A SURVEY OF HOMOMORPHIC ENCRYPTION OF DATA IN CLOUD FOR SECURE STORAGE

demonstrate how to develop and choose TVF to optimize the evaluation of consequences of different in a single bootstrapping call in this paper. They examining the configuration of FHEW-based bootstrapping algorithms and comparing the noise overhead performance and modularity.

Partially Homomorphic encryption (PHE) allows to select only the functions of mathematical which can be observed on encrypted values. Ie, only one operation either addition of multiplication which can be performed an multiple number of times on the ciphertext [8]. PHE with multiplicative operation is the basement of RSA algorithm, and it is used to authorize safe connection through SSL/TLS.
A Somewhat Homomorphic Encryption is one which can supports either addition or multiplication, and these operations can be performed a number of times.

Fully Homomorphic Encryption (FHE):
The functionality is more with isolation to carry information secure and available at the time of same . This is accomplished by using both addition and multiplication many number of times and looks secure multi-party calculation by more energetic. It can grasp irresponsible calculations on our ciphertext.

Related Work
Homomorphic encryption is the modification of data into cipher text. Without modifying the encryption, homomorphic encryptions allow complex mathematical functions to be achieved on the date after encryption. The aim of homomorphic encryption is to enable computing of encrypted data. Data may also stay private as it is being processed, allowing valuable activities to be drifting out with data existing in unauthenticated environments.

Researchers
Year . The handling of ciphertext data under privacy protection is made possible by homomorphic encryption technologies. It will retrieve, measure, and amount ciphertext directly in the cloud and return the results to users as ciphertext. This technology, unlike conventional encryption algorithms, does not require regular encryption and decryption between the cloud and consumers, lowering connectivity and processing costs. It was the most important technology for ensuring data protection in cloud environments. Main security problems in cloud systems can be addressed thanks to the homomorphic features of the technology, and cloud infrastructure can further accelerate the advancement of homomorphic encryption technology.
In 2020 Elmahdi, E., et.al [2] proposed through distributing the pieces of the whole message into different paths and using a HE mechanism for cryptography, an expanded AOMDV method to make data transfer safe and stable in the presence of malicious nodes in MANETs. The simulation findings reveal that the scheme has a higher packet distribution ratio and throughput, all of which are desirable characteristics for emergency applications in MANETs.

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In 2019 Ullah, et.al, [3] has been proposed a novel kernel homomorphic encryption scheme. The rate of development of sounds, glitches, and computation in the electronic world and cloud computing was growing day by day. The entire negotiation mechanism crashed after the number of noises was surpassed. They add a novel kernel HE schemes to reduce the development of noises and computation. By using kernel and kernel homomorphism, the Ker-HE scheme was used to remove the number of noises. These functions were used to prevent the ciphertext from being too long during decryption and to eliminate any noise or errors.
An effective secluded database inquiry by means of ring-LWE SHE was developed by Saha, et.al [4]. The decryption's ability to retrieve the unique result from the ciphertext determines the consistency of an encryption technique. The correctness of HE schemes was determined by recovering the unique consequence since the ciphertext via authentication after some homomorphic operations.
In 2017 Kim, et.al [5] proposed a modern HE-based stable kNN query processing algorithm They ensure that all encrypted data and user question information are kept private. They also devised an encrypted index method based that executes data filtering without exposing data access patterns in order to obtain high query system throughput.
The scheme outperforms the current scheme in terms of query processing costs while maintaining user anonymity, according to a results report.
In 2020 Li, Jing, et.al. [6] has been proposed establish the homomorphism operations in ciphertext space and propose a novel HE scheme over non-abelian rings. Based on the Conjugacy Search Issue, the scheme can achieve one-way protection. It directly involving authentication using the homomorphism of a 2-order distortion matrix coding function, allowing for a simple homomorphic comparison of ciphertexts against the need to decode any intermediate results.
In 2016 Wang, Xiaofen [7] proposed a one-round meeting position calculation protocol in which the location service provider consults with a semi-trusted cloud server that serves as a computing hub and performs the majority of the calculations. The computing hub, the meeting venue determination server, and participants all protected user location privacy from external and internal attackers. They use smartphones to measure the protocol's mathematical efficiency in order to research its efficiency. The simulation findings, as well as a performance analysis of their protocol to another protocol with similar functionalities, show that their solution was more effective and realistic.
In 2017 Vengadapurvaja, A.M. et.al [8] proposed the effective HE algorithm for encrypting medical images and performing useful operations on them while maintaining confidentiality. Electronic health reports were the safest way to keep track of a patient's records in order to increase the continuity of care. An electronic health record (EHR) was a multimedia record of a patient's medical information. The electronic health record allows us to keep track of a vast variety of records and makes it simple to optimize all facets of patient care, including quality and accurate record updates.
In 2017 Zhang, et.al [9] has developed a generic mechanism for creating a stable cloud storage protocol based on the HE scheme They were the first to investigate the intrinsic relationship between secure cloud storage and HE schemes, and present a Generic way to construct a Secure Cloud Storage protocol, denoted as G-SCS, that can be used for any HE scheme (HES). Under a concept that satisfies the security prerequisite of cloud storage, the proposed G-SCS was stable.
A Secure multi-label data classification over encrypted data has been developed by Liu, et.al [10]. Their approach offloads the multi-label sorting challenge to cloud servers, greatly reducing the storage and computing demands on data owners and customers. Their results can protect the privacy information of data owners and users, cloud servers cannot learn anything valuable about the input data, and multi-label marking effects can be output, according to theoretical proof.
Privacy preserving distributed optimization using homomorphic encryption has been developed by Lu, Y., and Zhu, M [11]. They investigate how a computer operator and a group of agents execute a hierarchical gradient-based algorithm while remaining anonymous. In the one hand, each agent's state and feasible set were private to it and should not be known to any other agent or the system operator; on the other hand, each agent and the data provider owned a set of private functions of the component functions, and each coefficient should not be disclosed to any person who did not initially own it.

