjThe calculation method of (2) is as follows:
Figure BDA0002654251570000074
wherein, OCjCiphertext representing an aggregation of edge nodes, G ═ G1,g2,…,g2w) Is that the service center generates a set of generator, riRepresentation SMiRandomly selecting random numbers, wherein T represents T messages, n represents the number of users, and w represents the number of data types;
service center receiving OC from edge nodejThen it calculates it separately for the s groups
Figure BDA0002654251570000075
T denotes T messages, mjiRepresenting data extracted by the Internet of things device, we define SEIs the sum of squares, S, within the groupAIs the sum of squares between groups, we define
Figure BDA0002654251570000076
Wherein i is 1,2, …, a, TiA timestamp representing the Internet of things equipment, T represents T messages, mjiThe data extracted by the equipment of the Internet of things can be calculated by the data service centers as follows:
Figure BDA0002654251570000077
Figure BDA0002654251570000078
Figure BDA0002654251570000079
SE＝ST-SA
wherein, TiTime stamp of the equipment of the Internet of things, a represents a group of data, and mjiData representing the extraction of Internet of things equipment, Q1，Q2Representing an intermediate variable, n representing the number of users, STDenotes the total variance, SEIs the sum of squares, S, within the groupAIs the intergroup sum of squares, i ═ 1,2, …, a;
substituting the corresponding data into a formula to obtain
Figure BDA0002654251570000081
Figure BDA0002654251570000082
Figure BDA0002654251570000083
Wherein S isEIs the sum of squares, S, within the groupAIs the sum of squares between groups, mjiRepresenting data extracted by equipment of the Internet of things, F representing mean square error, M representing the number of messages, and s representingDividing the data into s groups according to the demand factors of the cloud server;
from this data, the service center may perform a one-way analysis of variance to check whether a certain factor has a significant impact on the power consumption policy of the user.
The invention has the beneficial technical effects that: the data aggregation scheme of the Internet of things based on the edge computing architecture utilizes the low-delay characteristic of the edge node to realize high-efficiency communication; the identity-based aggregation signature scheme is used for ensuring that the data of the user is not maliciously tampered by an infringer, and an independent third-party Key Distribution Center (KDC) is used and a Paillier homomorphic password technology is applied to protect the privacy of the user from being infringed; experimental analysis shows that the scheme has low calculation amount and communication overhead, and realizes lightweight communication to a certain extent.
Drawings
The invention is further described below with reference to the following figures and examples:
fig. 1 is a comparison graph of the calculation cost of the internet of things device.
FIG. 2 is a graph comparing the computation costs at edge nodes according to the present invention.
Fig. 3 is a block diagram of the algorithm 1 of the present invention.
Fig. 4 is a block diagram of the service center SC operating algorithm 1 of the present invention.
Detailed Description
The invention is further described with reference to the accompanying drawings in which:
the invention provides a lightweight privacy protection multidimensional data polymerization method based on edge calculation, which is characterized by comprising the following steps: the system framework implemented by the method comprises the Internet of things equipment, the edge node, the service center SC and the key distribution center KDC, and the data aggregation method specifically comprises the following steps: system initialization, a registration phase, a usage data report generation phase, data aggregation, verification and decryption of aggregated data, data reading and analysis;
the system initialization comprises initialization of a signature scheme and initialization of a secure data aggregation scheme;
the initialization of the signature scheme comprises the following steps:
setting the safety parameter as K, KDC selecting two multiplication circulation groups G1,G2P is a group G1Generation of (e: G)1×G1→G2；
KDC selects three secure hash functions H1，H3：{0,1}*→G1，
Figure BDA0002654251570000091
Wherein
Figure BDA0002654251570000092
A multiplicative group representing q;
KDC selects a random number
Figure BDA0002654251570000093
As a private key, and the computing system public key is PpubsP; wherein, PpubPublic key representing system, s random number, P G1A generator of (2);
KDC release system parameters:<k,e,G1,G2,P,Ppub,H1,H2，H3>and keeping s secret;
the initialization of the secure data aggregation scheme comprises the steps of:
the KDC generates the following parameters for the Paillier cryptosystem: KDC randomly selects two independent large prime numbers P1And q, and determining a public key (N, g) and a private key (lambda, mu) of the Paillier cryptosystem:
the public key (N, g) is determined by the following method:
N＝p1q
where N denotes an element of the public key, p1Representing a random large prime number, q representing a random large prime number, p1And q represents that the KDC randomly selects two independent large prime numbers;
the private key (λ, μ) is determined using the following method:
λ＝lcm(p1-1，q-1)；
whereinλ denotes the element 1, p of the private key1Representing random big prime numbers, q representing random big prime numbers, and p and q representing that the KDC randomly selects two independent big prime numbers;
μ＝(L(gλmodN2))-1，
where μ denotes element 2 of the private key, L is defined as L (x) x-1/N, g denotes a random integer chosen by KDC, and g satisfies
Figure BDA0002654251570000101
λ represents an element of the private key, N represents an element of the public key;
the registration stage comprises the registration of the Internet of things equipment to the KDC, the registration of the edge node to the KDC and the registration of the service center to the KDC;
in the use data report generation stage, the Internet of things equipment collects use data from a user and reports the use data to the edge node periodically;
the specific steps of the generation phase of the usage data report comprise:
