scholarly journals Cloud Storage Protection Scheme Based on Fully Homomorphic Encryption

2020 ◽  
Vol 8 (2) ◽  
pp. 40-47
Author(s):  
Mohammed A. Mohammed ◽  
Fadhil S. Abed
Keyword(s):  
Homomorphic Encryption ◽  
Statistical Tests ◽  
Cloud Service ◽  
Prime Numbers ◽  
Secret Key ◽  
Fully Homomorphic Encryption ◽  
Cloud Data ◽  
Protection Scheme ◽  
Security Problem ◽  
Encryption Schemes

Cloud computing allows enterprises and individuals to have a less physical infrastructure of software and hardware. Nevertheless, there are some concerns regarding privacy protection which may turn out to be a strong barrier. Traditional encryption schemes have been used to encrypt the data before sending them to the cloud. However, the private key has to be provided to the server before any calculations on the data. To solve this security problem, this paper proposes a fully homomorphic encryption scheme for securing cloud data at rest. The scheme is based on prime modular operation, its security depends on factoring multiple large prime numbers (p1, p2,...pn) up to n, which is formed from very large prime numbers up to hundreds of digits as this is an open problem in mathematics. In addition, the elements of the secret key are derived from a series of mathematical operations and the calculation of an Euler coefficient within the modular of integers. Furthermore, it adds the complexity of noise to the plaintext using the number of users of the Cloud Service Provider. Moreover, its randomness is evaluated by the National Institute of Standards and Technology statistical tests, and the results demonstrating that the best statistical performance was obtained with this algorithm.

An Additively Homomorphic Encryption over Large Message Space

2015 ◽  
Vol 10 (3) ◽  
pp. 82-102 ◽  
Author(s):  
Hu Chen ◽  
Yupu Hu ◽  
Zhizhu Lian ◽  
Huiwen Jia ◽  
Xu An Wang
Keyword(s):  
Homomorphic Encryption ◽  
Prime Numbers ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
The Public ◽  
Real World Applications ◽  
Encryption Schemes ◽  
Setting Parameters ◽  
Message Space ◽  
The Ideal

Fully homomorphic encryption schemes available are not efficient enough to be practical, and a number of real-world applications require only that a homomorphic encryption scheme is somewhat homomorphic, even additively homomorphic and has much larger message space for efficiency. An additively homomorphic encryption scheme based heavily on Smart-Vercauteren encryption scheme (SV10 scheme, PKC 2010) is put forward, where both schemes each work with two ideals I and J. As a contribution of independent interest, a two-element representation of the ideal I is given and proven by factoring prime numbers in a number field. This two-element representation serves as the public key. The authors' scheme allows working over much larger message space than that of SV10 scheme by selecting the ideal I with larger decryption radius to generate public/private key pair, instead of choosing the ideal J as done in the SV10 scheme. The correctness and security of the scheme are shown, followed by setting parameters and computational results. The results indicate that this construction has much larger message space than SV10 scheme.

About Fully Homomorphic Encryption Improvement Techniques

2019 ◽  
Vol 10 (3) ◽  
pp. 1-20
Author(s):  
Ahmed El-Yahyaoui ◽  
Mohamed Daifr Ech-Cherif El Kettani
Keyword(s):  
Cloud Computing ◽  
Homomorphic Encryption ◽  
Quality Of Services ◽  
End User ◽  
Fully Homomorphic Encryption ◽  
Encrypted Data ◽  
Cloud Server ◽  
Encryption Schemes ◽  
Multiple Clients

