Oblivious Lookup-Tables

Abstract Evaluating arbitrary functions on encrypted data is one of the holy grails of cryptography, with Fully Homomorphic Encryption (FHE) being probably the most prominent and powerful example. FHE, in its current state is, however, not efficient enough for practical applications. On the other hand, simple homomorphic and somewhat homomorphic approaches are not powerful enough to support arbitrary computations. We propose a new approach towards a practicable system for evaluating functions on encrypted data. Our approach allows to chain an arbitrary number of computations, which makes it more powerful than existing efficient schemes. As with basic FHE we do not encrypt or in any way hide the function, that is evaluated on the encrypted data. It is, however, sufficient that the function description is known only to the evaluator. This situation arises in practice for software as a Software as a Service (SaaS)-scenarios, where an evaluator provides a function only known to him and the user wants to protect his data. Another application might be the analysis of sensitive data, such as medical records. In this paper we restrict ourselves to functions with only one input parameter, which allow arbitrary transformations on encrypted data.

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Secure Data Retrieval on the Cloud: Homomorphic Encryption meets Coresets

IACR Transactions on Cryptographic Hardware and Embedded Systems ◽

10.46586/tches.v2019.i2.80-106 ◽

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.

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Homomorphic Encryption Using Enhanced BGV Encryption Scheme For Cloud Security

International Journal Of Engineering And Computer Science ◽

10.18535/ijecs/v7i3.22 ◽

2018 ◽

Vol 7 (03) ◽

pp. 23785-23789

Author(s):

S.V.Suriya Prasad ◽

K. Kumanan

Keyword(s):

Homomorphic Encryption ◽

Cloud Service ◽

Cloud Security ◽

Encryption Scheme ◽

Public Cloud ◽

Fully Homomorphic Encryption ◽

Sensitive Data ◽

Encrypted Data ◽

Or Applications

Fully Homomorphic Encryption is used to enhance the security incase of un-trusted systems or applications that deals with sensitive data. Homomorphic encryption enables computation on encrypted data without decryption. Homomorphic encryption prevents sharing of data within the cloud service where data is stored in a public cloud . In Partially Homomorphic Encryption it performs either additive or multiplicative operation, but not both operation can be carried out at a same time. Whereas , in case of Fully Homomorphic Encryption both operations can be carried out at same time. In this model , Enhanced BGV Encryption Technique is used to perform FHE operations on encrypted data and sorting is performed using the encrypted data

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Computing Blindfolded on Data Homomorphically Encrypted under Multiple Keys: A Survey

ACM Computing Surveys ◽

10.1145/3477139 ◽

2022 ◽

Vol 54 (9) ◽

pp. 1-37

Author(s):

Asma Aloufi ◽

Peizhao Hu ◽

Yongsoo Song ◽

Kristin Lauter

Keyword(s):

Homomorphic Encryption ◽

Lessons Learned ◽

Secret Key ◽

Sensitive Data ◽

Encrypted Data ◽

Outsourced Computation ◽

Secret Keys ◽

Comprehensive Survey ◽

Multiple Keys ◽

Cryptographic Techniques

With capability of performing computations on encrypted data without needing the secret key, homomorphic encryption (HE) is a promising cryptographic technique that makes outsourced computations secure and privacy-preserving. A decade after Gentry’s breakthrough discovery of how we might support arbitrary computations on encrypted data, many studies followed and improved various aspects of HE, such as faster bootstrapping and ciphertext packing. However, the topic of how to support secure computations on ciphertexts encrypted under multiple keys does not receive enough attention. This capability is crucial in many application scenarios where data owners want to engage in joint computations and are preferred to protect their sensitive data under their own secret keys. Enabling this capability is a non-trivial task. In this article, we present a comprehensive survey of the state-of-the-art multi-key techniques and schemes that target different systems and threat models. In particular, we review recent constructions based on Threshold Homomorphic Encryption (ThHE) and Multi-Key Homomorphic Encryption (MKHE). We analyze these cryptographic techniques and schemes based on a new secure outsourced computation model and examine their complexities. We share lessons learned and draw observations for designing better schemes with reduced overheads.