the service center generates a group of super increasing sequences according to self requirements
Figure BDA0002654251570000102
Wherein
Figure BDA0002654251570000103
And i is less than or equal to w, w represents the data type needed to be known by the service center, ujRepresenting the upper limit of the jth data, and n representing the number of users;
the service center generates a group of generating elements G ═ G (G)1，g2，…,gl) Wherein
Figure BDA0002654251570000104
w represents the data type needed to be known by the service center, G represents the generator, G represents a random integer selected by KDC, and G satisfies
Figure BDA0002654251570000105
The service center sends the generator G through a secure channelFor SMi，SMiRepresenting Internet of things equipment i, SMiW data can be reported according to the requirements of the service center;
the data aggregation stage receives { c) from the Internet of things equipmenti,σi,Ti,IDiAfter the data is processed, the edge node judges whether the time stamp obtained after the Hash operation is consistent with the time stamp received by the edge node, if not, the encrypted data is maliciously tampered and is not accepted, and if so, an aggregate signature sigma is calculatedjAnd sending the aggregated data information to a service center;
the verification and decryption of the aggregated data comprises obtaining { c } at the service center SCj,σj,Tj,IDjAfter that, the current timestamp T is checkedjJudging whether the time stamp obtained after the Hash operation is consistent with the time stamp received by the service center, if not, indicating that the encrypted data is maliciously tampered and does not accept the data, and if so, executing the following steps to verify and recover the aggregated data
Service center calculation hi＝H2(cj,IDj) And T ═ H3(Ppub) Wherein h isiRepresenting an intermediate variable, cjIndicating ciphertext data, ID, generated by an edge nodejRepresenting the identity of the edge node, PpubRepresenting the public key of the system, T represents an intermediate variable,
when e (P, V)i)＝e(Ui,T)e(hiQi，Ppub) Time-accept message, where P denotes G1Is generated from the generator, ViPart yi, U representing a digital signatureiDenotes an intermediate variable, T denotes an intermediate variable, hiDenotes an intermediate variable, QiRepresenting a public key, PpubA public key representing the system is shown,
the service center SC may use its private key to recover the plaintext
Figure BDA0002654251570000111
Where M denotes a plaintext, L denotes L (u) ═ 1 ═ N, C denotes a ciphertext, and λ denotes an element of a private key1, N represents an element of a public key;
the service centre SC then runs algorithm 1 to recover the aggregated data (D)1,D2,…，Dj)，D1Representing the sum of intermediate variables, in which
Figure BDA0002654251570000112
DlDenotes the sum of the l-th intermediate variable, n denotes the number of users, dilRepresents the ith intermediate variable of the user, and we can then get it separately
Figure BDA0002654251570000113
Where n denotes the number of users, mi1Represents the plaintext after polymerization.
In this embodiment, the registering of the internet of things device to the KDC includes the following steps:
thing networking device SMiBased on IDiGenerating a hash function Hi＝H(IDi) And then SMiRequest to send { IDi,hiRegister to KDC, SMiRepresenting identity information as IDi(i is more than or equal to 1 and less than or equal to b), and n represents the number of users;
KDC received SMiAfter the registration request, h is judgediAnd h (ID)i) If not, then not registering, if yes, then KDC according to function
Figure BDA0002654251570000114
Qi＝H1(IDi) (ii) a Obtaining SMiPrivate key of
Figure BDA0002654251570000115
Wherein s is the private key of the system;
KDC sending private key
Figure BDA0002654251570000116
To the equipment SM of the Internet of thingsiThen, then
Figure BDA0002654251570000117
As SMiWith the public key being Qi；
The edge node registering to the service center comprises the following steps:
edge node ID basedjGenerating a hash function hj＝h(IDj) And sends a request { IDj,hjRegistering to KDC; IDjRepresenting the identity of the edge node;
after KDC receives the registration request, h is judgedjAnd h (ID)j) If not, then not registering, if yes, then KDC according to function
Figure BDA0002654251570000121
Obtaining a private key
Figure BDA0002654251570000122
Wherein s is the private key of the system;
KDC sending private key
Figure BDA0002654251570000123
To an edge node, then
Figure BDA0002654251570000124
As private key storage for edge nodes, while the public key is Qj，Qj＝H1(IDj)；
The registration of the service center with the KDC comprises the steps of:
service center ID-basedsGenerating a hash function hs＝h(IDs) And sends a request { IDs，hsRegistering to KDC; IDsAn identity representing a service center;
after KDC receives the registration request, h is judgedsAnd h (ID)s) If not, then not registering, if yes, then KDC according to function
Figure BDA0002654251570000125
Obtaining a private key
Figure BDA0002654251570000126
Wherein s is the private key of the system;
KDC sending private key
Figure BDA0002654251570000127
To a service center and then
Figure BDA0002654251570000128
As a private key store for the service center, while the public key is Qs，Qs＝H1(IDs)。
In this embodiment, the specific steps of generating the W data are as follows:
thing networking device SMiExtracting the collected data into M-M according to the requirements of the service centeri1,mi2…,miw}; m represents plaintext, Mi1Represents the plaintext after polymerization;
SMiselecting a random number
Figure BDA0002654251570000129
Determining a ciphertext, the ciphertext being represented as
Figure BDA00026542515700001210
Figure BDA00026542515700001211
Wherein, ciRepresentation SMiGenerated ciphertext, g1,g2,…,gwA group of generating elements generated by the service center are represented, and N represents one element of the public key;
determining SMiFor message miSignature σ ofi，σi＝(Ui，Vi)，
SMiRandom selection
Figure BDA00026542515700001212
Determining a signature Ui＝riP；
Calculate hi＝H2(mi，IDi，Ti)
And T ═ H3(Ppub)
Calculating Vi＝riT+hidID
Wherein, TiIndicates the current timestamp, hiAnd T represents an intermediate variable, PpubPublic key, SM, representing a systemiWill { c }i,σi,Ti，IDiIt is sent to the edge node.