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Confidentiality maintaining AI-based formulation approach in edge networks utilizing fully homomorphic encryption was developed by Rahman, M. S., et.al [12]. They implement an AI-based formulation method for edge services in the network edge. They also provide a private information AI task scheduling architecture that uses the fully homomorphic encryption (FHE) algorithm to compose encrypted QoS files. They use a simulated QoS dataset to test the efficiency of their privacy-preserving service composition system in many experiments.
Chillotti, I [13], have implemented faster compressed homomorphic procedures and effective circuit bootstrapping. They introduce several methods for improving homomorphic function evaluation, both for totally and leveled homomorphic encryption, in this article. They suggest two packing approaches in TRGSW-based homomorphic schemes to reduce the extension factor and improve the estimation of look-up tables and random functions.
Smart, N.P., and Vercauteren, F., developed fully homomorphic SIMD operations [14]. They demonstrate how to choose variables to allow SIMD processes in this article. As a result, they receive a homomorphic system that supports SIMD processes as well as procedures on massive finite fields of characteristic two. They prove that SIMD procedures can be utilized to parallelize the decryption process, resulting in a significant speedup. Finally, they examine two use cases to show how SIMD operations can be used to execute different tasks: encrypting and homomorphically applying AES database lookup.
In 2015 Cheon, J.H, et.al, [15] has proposed FHE over integers based on CRT. In this article, they return to one of their ideas, the third scheme, which is based on the Chinese Remainder Theorem and rang homomorphically. This system was known to be broken by just a single pair of known plaintext/ciphertext. They will, however, deal with this issue by using a common method to inject an error into a message before encryption. They introduce a stable improvement of their proposal by demonstrating that under the approximate GCD presumption and the sparse subset sum assumption, the scheme is totally homomorphic and stable against the chosen-plaintext attacks.
In 2017, Ishimaki, Y., et al. [16] introduced a private substring retrieval protocol based on HE that protects both the stored information and the query's confidentiality. They demonstrated that FHE's substring quest can be completed in a reasonable amount of time and that their Batch Recursive Oblivious Transfer ensures that the analyst knows little more than the server's searched result.
Li, R., et al. [17] suggested a LUT protocol for analyzing any single-integer input variable in order to create a privacy-preserving anomaly identification scheme on a smart grid with FHE in 2019. Integer encoding, which was more effective than bitwise encoding, was supported by the protocol. Since they used the LUT protocol, the assessment period was independent of the purpose. Other structures that need a single input complex function evaluation depend on FHE were also supported by this protocol.
In 2013, Bos, J. W., et al. [18] suggested a new FHE scheme based on the Stehl e and Steinfeld scheme, which eliminates the HE scheme's non-standard evaluative small computational ratio prediction. Their new structure eliminates modulus flipping and holds ciphertexts to a single ring variable in size. They've also proposed a more realistic version of their scheme that doesn't depend on the decisional small polynomial ratio assumption.
I. Chillotti et al. [19] have given a comprehensive description of the TFHE construction, from an analytical LWE and GSW perspective to a realistic and functional implementation. This paper presents a torus-based quick FHE scheme (TFHE) that revisits, generalizes, and strengthens the FHE based on GSW and its ring variants. Finally, they include an additional functional study of LWE-based systems, in which the protection parameter was specifically related to the LWE error rate and the entropy of the LWE hidden key, as well as explicit variable sets and timing comparisons for all of their structures.
In 2019, Carpov, S. [20] proposed a bootstrapping protocol based on the TFHE system of split test integrals that can be utilized to analyze multi-value parameters and improve the performance of multi-output function evaluation. This approach can be easily generalized to other FHEW-based bootstrapping protocols, they note. They demonstrate how to develop and choose TVF to optimize the evaluation of consequences of different in a single bootstrapping call in this paper. They examining the configuration of FHEW-based bootstrapping algorithms and comparing the noise overhead performance and modularity.

