A smart grid data aggregation method based on Lagrangian interpolation algorithm

Abstract

The present invention discloses a smart grid data aggregation method based on Lagrangian interpolation algorithm, including five entities: a data repository (DR) storing aggregated data, a user (User) downloading aggregated data from the data repository, a gateway (Gateway) aggregating messages from multiple smart meters, a smart meter (SM) and a key distribution center (KDC). In order to avoid network congestion in the data collection process in the smart grid, an aggregation protocol is used to aggregate messages from multiple smart meters into a short message. At present, the privacy problem is well solved by using a homomorphic encryption algorithm, in which multiple smart meters use the same encryption key to encrypt different messages. A new smart grid data aggregation protocol is also proposed. Since the smart grid data aggregation protocol can aggregate multiple messages into one message, it is very lightweight. The newly designed smart grid data aggregation protocol of the present invention can achieve security and efficiency goals in a smart grid environment.

Description

Technical Field

[0001] The invention relates to a smart grid data aggregation method based on a Lagrange interpolation algorithm, and belongs to the technical field of smart grid data aggregation. Background Art

[0002] In a smart grid environment, network elements of smart meters, users, and grid operators can communicate with each other for various applications, such as state estimation of distribution systems, demand side management, etc. Typically, traffic data in smart grid applications include billing data (such as active and passive consumption data) and operational data (such as power, voltage, current, outage logs and alarms, etc.).

[0003] In order to evaluate the working status of smart grid, users need to count the device status collected by multiple smart meters. In order to avoid network congestion during data collection in smart grid, an aggregation protocol is needed to aggregate messages from multiple smart meters into one short message. In addition, adversaries may track data flows and launch attacks on smart meters. Therefore, in order to avoid network congestion and data flow tracking in smart grid, a data aggregation protocol for smart grid is needed, which can aggregate multiple messages into one short message. This method reduces the number of messages transmitted through the operator network and avoids network congestion. In addition, since messages from multiple smart meters are aggregated into one short message, adversaries will no longer be able to track the data flow from smart meters.

[0004] However, since these messages may contain sensitive information of smart meters, privacy is a basic requirement for such data aggregation protocols. Meanwhile, in order to avoid tampering of the transmitted messages, data integrity is another important requirement in the data aggregation process. Currently, the privacy problem is well solved by using homomorphic encryption algorithms such as the Paillier encryption system, in which multiple smart meters encrypt different messages with the same encryption key. In this scheme, the smart meter encrypts the transmitted message with the user's public key, the gateway aggregates multiple encrypted messages into a short message without knowing the corresponding plaintext, and the user decrypts the aggregated short message to obtain the state information. However, since multiple smart meters sign different messages with different private keys, the integrity problem is more difficult to solve than the privacy problem. Since the multiple messages to be aggregated are signed with different private keys, the integrity problem is more difficult. Unfortunately, the integrity problem is very important for smart grid data aggregation protocols. If the adversary tampered with the state information contained in the data stream, the user may make wrong decisions based on the tampered data, resulting in chaos in the smart grid.

[0005] Efficiency is the second serious problem of smart grid data aggregation protocols. First, due to limited resources, smart meters are seriously concerned about the high computational and communication costs of processing data: smart meters usually process a variety of data, and in order to provide privacy and integrity protection, smart meters must run complex encryption algorithms on the collected data before sending it to the gateway, which will lead to high computational costs. Transmitting a large amount of data to the gateway will result in high communication costs. Second, since the gateway has to aggregate a large number of messages from multiple smart meters, its computational cost will be quite high. Summary of the invention

[0006] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a smart grid data aggregation method based on the Lagrange interpolation algorithm, which can achieve the integrity goal and ensure that the adversary cannot tamper with the data transmitted in this protocol.

[0007] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0008] The present invention provides a smart grid data aggregation method based on Lagrange interpolation algorithm, which is applied to a smart grid data aggregation system. The smart grid data aggregation system includes a data repository DR for storing aggregated data, a user User for downloading aggregated data from the data repository, a gateway Gateway for aggregating messages from multiple smart meters, a smart meter SM, and a key distribution center KDC;

[0009] The method includes a key distribution process and a data aggregation process, wherein:

[0010] During the key distribution process, the key distribution center runs the Lagrange interpolation algorithm to initialize the system parameters of the smart grid data aggregation protocol, and then runs the key generation algorithm to generate keys and distribute them to smart meters, gateways and users to protect subsequent data flows;

[0011] During the data aggregation process, each smart meter will send a message to the gateway. The gateway aggregates all messages into one SMS and calculates the corresponding signature from multiple signatures of the SMS. It sends the aggregated message to the data repository for storage so that users can download the aggregated message for status statistics.