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Arithmetic Operations on Encrypted Data using Fully Homomorphic Encryption

2017 14th IEEE India Council International Conference (INDICON) ◽

10.1109/indicon.2017.8487891 ◽

2017 ◽

Author(s):

Shiji Mariam Mathew ◽

S Sabitha

Keyword(s):

Homomorphic Encryption ◽

Arithmetic Operations ◽

Fully Homomorphic Encryption ◽

Encrypted Data

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About Fully Homomorphic Encryption Improvement Techniques

International Journal of Embedded and Real-Time Communication Systems ◽

10.4018/ijertcs.2019070101 ◽

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.

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An Efficient Fully Homomorphic Encryption Scheme for Private Information Retrieval in the Cloud

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001420550083 ◽

2019 ◽

Vol 34 (04) ◽

pp. 2055008

Author(s):

Xun Wang ◽

Tao Luo ◽

Jianfeng Li

Keyword(s):

Information Retrieval ◽

Theoretical Analysis ◽

Private Information ◽

Homomorphic Encryption ◽

Private Information Retrieval ◽

Encryption Scheme ◽

Fully Homomorphic Encryption ◽

Encrypted Data ◽

Privacy Concerns ◽

Simulation Results

Information retrieval in the cloud is common and convenient. Nevertheless, privacy concerns should not be ignored as the cloud is not fully trustable. Fully Homomorphic Encryption (FHE) allows arbitrary operations to be performed on encrypted data, where the decryption of the result of ciphertext operation equals that of the corresponding plaintext operation. Thus, FHE schemes can be utilized for private information retrieval (PIR) on encrypted data. In the FHE scheme proposed by Ducas and Micciancio (DM), only a single homomorphic NOT AND (NAND) operation is allowed between consecutive ciphertext refreshings. Aiming at this problem, an improved FHE scheme is proposed for efficient PIR where homomorphic additions and multiplications are based on linear operations on ciphertext vectors. Theoretical analysis shows that when compared with the DM scheme, the proposed scheme allows multiple homomorphic additions and a single homomorphic multiplication to be performed. The number of allowed homomorphic additions is determined by the ratio of the ciphertext modulus to the upper bound of initial ciphertext noise. Moreover, simulation results show that the proposed scheme is significantly faster than the DM scheme in the homomorphic evaluation for a series of algorithms.

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Statistical learning based fully homomorphic encryption on encrypted data

Soft Computing ◽

10.1007/s00500-016-2296-6 ◽

2016 ◽

Vol 21 (24) ◽

pp. 7473-7483 ◽

Cited By ~ 5

Author(s):

Linzhi Jiang ◽

Chunxiang Xu ◽

Xiaofang Wang ◽

Chao Lin

Keyword(s):

Statistical Learning ◽

Homomorphic Encryption ◽

Fully Homomorphic Encryption ◽

Encrypted Data

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A Proposed Fully Homomorphic for Securing Cloud Banking Data at Rest

UHD Journal of Science and Technology ◽

10.21928/uhdjst.v4n1y2020.pp87-95 ◽

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.

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A More Efficient Fully Homomorphic Encryption Scheme Based on GSW and DM Schemes

Security and Communication Networks ◽

10.1155/2018/8706940 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14 ◽

Cited By ~ 5

Author(s):

Xun Wang ◽

Tao Luo ◽

Jianfeng Li

Keyword(s):

Error Rate ◽

Homomorphic Encryption ◽

Computational Cost ◽

Encryption Scheme ◽

Fully Homomorphic Encryption ◽

Practical Applications ◽

Low Level ◽

Matrix Operations ◽

Major Bottleneck ◽

Overall Efficiency

Achieving both simplicity and efficiency in fully homomorphic encryption (FHE) schemes is important for practical applications. In the simple FHE scheme proposed by Ducas and Micciancio (DM), ciphertexts are refreshed after each homomorphic operation. And ciphertext refreshing has become a major bottleneck for the overall efficiency of the scheme. In this paper, we propose a more efficient FHE scheme with fewer ciphertext refreshings. Based on the DM scheme and another simple FHE scheme proposed by Gentry, Sahai, and Waters (GSW), ciphertext matrix operations and ciphertext vector additions are both applied in our scheme. Compared with the DM scheme, one more homomorphic NOT AND (NAND) operation can be performed on ciphertexts before ciphertext refreshing. Results show that, under the same security parameters, the computational cost of our scheme is obviously lower than that of GSW and DM schemes for a depth-2 binary circuit with NAND gates. And the error rate of our scheme is kept at a sufficiently low level.

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