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Chen. H, et al. [21] suggest an RGSW-like cryptosystem and two strategies for multiplying single-key encryption into a multi-key RLWE ciphertext in 2019. The first algorithm has two phases: multi-key RGSW ciphertext processing and multi-key external product formation. Their second hybrid product algorithm took a radically different approach to achieve the same features. The most significant technological achievement was the development of a new hybrid product that combines single-key and multi-key ciphertexts to improve storage, computation complexity, and noise development.
Cheon, Jung Hee, and colleagues [22] presented a procedure for effective estimated calculation on HE in 2017. The basic idea was to consider authentication noise to be a kind of error that occurs throughout the estimated calculations. They still keep their authentication representation small sufficiently in comparison to the ciphertext material properties for homomorphic operations such that the computation result was always smaller than q. They have an issue with the fact that the bit size of a message grows gradually with circuit depth without rounding. They propose a new technique called rescaling that tries to manipulate the communication of ciphertext to solve this problem.
Li, et.al. [23] suggested new security concepts in 2020, expanding the standard IND-CPA protection supposed to catch the passive protection criterion for (homomorphic) approximate encryption strategies. The need for appropriate authentication notions for approximate encryption tells us that correctness and security were two important aspects of cryptographic schemes that must be considered simultaneously.
Gentry, C, et al. [24] proposed the construction of FHE schemes for defense in 2012. To achieve low overhead, they employ Smart-Vercauteren and BrakerskiGentry-Vaikuntanathan's batch homomorphic evaluation methods which demonstrated that homomorphic operations can be applied to "filled" ciphertexts that encode vectors of plaintext elements. They apply to permute/routing strategies to effectively transfer plaintext components around these vectors in this paper. As a result, they can execute general arithmetic circuits in batches without ever having to "unpack" the plaintext vectors. It takes more computation to handle encrypted data homomorphically than it does to transfer unencrypted data.
Gentry, C, et al. [25] proposed a simplified solution in 2012 that partially by passes the homomorphic modularreduction bottleneck by dealing with a modulus similar to a power. Their solution was simpler to define and execute than a conventional binary circuit, and it was likely to be quicker in operation. It was also ability to handle an authentication of the secret key as a single ciphertext utilizing their methodology from this work.
[26] proposed a method for bootstrapping homomorphic encryption. They introduce a new method for homomorphically computing basic bit operations and refreshing (bootstrapping) the resulting output in less than half a second on a personal computer in this article. They offer a thorough theoretical description of the scheme (based on the worst-case hardness of regular lattice problems) and discuss how well their prototype implementation performed. The key benefit of their recent homomorphic NAND procedure was that it generates far less noise than previous approaches.
Bourse, F., et al. [27] established Quick homomorphic evaluation of deep discretized neural network. They introduce FHE DiNN, a new paradigm for homomorphic evaluation of neural networks whose complexity was purely linear in the network depth and whose parameters can be set beforehand, in this article. They view the problem from a scale-invariant perspective. Every neuron's performance was refreshed by bootstrapping in their system, FHE DiNN, allowing arbitrarily deep networks to be homomorphically examined

Conclusion:-
The existing literature study were studied in this paper. The cloud computing security based on homomorphic encryption is the latest concept. This paper analyzed the problem of homomorphic encryption, method, and their performance . This topic is considered as the major issue in the environment of cloud computing. Data hacking provides more problems for users on cloud storage.