CN114024685A - Data aggregation method based on ElGamal cryptosystem and Mercker hash tree - Google Patents

Data aggregation method based on ElGamal cryptosystem and Mercker hash tree Download PDF

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CN114024685A
CN114024685A CN202111190170.7A CN202111190170A CN114024685A CN 114024685 A CN114024685 A CN 114024685A CN 202111190170 A CN202111190170 A CN 202111190170A CN 114024685 A CN114024685 A CN 114024685A
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ciphertext
hash tree
aggregation
control center
mercker
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黄方蕾
胡麦芳
张珂杰
乔沛杨
张帅
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Hangzhou Qulian Technology Co Ltd
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Hangzhou Qulian Technology Co Ltd
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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
    • H04L9/3236—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
    • 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
    • H04L63/0442—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 asymmetric encryption, i.e. different keys for encryption and decryption
    • 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
    • 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
    • H04L9/0819—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s)
    • H04L9/0825—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s) using asymmetric-key encryption or public key infrastructure [PKI], e.g. key signature or public key certificates
    • 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
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords

Abstract

The invention discloses a data aggregation method based on an ElGamal cryptosystem and a Mercker hash tree. The control center generates a public and private key pair for encryption by utilizing an ElGamal cryptosystem; each user calculates a ciphertext for the multi-dimensional electricity consumption information by using the super-incremental sequence, calculates a hash value by using a Mercker hash tree, and sends the hash value to a fog node; after receiving the encrypted user electricity utilization information, the fog node performs batch verification by using the Mercker hash tree, generates an aggregation ciphertext and sends the aggregation ciphertext to the control center; and after receiving the aggregation ciphertext, the control center decrypts the aggregation ciphertext to finally obtain an aggregation result of the power consumption information of each dimension. The invention utilizes the Mercker hash tree to carry out batch verification of data, the fog node realizes verification according to the comparison of the hash values of all users and the root node of the Mercker hash tree, and heavy double-line type pairing operation is not needed, thereby saving the calculation expense.