Fully homomorphic encryption schemes (FHE) are a type of encryption algorithm dedicated to data security in cloud computing. It allows for performing computations over ciphertext. In addition to this characteristic, a verifiable FHE scheme has the capacity to allow an end user to verify the correctness of the computations done by a cloud server on his encrypted data. Since FHE schemes are known to be greedy in term of processing consumption and slow in terms of runtime execution, it is very useful to look for improvement techniques and tools to improve FHE performance. Parallelizing computations is among the best tools one can use for FHE improvement. Batching is a kind of parallelization of computations when applied to an FHE scheme, it gives it the capacity of encrypting and homomorphically processing a vector of plaintexts as a single ciphertext. This is used in the context of cloud computing to perform a known function on several ciphertexts for multiple clients at the same time. The advantage here is in optimizing resources on the cloud side and improving the quality of services provided by the cloud computing. In this article, the authors will present a detailed survey of different FHE improvement techniques in the literature and apply the batching technique to a promising verifiable FHE (VFHE) recently presented by the authors at the WINCOM17 conference.

scholarly journals LWR-Based Fully Homomorphic Encryption, Revisited

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Fucai Luo ◽  
Fuqun Wang ◽  
Kunpeng Wang ◽  
Jie Li ◽  
Kefei Chen
Keyword(s):  
Tensor Product ◽  
Gaussian Noise ◽  
Homomorphic Encryption ◽  
Matrix Multiplication ◽  
Public Key ◽  
Multiparty Computation ◽  
Secret Key ◽  
Fully Homomorphic Encryption ◽  
Private Key ◽  
Modulus Problem

Very recently, Costache and Smart proposed a fully homomorphic encryption (FHE) scheme based on the Learning with Rounding (LWR) problem, which removes the noise (typically, Gaussian noise) sampling needed in the previous lattices-based FHEs. But their scheme did not work, since the noise of homomorphic multiplication is complicated and large, which leads to failure of decryption. More specifically, they chose LWR instances as a public key and the private key therein as a secret key and then used the tensor product to implement homomorphic multiplication, which resulted in a tangly modulus problem. Recall that there are two moduli in the LWR instances, and then the moduli will tangle together due to the tensor product. Inspired by their work, we built the first workable LWR-based FHE scheme eliminating the tangly modulus problem by cleverly adopting the celebrated approximate eigenvector method proposed by Gentry et al. at Crypto 2013. Roughly speaking, we use a specific matrix multiplication to perform the homomorphic multiplication, hence no tangly modulus problem. Furthermore, we also extend the LWR-based FHE scheme to the multikey setting using the tricks used to construct LWE-based multikey FHE by Mukherjee and Wichs at Eurocrypt 2016. Our LWR-based multikey FHE construction provides an alternative to the existing multikey FHEs and can also be applied to multiparty computation with higher efficiency.

scholarly journals Privacy Preserving Outsourced Calculations With Symmetric Fully Homomorphic Encryption

2019 ◽  
Vol 8 (10) ◽  
pp. 3012-3015
Keyword(s):  
Service Providers ◽  
Homomorphic Encryption ◽  
Cloud Service ◽  
New Paradigm ◽  
Fully Homomorphic Encryption ◽  
Privacy And Security ◽  
Cloud Service Provider ◽  
Privacy Concerns ◽  
Private Data ◽  
Cloud Storage Service

Cloud computing is a new paradigm which provides cloud storage service to manage, maintain and back up private data remotely. For privacy concerns the data is kept encrypted and made available to users on demand through cloud service provider over the internet. The legacy encryption techniques rely on sharing of keys, so service providers and end users of the cloud have exclusive rights on the data thus the secrecy may loss. Homomorphic Encryption is a significant encryption technique which allows users to perform limited arithmetic on the enciphered data without loss of privacy and security. This paper addresses a new simple and non-bootstrappable Fully Homomorphic Encryption Scheme based on matrices as symmetric keys with access control.

scholarly journals A Proposed Fully Homomorphic for Securing Cloud Banking Data at Rest

