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Cloud Encrypted Data Retrieval Algorithm Based on Root Index Distance

In the data-as-a-service model of cloud computing, data of users is stored on servers in the cloud which provides services such as data storage and management. And this form of data management may reduce data security due to security threats to the cloud servers. The full homomorphic encryption data indexing algorithm (HEDR) can effectively solve the data security in the cloud computing environment, but with the increase of data volume, the retrieval efficiency and the accuracy of retrieval results of HEDR will be seriously affected. In this paper, aiming at solving the problem of HEDR, a root index distance (RID) based on the root index distance is proposed. By encrypting and processing the root index, the depth of the index is reduced in the case of irrelevant data volume. This reduces the impact of noise and improves the accuracy of data encryption index results. Finally, the analysis shows that the complexity of the RID algorithm does not increase, while the data security is significantly improved.

encryption greatly increases the user's ability to quickly retrieve data from the cloud [2] [3] . The time and resource consumption, especially if the data volume increases. Therefore, how to effectively encrypt data without increasing excessive search burden becomes another focus of current cloud security research. On the basis of full homomorphic encrypted data indexes, this paper proposes a root index distance (RID) index algorithm based on the root index distance. By encrypting the root index, the depth of the index is reduced and the noise is reduced. The impact of this improves the accuracy of the data encryption index results and is independent of the amount of data. Finally, through analysis, it is proved that the RID algorithm greatly improves the data security without increasing the complexity.

Cloud Encrypted Data Retrieval
In the past, telecommunications networks were often represented by clouds in the diagram, and later used to represent the abstraction of the Internet and underlying infrastructure. Therefore, cloud computing can even allow you to experience 10 trillion operations per second. With such a powerful computing capability, you can simulate a nuclear explosion, predict climate change and market trends. Users access the data center through computers, laptops, and mobile phones, and perform operations according to their own needs. There are many claims about the definition of cloud computing. For what exactly is cloud computing, at least 100 explanations can be found. It is widely accepted that the National Institute of Standards and Technology (NIST) defines: Cloud computing is a pay-per-use model that provides available, convenient, on-demand network access. Configurable computing resource sharing pool (resources include network, server, storage, application software, service and so on), these resources can be provided quickly, with little management effort or little interaction with the service provider. Cloud computing includes the following levels of services: Infrastructure as a Service (IaaS), Platform as a Service (PaaS) and Software as a Service (SaaS). This paper analyzes the data security issues of cloud computing systems and mainly considers the data security in the database as a data storage service (DAS) model. In the DAS model, the enterprise outsources data to the cloud service provider for management. The cloud service provider performs storage management and security management of the data, processes the data request of the user, and returns the data required by the user to the user. In order to ensure the security of data, the user encrypts the data and stores it in the cloud server provided by the supplier. When the user needs to query the data, the user needs to send the query condition and request to the cloud server, and then the cloud server pairs the stored encrypted data.
When the encryption algorithm is too complex, the retrieval speed drops quickly and resources are consumed too much. When the encryption algorithm is too simple, although the retrieval and processing speed is improved, the security of the data is seriously reduced. At present, some experts and scholars have begun to study the issue of retrieval of encrypted data. Song et al. proposed a linear retrieval scheme [4] to perform encrypted information retrieval in a one-time method. This method is highly secure, but there is a slow retrieval speed when searching for massive data in cloud services. Problem; Swaminathan proposed a sorting search algorithm [5] , but it does not apply to a query that contains multiple query conditions; the public key encryption search algorithm proposed by Boneh et al. is a kind of security index algorithm based on Boolean model [6] , and it cannot sort according to the query conditions and the relevance of the data to be retrieved.

Homomorphism Encryption Data Retrieval
Full homomorphic encryption is also known as privacy homomorphism [7] which is referred to as HEDR. It is an encrypted form that allows the user to perform operations on the encrypted data, and the result of the operation is also encrypted. This result is consistent with encrypting the result obtained by performing the same operation in plaintext. This cannot only guarantee the security and privacy of data, but also improve the efficiency of data processing. Therefore, full homomorphic encryption is considered to be the best way to solve cloud computing encrypted data retrieval [8] [9] . The fully homomorphic encrypted data retrieval algorithm considers both the user side and the cloud service provider. The user encrypts the search condition and then transmits it to the cloud service provider. The cloud service provider uses the homomorphic property to perform the user encrypted index condition. Operation, and send the encrypted result file to the user, and the user to decrypt the obtained encrypted file. During the entire data transmission process, the cloud service provider or the third party does not know the real data of the user, and thus can better protect the security of the user data. The definition of the full homomorphic encryption system is as follows: Let where Gen denotes a key generation algorithm for generating a public key and a private key in an encryption system; Enc denotes a data encryption algorithm; Dec denotes a data decryption algorithm. Let the plaintext space in the encryption system be M , and the cipher text space be C , the full homomorphic encryption system satisfies the following properties: Where, 1 f and 2 f denote functions that operate on the cipher text space C , " + " and " •" denote addition and multiplication operations for the plaintext space group respectively, and , a b M ∈ . Data encryption using HEDR generates a superimposable noise 0 r R ∈ in a relatively small random space 0 R . To be able to decrypt the encrypted cipher text correctly, the noise must belong to a large random space 1 R , and 0 1 pk pk pk Enc a r Enc a r Enc a a r r pk pk pk Enc a r Enc a r Enc a a r r As shown in Equation (3) and Equation (4), since the introduced noise can be superimposable and unrestricted growth, then the range of " + " and " • " must be controlled to avoid excessive noise.
In the cloud computing environment, although the HEDR algorithm is more suitable for cloud computing environment, it has the following two defects: 1) The amount of data in the cloud computing environment is huge, so the number of bits generated when indexing data blocks under this environment will also become larger and larger, eventually leading to excessive data index overhead, making the efficiency of encrypted data indexes.
2) As the amount of data increases, the HEDR algorithm will generate errors due to the presence of noise. When the cumulative error exceeds a certain threshold, the final result will become deviant or even wrong, so the amount of data to be encrypted and the noise must be controlled.