[0012] Furthermore, during the key distribution process, the key distribution center initializes the system parameters of the smart grid data aggregation protocol through the key generation algorithm, including:

[0013] The key distribution center generates a group G with a random generator G and a λ-bit prime order p;

[0014] The key distribution center randomly generates two private keys sk a ,sk b ∈Z p, we get L(x)=sk a +sk b xmodp, where L(x) is the Lagrange interpolation function and p is a prime order;

[0015] The key distribution center calculates the public key and Where g is the generator of group G;

[0016] The key distribution center obtains the private key sk KDC = {sk a ,sk b} and pk KDC = {G,g,p,pk a ,pk b}.

[0017] Furthermore, during the key distribution process, the key distribution center runs a key generation algorithm to generate a public key and a private key for the gateway, including:

[0018] The key distribution center calculates the aggregate key as sk GW =sk a +sk b h(GW)∈Z p , where h:Z p →Z p is a hash function;

[0019] The key distribution center calculates the corresponding public key,

[0020] Furthermore, during the key distribution process, the key distribution center runs a key generation algorithm to generate a public key and a private key for the i-th smart meter, including:

[0021] The key distribution center calculates the signature key as sk SMi =sk a +sk b h(SM i )∈Z p , where h:Zp→Zp is a hash function;

[0022] Second, the key distribution center calculates the corresponding public key

[0023] Furthermore, during the data aggregation process, the smart meter SMi runs the homomorphic signature algorithm on the message m i Signature, including:

[0024] SM i Randomly generate r i ∈Z p ;

[0025] SM i Calculate C i1 =g ri , is the signature parameter 1;

[0026] SM i calculate g is the generator of group G, m i is the message body, sk SMi For smart electric

[0027] Table private key, which is signature parameter 2;

[0028] SM i Get the signature τ i ={C i1 , C i2}.

[0029] Furthermore, during the data aggregation process, the gateway runs a signature mechanism based on the Lagrange interpolation algorithm to aggregate the message set (η={m1,…,m t}) and the corresponding signature set (τ={τ1,…,τ t}), and aggregated from multiple smart meters, including:

[0030] The gateway aggregates the messages into

[0031] Gateway Computing and

[0032] The gateway obtains the message aggregate Ω={C1, C2} of multiple smart meters.

[0033] Furthermore, after receiving the aggregate message, the user uses the corresponding verification algorithm to verify the correctness of the aggregate signature: in is a hash function with two parameters; if the above formula holds, this algorithm returns True, otherwise, it returns False.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] (1) The smart grid data aggregation method based on the Lagrange interpolation algorithm provided by the present invention includes state information (m i ) is signed by the smart meter, then the gateway aggregates multiple messages and corresponding signatures into a short message and the corresponding short signature, finally, the user uses the public key of the key distribution center to check the integrity of the aggregated short message, so the smart grid data aggregation protocol can achieve the integrity goal. Therefore, the newly designed protocol has integrity characteristics.

[0036] (2) The smart grid data aggregation method based on the Lagrange interpolation algorithm provided by the present invention includes the state information (m1, ..., m t ) by adding multiple messages, the user can get the sum (π) contained in the aggregated short message. Since τ is the sum of messages from multiple smart meters, the newly designed protocol, the smart grid data aggregation protocol, can achieve the goal of state statistics.

[0037] (3) In the smart grid data aggregation method based on the Lagrange interpolation algorithm provided by the present invention, the smart meter and the gateway only use a few modular exponential operations to sign and aggregate multiple messages. For multiple manuscript messages from the smart meter, the user only needs to perform two bilinear pairing operations. Therefore, the smart grid data aggregation protocol can enjoy high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of a smart grid data aggregation method based on Lagrange interpolation algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0040] Example 1

[0041] This embodiment introduces a smart grid data aggregation method based on the Lagrange interpolation algorithm, including:

[0042] Applied to a smart grid data aggregation system, the smart grid data aggregation system includes a data repository DR for storing aggregated data, a user User for downloading aggregated data from the data repository, a gateway Gateway for aggregating messages from multiple smart meters, a smart meter SM, and a key distribution center KDC;

[0043] The method includes a key distribution process and a data aggregation process, wherein:

[0044] During the key distribution process, the key distribution center runs the Lagrange interpolation algorithm to initialize the system parameters of the smart grid data aggregation protocol, and then runs the key generation algorithm to generate keys and distribute them to smart meters, gateways and users to protect subsequent data flows;

[0045] During the data aggregation process, each smart meter will send a message to the gateway. The gateway aggregates all messages into one SMS and calculates the corresponding signature from multiple signatures of the SMS. It sends the aggregated message to the data repository for storage so that users can download the aggregated message for status statistics.