In this embodiment, the validation of n signatures is valid if and only if the following n equations are true;
e(P,Vi)＝e(Ui,T)e(hiQi,Ppub) (1≤i≤n)
hi＝H2(mi,IDi)
T＝H3(Ppub)
wherein P is a group G1One generator of, ViRepresenting part of a digital signature, UiDenotes the intermediate variable, hiAnd T represents an intermediate variable, QiRepresenting a public key, PpubPublic key, m, representing the systemiRepresenting the plaintext, ID, after aggregationiRepresenting the identity of the internet of things device;
the aggregate signature σiThe method comprises the following steps:
Figure BDA0002654251570000131
get
Figure BDA0002654251570000132
And
Figure BDA0002654251570000133
wherein, cjRepresenting ciphertext generated by an edge node, ciRepresenting a ciphertext generated by the intelligent ammeter; g1,g2，…，gwRepresenting a set of generators generated by a service centre, N representing an element of a public key, a1，a2，…，awRepresenting a set of super-increment sequences.
Determining edge node aggregate signatures σj，
Figure BDA0002654251570000134
And
Figure BDA0002654251570000135
n represents the number of users, and the aggregation signature sigma of n users is obtainedj(U, V), the edge node will { C }j，σj，Tj,IDjIt is sent to the service center.
In this embodiment, the method further includes data reading and analysis, and when analyzing the data obtained by the service center, the service provider may perform one-way analysis of variance (ANOVA) on the usage data of the user, and check whether a change of a certain factor may affect the data usage policy of the user:
the service center needs to regenerate a group of super-increment sequences
Figure BDA0002654251570000141
Wherein the content of the first and second substances,
Figure BDA0002654251570000142
representing a super-increasing sequence, a1，a2，…,a2wRepresenting elements in a set of super-increment sequences;
wherein a is1＝1i≤(w+1)，
Figure BDA0002654251570000143
When i is>When (l +1), there are
Figure BDA0002654251570000144
ujRepresenting the upper limit of the jth data, and n representing the number of users;
the service center generates a group of generating elements G ═ G (G)1，g2，…，g2w) Wherein
Figure BDA0002654251570000145
The specific steps are as follows;
the service center SC sends a request for carrying out one-way variance analysis on the user data, and then the Internet of things equipment extracts data mi1，mi2…miwAnd separately calculate
Figure BDA0002654251570000146
Then the Internet of things equipment generates ciphertext
Figure BDA0002654251570000147
Where i is 1,2 …, M, and sends these ciphertexts to the edge node
The edge node receives the ciphertexts, divides the M messages into s according to certain factors, each set has T messages, and then the ciphertexts aggregated by the edge node are expressed as OCj，OCjThe calculation method of (2) is as follows:
Figure BDA0002654251570000148
wherein, OCjCiphertext representing an aggregation of edge nodes, G ═ G1，g2，…，g2w) Is that the service center generates a set of generator, riRepresentation SMiRandomly selecting random numbers, wherein T represents T messages, n represents the number of users, and w represents the number of data types;
service center receiving OC from edge nodejThen it calculates it separately for the s groups
Figure BDA0002654251570000149
T denotes T messages, mjiRepresenting data extracted by the Internet of things device, we define SEIs the sum of squares, S, within the groupAIs the sum of squares between groups, we define
Figure BDA00026542515700001410
Wherein i is 1,2, …, a, TiA timestamp representing the Internet of things equipment, T represents T messages, mjiThe data extracted by the equipment of the Internet of things can be calculated by the data service centers as follows:
Figure BDA0002654251570000151
Figure BDA0002654251570000152
Figure BDA0002654251570000153
SE＝ST-SA
wherein, TiTime stamp of the equipment of the Internet of things, a represents a group of data, and mjiData representing the extraction of Internet of things equipment, Q1，Q2Representing an intermediate variable, n representing the number of users, STDenotes the total variance, SEIs the sum of squares, S, within the groupAIs the intergroup sum of squares, i ═ 1,2, …, a;
substituting the corresponding data into a formula to obtain
Figure BDA0002654251570000154
Figure BDA0002654251570000155
Figure BDA0002654251570000156
Wherein S isEIs the sum of squares, S, within the groupAIs the sum of squares between groups, mjiData representing extraction of internet of things equipmentF represents an error mean square, M represents the number of messages, M represents M messages, and s represents the division into s groups according to the demand factors of the cloud server;
from this data, the service center may perform a one-way analysis of variance to check whether a certain factor has a significant impact on the power consumption policy of the user.