Principle
For the characteristics of encrypted data retrieval in cloud environment, in order to avoid the defects of the above HEDR algorithm, a search algorithm RID based on the root index distance is proposed. The specific principles are as follows: When the user queries the cloud server for the encrypted data file, it first calculates the index of the encrypted root, and the distance between other index files and the index root, and sends the whole to the cloud server; the cloud server calculates the user data query condition according to the encryption property. The corresponding root index value, combined with the data transmitted by the user, to obtain the corresponding encrypted data block stored in the cloud computing end for the index value corresponding to the final ciphertext data; the client uses the private key to encrypt the data block returned by the cloud server. Decrypt and recover the plaintext file. During the entire process, because the data is encrypted, the server cannot know the user's query condition information, nor can it directly contact the user's original data file stored on the cloud, ensuring data security.

Implementation
Assume that the user's file data block size is n , the cloud server side stores the data block is , the user establishes the data index is , according to the data index classification, establishes the directory tree , and calculates the root index distance j l . When the user performs data query, the public key encrypted by the data, the index of the root directory of the query, and the distance of the index j l from the root index are sent to the cloud server. Enc d and obtain the final plaintext x d . The RID algorithm execution process can be divided into three steps as shown in Figure 1, the specific process is as follows: Step 1: A module is generated through the key algorithm Gen , the user generates the public and private key pairs ( ) , pk sk , and the root index in the file data block. The root index will be encrypted : When the user submits a data query request to the cloud server, the public key pk , the encrypted root index k x , and the index of the other file are sent together with the distance ( ) 0 1 j i n l ≤ ≤ − from the root node to the cloud server.
Step 2: After the cloud server receives the search condition ( ) , , k j pk a l from the user query data, the public key pk is used to perform the following operations for k x : For ( ) where, j e satisfies the formula (5). According to the properties of additive homomorphism, we will have: Enc d using the private key he holds, and finally obtains the required data. During the entire process, the data and retrieval information stored in the cloud server and in the transmission process are all in cipher text. The cloud server and other third parties cannot obtain real user plaintext information, effectively reducing the noise impact of the retrieval data and ensuring the data security in a cloud server environment.

RID algorithm analysis
When retrieving the data in the cloud system, the retrieval conditions are passed to the cloud server, but the retrieval of the plaintext will leak the user's data privacy, and the retrieval of the cipher text will increase the resource cost of the server and affect the accuracy of the retrieved data. The following section analyzes the RID algorithm from the aspects of security and algorithm performance.

Security Analysis
Before analyzing the security of the RID algorithm, it is assumed that the full homomorphic encryption algorithm running on the cloud server is correct, and the plaintext attack can be selected. The user and the cloud server are all honest, and the user and the cloud server will not actively divulge the keys that are in hand and perform the operations strictly in accordance with the algorithm's flow.
In the RID algorithm, its security is based on the correctness of the calculation of , although it will increase the computational load of the cloud server due to the noise reduction operation, it does not affect the accuracy of the data encryption result. Therefore, the RID algorithm retains the security of the HEDR encryption algorithm in response to the plaintext attack, and at the same time, encrypts the root index, reduces the depth of the index, reduces the impact of noise, and improves the accuracy of the data encryption index result.

Performance Analysis
When a user initiates a retrieval request for data from a cloud server, there are operations such as encryption and decryption on the local server. Similarly, there are calculation requirements on the server side. The performance of the RID algorithm is considered from both the server side and the client side.
1) Client complexity: The amount of computation required by the client is that encrypting the root index therefore, the server-side computational complexity is ( ) log O n n . We can see that, RID algorithm increases the security of data flow without increasing the complexity of the algorithm.

Conclusion
For the special environment of cloud computing, this paper proposes a cloud-encrypted data retrieval algorithm RID based on the root index distance. Through the comprehensive analysis of the performance of RID algorithm, it shows that this RID algorithm did not increase the complexity, effectively eliminated the influence of noise and improved the security of data retrieval. The RID algorithm has very important significance for the retrieval of massive cloud-encrypted data. In the follow-up further research, the security of the algorithm in the event of a plaintext attack will be studied.