[0046] In addition, this paper proposes a new smart grid data aggregation protocol, which can meet all the above security and efficiency requirements. In addition, unlike the current data aggregation protocol in smart grid, the smart grid data aggregation protocol mainly focuses on the integrity problem. In order to meet all the above requirements, we will design a homomorphic signature algorithm based on Lagrange interpolation function, which allows the gateway to aggregate multiple messages signed by different private keys. Since this technology is very lightweight, the smart grid data aggregation protocol can enjoy the characteristics of high efficiency.

[0047] There are five entities in the smart grid data aggregation protocol, namely KDC, User, DR, Gateway and SMs.

[0048] To achieve the above purpose, these five entities are included in two processes, namely the key distribution process and the data aggregation process. In the key distribution process, KDC distributes key materials to users, gateways and SMs to protect messages transmitted in the subsequent data aggregation process. The main process of the present invention is briefly described as follows:

[0049] Key distribution process:

[0050] (1.1) KDC first initializes the public key and private key data set of the data aggregation system. The initialization algorithm (Initialize-Keys) is defined in the specific implementation (hereinafter the same). This algorithm is run by the key distribution center and is used to initialize the system parameters of the smart grid data aggregation protocol. It takes the security strength parameter λ as input and outputs the KDC's private key SK KDC and the corresponding KDC public key PK KDC .

[0051] (1.2) For users (UID) who want to authenticate and use aggregate messages, KDC will distribute PK KDC .

[0052] (1.3) For a gateway (GW) that aggregates messages received from multiple SMs, the KDC generates a private key SK for the gateway GW and the corresponding public key PK GW Then, KDC will (SK GW ,PK GW ,PK KDC ) to the gateway. The gateway's key generation algorithm is run by the key distribution center to generate public and private keys for the gateway. It uses the KDC's private key SK KDC 、KDC's public key PK KDC and the gateway's identity (GW) as input, and outputs the gateway's private key SK GW and the corresponding public key PK of the gateway GW .

[0053] (1.4) For the i-th smart meter (SM i ), KDC will provide SM i Generate private key SK SMi and the corresponding public key PK SMi Then, KDC will (SK SMi ,PK SMi ,PK KDC ) is assigned to the i-th smart meter. The algorithm is run by the key distribution center to generate the public key and private key for the i-th smart meter. It converts the private key SK of KDC into KDC 、KDC's public key PK KDC and the identifier SM of the i-th smart meter i As input, and output the gateway's private key SK GW and the corresponding gateway public key PK GW .

[0054] (1.5) After the initialization phase, the data center retains (SK KDC , PK KDC ), user retains PK KDC , Gateway Reserved (SK GW , PK GW , PK KDC ), SM i Reserved(SK SMi ,PK SMi ,PK KDC ).

[0055] Data aggregation process:

[0056] Assuming there are t smart meters, the data aggregation process mainly includes three steps. First, each smart meter will send a message to the gateway. Second, the gateway aggregates all messages into a text message and calculates the corresponding signature from the multiple signatures of the text message. Finally, the user will verify the aggregated message. The details of these three steps are as follows:

[0057] (2.1) In each smart meter (SM i ) sends a message to the gateway (m i ) before aggregation, it will sign the message using a signature algorithm that is defined by SM i Run, used to respond to the message m i Sign. It will sign the message (m i ), SM i The private key SK SMi , SM i The public key PK SMi 、KDC's public key PK KDC As input, and output signature (τ i).

[0058] (2.2) When receiving t message sets (η={m i , 1≤i≤t}) and the corresponding signature (τ={τ i , 1≤i≤t}), the gateway aggregates η and τ into a short message π and a short signature Ω respectively using an aggregation algorithm, which is run by the gateway to aggregate the message set (η) and the corresponding signature set (τ) from multiple smart meters. It aggregates the message set (η), the signature set (τ), and the gateway private key SK GW , Gateway public key PK GW 、KDC public key PK KDC It takes as input, and outputs the aggregate message (π) and the corresponding aggregate signature (Ω).