Data aggregation refers to the selection, analysis, and classification of relevant data in information science, and the final analysis of the data to obtain the desired result, and mainly refers to any data conversion process capable of generating scalar values from arrays.
Next, the computational complexity, communication overhead, features and security of the present invention are explained as follows:
we compare this scheme with the pan scheme, which proposes a privacy-preserving data aggregation scheme in smart grids that aggregates user electricity usage data in two dimensions through gateways (acting as aggregators), and the lu scheme. The lu scheme adopts a Paillier cryptosystem and utilizes a super-increasing sequence to construct multidimensional data. Thus, multiple types of data can be reported in one ciphertext message. The first scheme uses the Lagrangian polynomial theorem to encrypt the usage data, and the second scheme is the same as our scheme, and uses the paillier encryption scheme.
A. Computational complexity and efficiency
At first we first define at 2048bits
Figure BDA0002654251570000161
Calculation of exponentiation, 160bits
Figure BDA0002654251570000162
Multiplication operation, multiplicative group
Figure BDA0002654251570000163
A pairing operation on, a Paillier public key encryption operation, and one at 1024bits
Figure BDA0002654251570000164
The exponentiation operation above is respectively represented as Te，Tm，Tp，TEAnd Tn. Specifically, we implemented our scheme through the MIRACL library and performed experiments on a computer with 3.2GHz, i7 CPU, 8GB memory, 64-bit windows 10 operating system. The data in table two simulate the average of 20,000 runs.
Table two: calculating time consumption
Figure BDA0002654251570000165
First, we analyze the computational complexity of the internet of things devices in different schemes. In this phase, the lu scheme needs to be
Figure BDA0002654251570000166
Upper w +1 exponentiation and in groups
Figure BDA0002654251570000167
Four multiplication operations on, while the pan scheme, SMiThen a scaled multiplication operation in 4w +2 bilinear pairings, one Paillier public key encryption operation and 3n ones are required
Figure BDA0002654251570000168
The exponentiation operation above. Also, SM in our schemeiIn that
Figure BDA0002654251570000169
In which w +1 exponentiation operations are required, in groups
Figure BDA00026542515700001610
Requiring 1 multiplication operation. The computational cost at this stage is comparable to that shown in fig. 2, and the proposed method requires less computational overhead than the Lu and Pan methods.
Then, we calculate the computational overhead of the edge nodes for three different schemes. Scheme at lu]In (1), the edge node requires n +3 bilinear pairing operations, and the group
Figure BDA00026542515700001611
One multiplication operation in (1), a scale multiplication operation in (4 n +1) bilinear pairings of edge nodes, and
Figure BDA00026542515700001612
is the nth power operation in (1). In our scheme, the edge nodes only need to perform n pairing operations and one cluster
Figure BDA00026542515700001613
The multiplication of (2). Computational cost at edge nodes versus, for example, fig. 3, our scheme requires less computational cost than the lu scheme but more than the pan scheme, but this difference is acceptable in view of the stronger data processing capabilities of the edge nodes.
And finally, calculating the calculation overhead of the three schemes on the cloud server in sequence. In the lu scheme, the cloud server needs to perform two pairing operations, obtain data through Paillier decryption, and need to perform the pairing operation for two times
Figure BDA0002654251570000171
Performing an exponentiation operation once. For the pan solution, the cloud server needs to be in
Figure BDA0002654251570000172
Performing an exponentiation operation once, and a scale multiplication operation in two bilinear pairings. Similar to the lu scheme, our scheme also requires two pairing operations to validate the data collected from the edge nodes, where
Figure BDA0002654251570000173
An exponentiation operation is required to obtain the data through Paillier decryption.
Based on the experimental results, the calculated costs for each of the pan, lu and our protocols are shown in Table three. It can be seen from experimental graphs that our scheme uses less computational cost than the lu scheme, but the pan scheme uses less computational cost than our scheme, however, given that our scheme has greater security and can implement more functions than the pan scheme, the difference in computational cost is acceptable.
Table three: comparison of computational costs
scheme sM Edge node SC
Lu[7] (w+1)Te+4Tm＝1.32w+5.40ms (n+3)Tp+1Tm＝6.2n+19.62ms 2Tp+1Te＝13.72ms
Pan[15] (4w+2)Tm+3Tn＝4.08w+3.27ms (4n+1)Tm+nTn+1TE＝4.49n+8.94ms 1Te+2Tm＝3.36ms
Ours (w+1)Te+1Tm＝1.32w+2.34ms nTp+1Tm＝6.2n+1.02ms 2Tp+1Te＝13.72ms
In the application scenario of the internet of things, the communication overhead is mainly generated in the communication between the internet of things device and the edge node and the communication between the edge node and the service center. As has been described in the foregoing, the present invention,
Figure BDA0002654251570000174
is 512bits in size and is,
Figure BDA0002654251570000175
is a length of 1024bits, and,
Figure BDA0002654251570000176
is 160bits in length and is,
Figure BDA0002654251570000177
is a size of 1024bits, and,
Figure BDA0002654251570000178
is 2048bits, and has a one-way hash function with a length of 160bits, and the length of the identity and timestamp is set to 32 bits.