2020 ◽  
Vol 4 (1) ◽  
pp. 87
Author(s):  
Zana Thalage Omar ◽  
Fadhil Salman Abed
Keyword(s):  
Homomorphic Encryption ◽  
Prime Numbers ◽  
Data Encryption ◽  
Theoretical Research ◽  
Significant Progress ◽  
Arithmetic Operations ◽  
Fully Homomorphic Encryption ◽  
Encrypted Data ◽  
Encryption And Decryption ◽  
Local Cloud

Fully homomorphic encryption (FHE) reaped the importance and amazement of most researchers and followers in data encryption issues, as programs are allowed to perform arithmetic operations on encrypted data without decrypting it and obtain results similar to the effects of arithmetic operations on unencrypted data. The first (FHE) model was introduced by Craig Gentry in 2009, and it was just theoretical research, but later significant progress was made on it, this research offers FHE system based on directly of factoring big prime numbers which consider open problem now, The proposed scheme offers a fully homomorphic system for data encryption and stores it in encrypted form on the cloud based on a new algorithm that has been tried on a local cloud and compared with two previous encryption systems (RSA and Paillier) and shows us that this algorithm reduces the time of encryption and decryption by 5 times compared to other systems.

scholarly journals Secure Data Retrieval on the Cloud: Homomorphic Encryption meets Coresets

2019 ◽  
pp. 80-106
Author(s):  
Adi Akavia ◽  
Dan Feldman ◽  
Hayim Shaul
Keyword(s):  
Reporting System ◽  
Homomorphic Encryption ◽  
Data Retrieval ◽  
Secret Key ◽  
Fully Homomorphic Encryption ◽  
Database Queries ◽  
Encrypted Data ◽  
Current State ◽  
Database Table ◽  
Core Sets

Secure report is the problem of a client that retrieves all records matching specified attributes from a database table at the server (e.g. cloud), as in SQL SELECT queries, but where the query and the database are encrypted. Here, only the client has the secret key, but still the server is expected to compute and return the encrypted result. Secure report is theoretically possible with Fully Homomorphic Encryption (FHE). However, the current state-of-the-art solutions are realized by a polynomial of degree that is at least linear in the number m of records, which is too slow in practice even for very small databases. We present the first solution that is realized by a polynomial that attains degree independent of the number of records m, as well as the first implementation of an FHE solution to Secure report. This is by suggesting a novel paradigm that forges a link between cryptography and modern data summarization techniques known as coresets (core-sets), and sketches in particular. The key idea is to compute only a coreset of the desired report. Since the coreset is small, the client can quickly decode the desired report that the server computes after decrypting the coreset. We implemented our main reporting system in an open source library. This is the first implemented system that can answer such database queries when processing only FHE encrypted data and queries. As our analysis promises, the experimental results show that we can run Secure report queries on billions records in minutes on an Amazon EC2 server, compared to less than a hundred-thousands in previous FHE based solutions.

scholarly journals Two-Party Privacy-Preserving Set Intersection with FHE

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1339
Author(s):  
Yunlu Cai ◽  
Chunming Tang ◽  
Qiuxia Xu
Keyword(s):  
Private Information ◽  
Homomorphic Encryption ◽  
Bloom Filter ◽  
Cloud Service ◽  
Fully Homomorphic Encryption ◽  
Cloud Service Provider ◽  
Set Size ◽  
Set Intersection ◽  
Learning With Errors ◽  
Private Set Intersection

A two-party private set intersection allows two parties, the client and the server, to compute an intersection over their private sets, without revealing any information beyond the intersecting elements. We present a novel private set intersection protocol based on Shuhong Gao’s fully homomorphic encryption scheme and prove the security of the protocol in the semi-honest model. We also present a variant of the protocol which is a completely novel construction for computing the intersection based on Bloom filter and fully homomorphic encryption, and the protocol’s complexity is independent of the set size of the client. The security of the protocols relies on the learning with errors and ring learning with error problems. Furthermore, in the cloud with malicious adversaries, the computation of the private set intersection can be outsourced to the cloud service provider without revealing any private information.

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