[0059] (2.3) After data aggregation, the gateway stores π and Ω to the data repository. The user downloads π and Ω to verify the aggregate message (π) and the corresponding signature (Ω). The verification algorithm is used. This algorithm is run by the user to verify the aggregate message π. It takes the aggregate message (π) as input, i.e., the aggregate signature (Ω), the public key PK of the KDC KDC , if the message passes the validation, it outputs True. Otherwise, it also outputs False.

[0060] (2.4) After the data aggregation process, users collect data from multiple smart meters and use a verification algorithm to check the integrity of τ, which is the status statistics of the smart grid.

[0061] See attached Figure 1 The smart grid data aggregation method based on the Lagrange interpolation algorithm provided in this embodiment includes two stages: key distribution and data aggregation. The application process specifically involves the following steps:

[0062] Step 1: In the key distribution phase, the main steps of key distribution are: KDC ,pk KDC}←Initialize-Keys(λ), the key distribution center runs this algorithm to initialize the system parameters of the smart grid data aggregation protocol, as shown below.

[0063] Step 101: The key distribution center generates a group G with a random generator G and a λ-bit prime order p.

[0064] Step 102: Next, the key distribution center randomly generates two private keys sk a ,sk b ∈Z p , we get L(x)=sk a +sk b xmodp, where L(x) is the Lagrange interpolation function and p is the prime order;

[0065] Step 103: Key Distribution Center Calculation and

[0066] Step 104: The key distribution center obtains sk KDC = {sk a ,sk b} and pk KDC = {G,g,p,pk a ,pk b}.

[0067] Step 2: In the key distribution phase, the main steps of key distribution are:

[0068] {sk GW ,pk GW}←Key_DistributionGW(sk KDC ,pk KDC ,GW), the key distribution center runs this algorithm to generate public and private keys for the gateway, as shown below.

[0069] Step 201: The key distribution center calculates the aggregate key as sk GW =sk a +sk b h(GW)∈Z p , where h:Zp→Zp is a hash function.

[0070] Step 202: The key distribution center calculates the corresponding public key.

[0071] Step 3: In the key distribution phase, the main steps of key distribution are:

[0072] {sk SMi ,pk SMi}←Key_DistributionSM(sk KDC ,pk KDC ,SM i ). The key distribution center runs this algorithm to generate public and private keys for the i-th smart meter.

[0073] Step 301: The key distribution center calculates the signature key as sk SMi =sk a +sk b h(SM i )∈Z p , where h:Zp→Zp is a hash function.

[0074] Step 302: Next, the key distribution center calculates the corresponding public key

[0075] Step 4: In the data aggregation stage, the main steps of data aggregation are:

[0076] {τ i}←Sign(m i ,sk SMi ,pk SMi ,pk KDC ), SMi runs this algorithm to sign and encrypt message mi as shown below.

[0077] Step 401: First, SM i Randomly generate r i ∈Z p .

[0078] Step 402: Next, SM i Calculate C i1 =g ri , is signature parameter 1.

[0079] Step 403: Third, SM i calculate g is the generator of group G, m i is the message body, sk SMi is the private key of the smart meter, is the signature parameter 2

[0080] Step 404: Finally, SM i Get the signature τ i ={C i1 , C i2}.

[0081] Step 5: In the data aggregation stage, the main steps of data aggregation are:

[0082] {π,Ω}←Aggregation(η,τ,sk GW ,pk GW ,pk KDC ), the gateway runs this algorithm to aggregate the message set (η={m1,…,m t}) and the corresponding signature set (τ={τ1,…,τ t}) and aggregated from multiple smart meters as shown below.

[0083] Step 501: First, the gateway aggregates the message into

[0084] Step 502: Next, the gateway calculates and

[0085] Step 503: Finally, the gateway obtains the message aggregate Ω={C1, C2} of multiple smart meters.

[0086] Step 6: In the data verification stage, the main steps of data verification are:

[0087] {True,False}←Verify_Message(π,Ω,pk KDC ), users run this algorithm to verify the aggregated message in is a hash function with two parameters. If the above formula holds, then this algorithm returns True. Otherwise, it returns False.