First, we consider the communication overhead between edge nodes to the service center. Scheme at lu[7]In the method, the equipment of the Internet of things sends { C to the edge nodei，σi，RA，UiTS }, wherein
Figure BDA0002654251570000179
Has a bit length of 2048bits, and
Figure BDA00026542515700001710
has a bit length of 512bits, RA and UiIs 32bits identity information and TS is a 32bits timestamp. The communication cost is summed to | Ci|+|σi|+|RA|+|UiTS | + | 2048+512+32+32+32 ═ 2659 bits. For the pan scheme, the IOT device sends { c }i1,ci2,…,cinTo edge nodes, where
Figure BDA0002654251570000181
Is 1024bits long, and
Figure BDA0002654251570000182
is 1024bits, the communication overhead is cij1024n bits. Then, discussing our scheme, the internet of things device sends { c }i,σi,IDi,TiTo edge nodes, where
Figure BDA0002654251570000183
Its length is 2048bits, and
Figure BDA0002654251570000184
wherein
Figure BDA0002654251570000185
Is 160bits, and further, the IDiIs an identity information of 32bits, TiIs a 32bits timestamp, we can conclude that the sum of the communication overhead is | Ci|+|σi|+|IDi|+|Ti|＝ 2048+160+32+32＝2272bits。
On the other hand, we analyze the communication overhead generated between the edge node and the service center by three schemes. In the lu scheme, the edge node sends { C, σ }gRA, GW, TS to a service center, wherein
Figure BDA0002654251570000186
Has a bit length of 2048bits, and
Figure BDA0002654251570000187
the bit length of (A) is 512bits, RA and GW are both 32bits identity information, and TS is a 32bits time stamp. The total communication overhead is therefore | C | + | σgI + | RA | + | GW | + | TS | ═ 2048+512+32+32+32 ═ 2659 bits. While in the scheme of pan the edge node sends { R (i), C (j) } to the cloud server, where
Figure BDA0002654251570000188
And is
Figure BDA0002654251570000189
Figure BDA00026542515700001810
The corresponding bit length is 2048bits, so the communication cost is | r (i) | + | c (j) | 2048w +2048n bits. For our scheme, the edge node sends { c }j,σj,IDj,TjTo a cloud server, where
Figure BDA00026542515700001811
The corresponding bit length is 2048bits, and
Figure BDA00026542515700001812
is 160bits in length, IDjIs an identity mark of 32bits, TjIs a 32bits timestamp, we can find that the sum of the communication costs is | Cj|+|σj|+|IDj|+|Tj|＝2048+160+32+32＝2272bits。
The comparison of the communication overhead of the three schemes is shown in table four in a tabular form, and by comparison, we can obtain that the communication overhead is lower compared with the LU scheme, and the calculation overhead is much lower compared with the pan scheme, because in the scheme, one piece of ciphertext data can report a plurality of information at the same time, and in the pan scheme, the report is required one by one, so that a lot of additional communication overhead is increased.
Table four: communication overhead comparison
Algorithm Meter to Edge node Edge node to SC
Lu[7] 2659bits 2659bits
Pan[15] 1024n bits 2048w+2048n bits
Our scheme 2272bits 2272bits
C. Characteristic and safety comparison
The characteristics and safety of our protocol were compared to the other two protocols and the results are shown in table five. On the one hand, we compared the capabilities of the three schemes for replay attacks, spoofing attacks and man-in-the-middle attacks. On the other hand, the functional characteristics of the three schemes can be realized.
Table five: functional and security comparisons
Lu[7] Pan[15] Our
Replay attack √ √ √
Impersonation attack √ × √
Man-in-the-middle attack × √ √
Multi-dimensional √ √ √
ANOVA × × √
Identity-based × × √
Edge computing support × × √
In the proposed scheme, a time stamp TiFor messages ci，σi，IDi，TiUse in (1) }, TjFor { cj，σj，IDj，TjUsing by adding a timestamp TiAnd TjThe edge node and the server can resist replay attack, so our scheme can resist replay attack, like our scheme, lu scheme adds a time stamp, and can resist replay attack similarly, but pan scheme cannot resist the effect of replay attack because it does not have a time stamp. Then we have analysed the man-in-the-middle attack, and in the previous analysis it was shown that in the proposed solution edge nodes can pass the checking equation e (P, V)i)＝e(Ui，T)e(hiQi，Ppub) The equipment of the Internet of things is authenticated, and the cloud server passes the check equation
Figure BDA0002654251570000191
To authenticate the edge node; thus, the scheme is resistant to man-in-the-middle attacks. From our analysis, it can be concluded that the lu's solution can resist this attack, while the pan's solution cannot resist man-in-the-middle attacks. Next, we analyzed the internal attack, and in the proposed scheme, each internet of things device obtains its own private key from KDC
Figure BDA0002654251570000192
If there is no SMiThe corresponding private key can not recover the use data of a single user, so the proposed scheme can resist internal attack. For the lu scheme, since there is no trusted third party key generation center to generate corresponding blinding factors for the internet of things device, the capability of resisting internal attack is insufficient, while the pan scheme can resist internal attack.