Description

Data aggregation method based on ElGamal cryptosystem and Mercker hash tree
Technical Field
The invention belongs to the field of information security technology and smart grid privacy protection data aggregation, and particularly relates to a data aggregation method based on an ElGamal cryptosystem and a Mercker hash tree.
Background
The internet of things (IoT) has brought various ubiquitous service evolutions that are expected to advance in various fields such as medical, logistics, and smart grid. The internet of things (IoT) has become an important component of smart grid systems.
Due to limitations in communication, such as power, storage, computing power of sensors, etc., data aggregation techniques are employed in the internet of things (IoT) to reduce communication overhead for real-time data transmission.
However, due to the large amount of sensitive electricity data transmitted in the smart grid, data security and data privacy as well as data aggregation efficiency are a major issue. In addition, the traditional data aggregation technology using the ElGamal cryptosystem does not support multidimensional data aggregation, and the digital signature technology needs a large amount of calculation overhead. Therefore, it is important to invent an efficient method that supports multidimensional data aggregation and has low computational and communication overhead.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a data aggregation method based on an ElGamal cryptosystem and a Merckel hash tree. The technical scheme adopted by the invention is as follows: the control center generates a public and private key pair for encryption by utilizing an ElGamal cryptosystem; each user calculates a ciphertext for the multi-dimensional electricity consumption information by using the super-incremental sequence, calculates a hash value by using a Mercker hash tree, and sends the hash value to a fog node; after receiving the encrypted user electricity utilization information, the fog node performs batch verification by using the Mercker hash tree, generates an aggregation ciphertext and sends the aggregation ciphertext to the control center; and after receiving the aggregation ciphertext, the control center decrypts the aggregation ciphertext to finally obtain an aggregation result of the power consumption information of each dimension.
The method comprises the following steps:
step one, an initialization stage:
control center utilizationThe ElGamal cryptosystem generates a public and private key pair: based on the security parameter λ, a tuple gk ═ (p, g) is generated1,g2,G,GTE, H); then generating a super-increment sequence a1,a2,...,al(ii) a Randomly selecting variable u per useri∈ZpThen the control center generates a group of public and private key pairs by a key generation algorithm
Figure BDA0003300233450000011
For encryption;
wherein, GTIs a group of two multiplication cycles, g1,g2Are respectively two multiplication cycle groups G, GTIs g, p is1,g2E is G × G → GTH is a one-way hash function H: {0,1}*→G；ZpRepresents an integer from 0 to p-1;
Figure BDA0003300233450000021
is to calculate the public key of the ciphertext,
Figure BDA0003300233450000022
is the private key of the computed ciphertext;
step two, ciphertext generation stage:
the multidimensional power consumption information of each user is represented as di1,di2,...,dilRandomly choosing the variable ri∈ZpAnd calculating a ciphertext:
Figure BDA0003300233450000023
wherein, C1、C2Two ciphertexts; m isi＝a1·di1+a2·di2+...+al·dil；
Each user calculates a hash value according to the merkel hash tree:
li＝H(CTi||TS)
each user will encrypt and signCTi||TS||liSending the data to a fog node;
wherein TS is the current timestamp;
step three, ciphertext aggregation stage:
when the fog node receives the CT of n usersi||TS||liSecondly, verifying the integrity of the data in batches by using a Mercker hash tree;
and then, carrying out ciphertext aggregation to generate an aggregated ciphertext:
Figure BDA0003300233450000024
then sending the aggregation ciphertext and the aggregation signature CT to a control center;
step four, the control center decrypts the stage:
after the control center receives the CT sent by the fog node, the control center utilizes a private key
Figure BDA0003300233450000025
And (3) carrying out decryption calculation on the aggregate ciphertext CT:
Figure BDA0003300233450000026
wherein the content of the first and second substances,
Figure BDA0003300233450000031
according to super-increment sequence a1,a2,...,alObtaining the aggregation result of the power consumption information of each dimension
Figure BDA0003300233450000032
Further, in step two, the hash value l calculated by each useriStored on leaf nodes of the merkel hash tree.
Further, in the third step, the batch verification of data integrity specifically includes: the fog node can be based on all usersHash value liAnd comparing with the root node of the Mercker hash tree, and if the root node of the Mercker hash tree is equal, indicating that the verification is successful.
Compared with the prior art, the invention has the beneficial effects that:
the invention utilizes the Mercker hash tree to carry out batch verification of data, the fog node can realize verification by comparing the hash values of all users with the root node of the Mercker hash tree, and heavy double-line type pairing operation is not needed, thereby saving the calculation expense.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The technical contents of the present invention will be further explained with reference to the accompanying drawings.
As shown in fig. 1, the data aggregation method based on ElGamal cryptosystem and merkel hash tree includes the following steps:
1. initialization phase
In the initialization phase, the control center can boot the entire system. The ElGamal cryptosystem is utilized to generate public-private key pairs. And the public and private key pair is used for encryption generation.
Based on the security parameter λ, a tuple gk ═ (p, g) is generated1,g2,G,GTE, H), then a super-increment sequence a is generated1,a2,...,al. Wherein G, GTIs a group of two multiplication cycles, g1,g2Are respectively the generator of two multiplication cycle groups, p is g1,g2E is G × G → GTH is a one-way hash function H: {0,1}*→G。
User for each useriRandomly selecting a variable ui∈Zp，ZpRepresents an integer from 0 to p-1. Then generating a group of public and private key pairs by a key generation algorithm
Figure BDA0003300233450000041
For encryption.
2. Ciphertext generation stage
User for each useriExpressed as di1,di2,...,dilRandomly choosing the variable ri∈Zp，ZpRepresents an integer from 0 to p-1, and computes a ciphertext CTi＝(C1,C2)：
Figure BDA0003300233450000042
Wherein, C1 and C2 are two ciphertexts, m isi＝a1·di1+a2·di2+...+al·dil。
User for each useriThe hash value is calculated according to the merkel hash tree:
li＝H(CTi||TS)
the hash value liStored on leaf nodes of the merkel hash tree. Where TS is the current timestamp, it can resist message replay attacks.
We can use the Mercker hash tree to perform batch verification, and each user usesiTo encrypt data and hash value CTi||TS||liAnd sending the data to the fog node.
3. Aggregate ciphertext generation stage
When the fog node receives the CT of n usersi||TS||liThereafter, verification checking of the integrity of the data is first performed. Batch verification can be carried out by utilizing the Mercker hash tree, and the fog nodes can be verified according to the hash values l of all usersiAnd comparing with the root node of the Mercker hash tree, and if the root node of the Mercker hash tree is equal, indicating that the verification is successful. No heavy two-wire type pairing operation is required, thus saving computational overhead.
And then, carrying out ciphertext aggregation to generate an aggregated ciphertext:
Figure BDA0003300233450000043
and then the aggregate ciphertext CT is sent to the control center.
4. Control center side decryption stage
After the control center receives the aggregated ciphertext CT sent by the fog node, the control center utilizes a private key
Figure BDA0003300233450000051
And (3) carrying out decryption calculation on the aggregate ciphertext CT:
Figure BDA0003300233450000052
wherein the content of the first and second substances,
Figure BDA0003300233450000053
aggregated electricity usage data can thus be obtained. Then obtaining the poly of each dimension according to the super-increasing sequence
Result of synthesis
Figure BDA0003300233450000054