[0088] Compared with the prior art, in the context of 5G networks, the present invention has the following advantages:

[0089] First, in the above system model, the state information (m i ) is signed by the smart meter. Then, the gateway aggregates multiple messages and corresponding signatures into a short message and the corresponding short signature. Finally, the user uses the public key of the key distribution center to check the integrity of the aggregated short message. Therefore, the smart grid data aggregation protocol can achieve the integrity goal. Therefore, the newly designed protocol smart grid data aggregation protocol has integrity characteristics.

[0090] Second, in the above system model, the gateway will contain state information (m1, ..., m t ) by adding multiple messages, the user can get the sum (π) contained in the aggregated short message. Since τ is the sum of messages from multiple smart meters, the newly designed protocol, the smart grid data aggregation protocol, can achieve the goal of state statistics.

[0091] Third, in the above system model, smart meters and gateways only use a few modular exponential operations to sign and aggregate multiple messages. For multiple manuscript messages from smart meters, users only need to perform two bilinear pairing operations. Therefore, the smart grid data aggregation protocol can enjoy high efficiency.

[0092] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A smart grid data aggregation method based on Lagrange interpolation algorithm, characterized in that: Applied to a smart grid data aggregation system, the smart grid data aggregation system includes a data repository DR for storing aggregated data, a user User for downloading aggregated data from the data repository, a gateway Gateway for aggregating messages from multiple smart meters, a smart meter SM, and a key distribution center KDC; The method includes a key distribution process and a data aggregation process, wherein: During the key distribution process, the key distribution center runs the Lagrange interpolation algorithm to initialize the system parameters of the smart grid data aggregation protocol, and then runs the key generation algorithm to generate keys and distribute them to smart meters, gateways and users to protect subsequent data flows; During the data aggregation process, each smart meter will send a message to the gateway. The gateway aggregates all messages into one short message, calculates the corresponding signature from multiple signatures of the short message, and sends the aggregated message to the data repository for storage, so that users can download the aggregated message for status statistics. During the key distribution process, the key distribution center initializes the system parameters of the smart grid data aggregation protocol through the key generation algorithm, including: The key distribution center generates a group G with a random generator G and a λ-bit prime order p; The key distribution center randomly generates two private keys sk a ,sk b ∈Z p , we get L(x)=sk a +sk b xmodp, where L(x) is the Lagrange interpolation function, p is a prime number, and Z p represents a positive integer less than p, sk a ,sk b are the coefficients of the Lagrange interpolation function, all of which are positive integers less than p; The key distribution center calculates the public key and , where g is the generator of group G, pk a and pk b are all elements of group G; The key distribution center obtains the private key sk KDC = {sk a ,sk b } and pk KDC = {G,g,p,pk a ,pk b }; During the key distribution process, the key distribution center runs the key generation algorithm to generate public and private keys for the gateway, including: The key distribution center calculates the aggregate key as sk GW =sk a +sk b h(GW)∈Z p , where h:Z p →Z p is a hash function, GW is the gateway identifier; The key distribution center calculates the corresponding public key, During the key distribution process, the key distribution center runs the key generation algorithm to generate a public key and a private key for the i-th smart meter, including: The key distribution center calculates the signature key as sk SMi =sk a +sk b h(SM i )∈Z p , where h:Zp→Zp is a hash function; Second, the key distribution center calculates the corresponding public key In the data aggregation process, the smart meter SMi runs the homomorphic signature algorithm to sign the message m i Signature, including: SM i Randomly generate r i ∈Z p ; SM i Calculate C i1 =g ri , is the signature parameter 1; SM i calculate g is the generator of group G, m i is the message body, sk SMi is the private key of the smart meter, which is the signature parameter 2; SM i Get the signature τ i ={C i1 , C i2 }; In the data aggregation process, the gateway runs a signature mechanism based on the Lagrange interpolation algorithm to aggregate the message set (η = {m1, ..., m t }) and the corresponding signature set (τ={τ1,…,τ t }), and aggregated from multiple smart meters, including: The gateway aggregates the messages into Gateway Computing and The gateway obtains the message aggregate Ω={C1, C2} of multiple smart meters.

2. The smart grid data aggregation method based on Lagrange interpolation algorithm according to claim 1 is characterized in that: After receiving the aggregate message, the user uses the corresponding verification algorithm to verify the correctness of the aggregate signature: in is a hash function with two parameters; if the above formula holds, this algorithm returns True, otherwise, it returns False.

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