We will then compare the functional properties of the three schemes. In the lu scheme, a mathematical approach is proposed to support multidimensional data aggregation using super-increasing sequences. Since our scheme is the Paillier cryptosystem used in lu-based schemes, our scheme can achieve multidimensional data aggregation. Likewise, the scheme of pan can also achieve multidimensional data aggregation. In addition, by collecting the sum of squares of the data used by the internet of things devices, the scheme also realizes one-way analysis of data variance, so that more accurate service is provided for users, which cannot be realized by the other two schemes.
In this scheme, we use an identity-based aggregated signature scheme that generates an identity-based private key for each internet-of-things equipped device user through a trusted third party Key Distribution Center (KDC). Therefore, the overhead of storing the public key list on the edge node and the cloud server is saved. For the lu scheme, the cloud server needs to store the registered device list and rearrange the identity and public key of the internet of things device. Since, in the reporting phase, the aggregator must search the list to find the public key of the internet of things device in order to verify the validity of the message, this will undoubtedly add additional storage and computational costs. Similarly, the scheme of pan also does not use an identity-based signature scheme. In addition, the scheme also supports an edge calculation paradigm, and fully utilizes the advantages of the edge calculation paradigm in the aspects of efficiency and privacy protection. Compared with the traditional scheme of the Internet of things, the scheme is more efficient and can provide safer services.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (5)

1. A lightweight privacy protection multidimensional data polymerization method based on edge calculation is characterized in that: the system framework implemented by the method comprises the Internet of things equipment, the edge node, the service center SC and the key distribution center KDC, and the data aggregation method specifically comprises the following steps: system initialization, a registration phase, a usage data report generation phase, data aggregation, verification and decryption of aggregated data, data reading and analysis;
the system initialization comprises initialization of a signature scheme and initialization of a secure data aggregation scheme;
the initialization of the signature scheme comprises the following steps:
setting the safety parameter as K, KDC selecting two multiplication circulation groups G1，G2P is a group G1The generator of (e): g1×G1→G2；
KDC selects three secure hash functions H1，H3：{0，1}*→G1，H2：
Figure FDA0002654251560000011
Wherein
Figure FDA0002654251560000012
A multiplicative group representing q;
KDC selects a random number
Figure FDA0002654251560000013
As a private key, and the computing system public key is PpubsP; wherein, PpubPublic key representing system, s random number, P G1A generator of (2);
KDC release system parameters: < k, e, G1，G2，P，Ppub，H1，H2，H3>And keeping s secret;
the initialization of the secure data aggregation scheme comprises the steps of:
the KDC generates the following parameters for the Paillier cryptosystem: KDC randomly selects two independent large prime numbers P1And q, and determining a public key (N, g) and a private key (lambda, mu) of the Paillier cryptosystem:
the public key (N, g) is determined by the following method:
N＝p1q
where N denotes an element of the public key, p1Representing a random large prime number, q representing a random large prime number, p1And q represents that the KDC randomly selects two independent large prime numbers;
the private key (λ, μ) is determined using the following method:
λ＝lcm(p1-1，q-1)；
where λ represents the element 1, p of the private key1Representing random big prime numbers, q representing random big prime numbers, and p and q representing that the KDC randomly selects two independent big prime numbers;
μ＝(L(gλmodN2))-1，
where μ denotes element 2 of the private key, L is defined as L (x) x-1/N, g denotes a random integer chosen by KDC, and g satisfies
Figure FDA0002654251560000021
λ represents an element of the private key, N represents an element of the public key;
the registration stage comprises the registration of the Internet of things equipment to the KDC, the registration of the edge node to the KDC and the registration of the service center to the KDC;
in the use data report generation stage, the Internet of things equipment collects use data from a user and reports the use data to the edge node periodically;
the specific steps of the generation phase of the usage data report comprise:
the service center generates a group of super increasing sequences according to self requirements
Figure FDA0002654251560000022
Wherein
Figure FDA0002654251560000023
And i is less than or equal to w, w represents the data type needed to be known by the service center, ujRepresenting the upper limit of the jth data, and n representing the number of users;
the service center generates a group of generating elements G ═ G (G)1，g2，...，gl) Wherein
Figure FDA0002654251560000024
w represents the data type needed to be known by the service center, G represents the generator, G represents a random integer selected by KDC, and G satisfies
Figure FDA0002654251560000025
The service center sends the generated element G to the SM through a secure channeli，SMiRepresenting Internet of things equipment i, SMiW data can be reported according to the requirements of the service center;