Claims (3)

1. A data aggregation method based on an ElGamal cryptosystem and a Merckel hash tree is characterized by comprising the following steps:
step one, an initialization stage:
the control center generates a public and private key pair by utilizing an ElGamal cryptosystem: based on the security parameter λ, a tuple gk ═ (p, g) is generated1,g2,G,GTE, H); then generating a super-increment sequence a1,a2,...,al(ii) a Randomly selecting variable u per useri∈ZpThen the control center generates a group of public and private key pairs by a key generation algorithm
Figure FDA0003300233440000011
For encryption;
wherein, GTIs a group of two multiplication cycles, g1,g2Are respectively two multiplication cycle groups G, GTIs g, p is1,g2E is G × G →GTH is a one-way hash function H: {0,1}*→G；ZpRepresents an integer from 0 to p-1;
Figure FDA0003300233440000012
is to calculate the public key of the ciphertext,
Figure FDA0003300233440000013
is the private key of the computed ciphertext;
step two, ciphertext generation stage:
the multidimensional power consumption information of each user is represented as di1,di2,...,dilRandomly choosing the variable ri∈ZpAnd calculating a ciphertext:
Figure FDA0003300233440000014
wherein, C1、C2Two ciphertexts; m isi＝a1·di1+a2·di2+...+al·dil；
Each user calculates a hash value according to the merkel hash tree:
li＝H(CTi||TS)
each user will encrypt and sign CTi||TS||liSending the data to a fog node;
wherein TS is the current timestamp;
step three, ciphertext aggregation stage:
when the fog node receives the CT of n usersi||TS||liSecondly, verifying the integrity of the data in batches by using a Mercker hash tree;
and then, carrying out ciphertext aggregation to generate an aggregated ciphertext:
Figure FDA0003300233440000021
then sending the aggregation ciphertext and the aggregation signature CT to a control center;
step four, the control center decrypts the stage:
after the control center receives the CT sent by the fog node, the control center utilizes a private key
Figure FDA0003300233440000022
And (3) carrying out decryption calculation on the aggregate ciphertext CT:
Figure FDA0003300233440000023
wherein the content of the first and second substances,
Figure FDA0003300233440000024
according to super-increment sequence a1,a2,...,alObtaining the aggregation result of the power consumption information of each dimension
Figure FDA0003300233440000025
2. The data aggregation method based on the ElGamal cryptosystem and the Mercker hash tree according to claim 1, wherein:
in step two, the hash value l calculated by each useriStored on leaf nodes of the merkel hash tree.
3. The data aggregation method based on the ElGamal cryptosystem and the Mercker hash tree according to claim 1, wherein:
in the third step, the batch verification of the data integrity specifically includes: the fog node can be based on the hash values l of all usersiAnd comparing with the root node of the Mercker hash tree, and if the root node of the Mercker hash tree is equal, indicating that the verification is successful.
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