the data aggregation stage receives { c) from the Internet of things equipmenti，σi，Ti，IDiAfter the data is processed, the edge node judges whether the time stamp obtained after the Hash operation is consistent with the time stamp received by the edge node, if not, the encrypted data is maliciously tampered and is not accepted, and if so, an aggregate signature sigma is calculatedjAnd sending the aggregated data information to a service center;
the verification and decryption of the aggregated data comprises obtaining { c } at the service center SCj，σj，Tj，IDjAfter that, the current timestamp T is checkedjJudging whether the time stamp obtained after the Hash operation is consistent with the time stamp received by the service center, if not, indicating that the encrypted data is maliciously tampered and does not accept the data, and if so, executing the following steps to verify and recover the aggregated data
Service center calculation hi＝H2(cj，IDj) And T ═ H3(Ppub) Wherein h isiRepresenting an intermediate variable, cjIndicating ciphertext data, ID, generated by an edge nodejRepresenting the identity of the edge node, PpubRepresenting the public key of the system, T represents an intermediate variable,
when e (P, V)i)＝e(Ui，T)e(hiQi，Ppub) Time-accept message, where P denotes G1Is generated from the generator, ViPart yi, U representing a digital signatureiDenotes an intermediate variable, T denotes an intermediate variable, hiDenotes an intermediate variable, QiRepresenting a public key, PpubA public key representing the system is shown,
the service center SC may use its private key to recover the plaintext
Figure FDA0002654251560000031
Where M denotes a plaintext, L denotes L (u) ═ 1 ═ N, C denotes a ciphertext, λ denotes an element 1 of a private key, and N denotes one element of a public key;
the service centre SC then runs algorithm 1 to recover the aggregated data (D)1，D2，...，Dj)，D1Representing the sum of intermediate variables, in which
Figure FDA0002654251560000032
DlRepresents the sum of the 1 st intermediate variable, n represents the number of users, dilRepresent the 1 st intermediate variable of the user, and we can then get it separately
Figure FDA0002654251560000033
Where n denotes the number of users, mi1Represents the plaintext after polymerization.
2. The lightweight privacy protection multidimensional data aggregation method based on edge computing as claimed in claim 1, wherein: the registration of the Internet of things equipment to the KDC comprises the following steps:
thing networking device SMiBased on IDiGenerating a hash function Hi＝H(IDi) And then SMiRequest to send { IDi，hiRegister to KDC, SMiRepresenting identity information as IDi(i is more than or equal to 1 and less than or equal to n), wherein n represents the number of users;
KDC received SMiAfter the registration request, h is judgediAnd h (ID)i) If not, then not registering, if yes, then KDC according to function
Figure FDA0002654251560000034
Qi＝H1(IDi) (ii) a Obtaining SMiPrivate key of
Figure FDA0002654251560000038
Wherein s is the private key of the system;
KDC sending private key
Figure FDA0002654251560000036
To the equipment SM of the Internet of thingsiThen, then
Figure FDA0002654251560000037
As SMiWith the public key being Qi；
The edge node registering to the service center comprises the following steps:
edge node ID basedjGenerating a hash function hj＝h(IDj) And sends a request { IDj，hjRegistering to KDC; IDjRepresenting the identity of the edge node;
after KDC receives the registration request, h is judgedjAnd h (ID)j) If not, then not registering, if yes, then KDC according to function
Figure FDA0002654251560000041
Obtaining a private key
Figure FDA0002654251560000042
Wherein s is the private key of the system;
KDC sending private key
Figure FDA0002654251560000043
To an edge node, then
Figure FDA0002654251560000044
As private key storage for edge nodes, while the public key is Qj，Qj＝H1(IDj)；
The registration of the service center with the KDC comprises the steps of:
service center ID-basedsGenerating a hash function hs＝h(IDs) And sends a request { IDs，hsRegistering to KDC; IDsAn identity representing a service center;
after KDC receives the registration request, h is judgedsAnd h (ID)s) If not, then not registering, if yes, then KDC according to function
Figure FDA0002654251560000045
Obtaining a private key
Figure FDA0002654251560000046
Wherein s is the private key of the system;
KDC sending private key
Figure FDA0002654251560000047
To a service center and then
Figure FDA0002654251560000048
As a private key store for the service center, while the public key is Qs，Qs＝H1(IDs)。
3. The lightweight privacy protection multidimensional data aggregation method based on edge computing as claimed in claim 1, wherein: the specific steps of the W data generation are as follows:
thing networking device SMiExtracting the collected data into M-M according to the requirements of the service centeri1，mi2…，miw}; m represents plaintext, Mi1Represents the plaintext after polymerization;
SMiselecting a random number
Figure FDA0002654251560000049
Determining a ciphertext, the ciphertext being represented as
Figure FDA00026542515600000410
Figure FDA00026542515600000411
Wherein, ciRepresentation SMiGenerated ciphertext, g1，g2，...，gwA group of generating elements generated by the service center are represented, and N represents one element of the public key;
determining SMiFor message miSignature σ ofi，σi＝(Ui，Vi)，
SMiRandom selection
Figure FDA00026542515600000412
Determining a signature Ui＝riP；
Calculate hi＝H2(mi，IDi，Ti)
And T ═ H3(Ppub)
Calculating Vi＝riT+hidID
Wherein, TiIndicates the current timestamp, hiAnd T represents an intermediate variable, PpubA public key representing the system is shown,
SMiwill { c }i，σi，Ti，IDiIt is sent to the edge node.
4. The lightweight privacy protection multidimensional data aggregation method based on edge computing as claimed in claim 1, wherein: said verifying the validity of the n signatures if and only if the following n equations are true, the validity of the n signatures;
e(P，Vi)＝e(Ui，T)e(hiQi，Ppub) (1≤i≤n)
hi＝H2(mi，IDi)
T＝H3(Ppub)
wherein P is a group G1One generator of, ViRepresenting part of a digital signature, UiDenotes the intermediate variable, hiAnd T represents an intermediate variable, QiRepresenting a public key, PpubPublic key, m, representing the systemiRepresenting the plaintext, ID, after aggregationiRepresenting the identity of the internet of things device;
the aggregate signature σiThe method comprises the following steps:
Figure FDA0002654251560000051
get
Figure FDA0002654251560000052
And
Figure FDA0002654251560000053
wherein, cjRepresenting ciphertext generated by an edge node, ciRepresenting a ciphertext generated by the intelligent ammeter; g1，g2，...，gwRepresenting a set of generators generated by a service centre, N representing an element of a public key, a1，a2，...，awRepresenting a set of super-increment sequences.
Determining edge node aggregate signatures σj，
Figure FDA0002654251560000054
And
Figure FDA0002654251560000055
n represents the number of users, and the aggregation signature sigma of n users is obtainedj(U, V), the edge node will { c }j，σj，Tj，IDjIt is sent to the service center.
5. The lightweight privacy protection multidimensional data aggregation method based on edge computing as claimed in claim 1, wherein: the method further comprises data reading and analysis, and when analyzing the data obtained by the service center, the service provider can perform one-way analysis of variance (ANOVA) on the usage data of the user, and check whether the change of a certain factor affects the data usage policy of the user:
the service center needs to regenerate a group of super-increment sequences
Figure FDA0002654251560000061
Wherein the content of the first and second substances,
Figure FDA0002654251560000062
representing a super-increasing sequence, a1，a2，...，a2wRepresenting elements in a set of super-increment sequences;
wherein a is1＝1i≤(w+1)，
Figure FDA0002654251560000063
When i > (l +1), there are
Figure FDA0002654251560000064
ujRepresenting the upper limit of the jth data, and n representing the number of users;
the service center generates a group of generating elements G ═ G (G)1，g2，...，g2w) Wherein
Figure FDA0002654251560000065
The specific steps are as follows;
the service center SC sends a request for carrying out one-way variance analysis on the user data, and then the Internet of things equipment extracts data mi1，mi2…miwAnd separately calculate
Figure FDA0002654251560000066
Then the Internet of things equipment generates ciphertext
Figure FDA0002654251560000067
Where i 1,2, M, and sends these ciphertexts to the edge node
The edge node receives the ciphertexts and divides the M messages into s according to certain factorsEach group has T messages, then we represent the ciphertext of the edge node aggregation as OCj，OCjThe calculation method of (2) is as follows:
Figure FDA0002654251560000068
wherein, OCjCiphertext representing an aggregation of edge nodes, G ═ G1，g2，...，g2w) Is that the service center generates a set of generator, riRepresentation SMiRandomly selecting random numbers, wherein T represents T messages, n represents the number of users, and w represents the number of data types;
service center receiving OC from edge nodejThen it calculates it separately for the s groups
Figure FDA0002654251560000069
T denotes T messages, mjiRepresenting data extracted by the Internet of things device, we define SEIs the sum of squares, S, within the groupAIs the sum of squares between groups, we define
Figure FDA00026542515600000610
Wherein i 1,2iA timestamp representing the Internet of things equipment, T represents T messages, mjiThe data extracted by the equipment of the Internet of things can be calculated by the data service centers as follows:
Figure FDA0002654251560000071
Figure FDA0002654251560000072
Figure FDA0002654251560000073
SE＝ST-SA
wherein, TiTime stamp of the equipment of the Internet of things, a represents a group of data, and mjiData representing the extraction of Internet of things equipment, Q1，Q2Representing an intermediate variable, n representing the number of users, STDenotes the total variance, SEIs the sum of squares, S, within the groupAIs the sum of squares between groups, i ═ 1, 2., a;
substituting the corresponding data into a formula to obtain
Figure FDA0002654251560000074
Figure FDA0002654251560000075
Figure FDA0002654251560000076
Wherein S isEIs the sum of squares, S, within the groupAIs the sum of squares between groups, mjiThe data extracted by the equipment of the Internet of things is represented, F represents the mean square error, M represents the number of messages, M represents M messages, and s represents the number of the messages divided into s groups according to the demand factors of the cloud server;
from this data, the service center may perform a one-way analysis of variance to check whether a certain factor has a significant impact on the power consumption policy of the user.
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