Setup-Free Secure Search on Encrypted Data: Faster and Post-Processing Free

Abstract We present a novel secure search protocol on data and queries encrypted with Fully Homomorphic Encryption (FHE). Our protocol enables organizations (client) to (1) securely upload an unsorted data array x = (x[1], . . . , x[n]) to an untrusted honest-but-curious sever, where data may be uploaded over time and from multiple data-sources; and (2) securely issue repeated search queries q for retrieving the first element (i*, x[i*]) satisfying an agreed matching criterion i* = min { i ∈ [n] | IsMatch(x[i], q) = 1 }, as well as fetching the next matching elements with further interaction. For security, the client encrypts the data and queries with FHE prior to uploading, and the server processes the ciphertexts to produce the result ciphertext for the client to decrypt. Our secure search protocol improves over the prior state-of-the-art for secure search on FHE encrypted data (Akavia, Feldman, Shaul (AFS), CCS’2018) in achieving: – Post-processing free protocol where the server produces a ciphertext for the correct search outcome with overwhelming success probability. This is in contrast to returning a list of candidates for the client to postprocess, or suffering from a noticeable error probability, in AFS. Our post-processing freeness enables the server to use secure search as a sub-component in a larger computation without interaction with the client. – Faster protocol: (a) Client time and communication bandwidth are improved by a log2 n/ log log n factor. (b) Server evaluates a polynomial of degree linear in log n (compare to cubic in AFS), and overall number of multiplications improved by up to log n factor. (c) Employing only GF(2) computations (compare to GF(p) for p ≫ in AFS) to gain both further speedup and compatibility to all current FHE candidates. – Order of magnitude speedup exhibited by extensive benchmarks we executed on identical hardware for implementations of ours versus AFS’s protocols. Additionally, like other FHE based solutions, our solution is setup-free: to outsource elements from the client to the server, no additional actions are performed on x except for encrypting it element by element (each element bit by bit) and uploading the resulted ciphertexts to the server.

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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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Oblivious Lookup-Tables

Tatra Mountains Mathematical Publications ◽

10.1515/tmmp-2016-0039 ◽

2016 ◽

Vol 67 (1) ◽

pp. 191-203

Author(s):

Markus Stefan Wamser ◽

Stefan Rass ◽

Peter Schartner

Keyword(s):

Medical Records ◽

Homomorphic Encryption ◽

Input Parameter ◽

Software As A Service ◽

Fully Homomorphic Encryption ◽

Sensitive Data ◽

New Approach ◽

Encrypted Data ◽

Practical Applications ◽

Current State

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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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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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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An Effective NTRU-Based Fully Homomorphic Encryption Scheme

Mathematical Problems in Engineering ◽

10.1155/2021/9914961 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Xiaoyue Qin ◽

Ruwei Huang ◽

Huifeng Fan

Keyword(s):

Chinese Remainder Theorem ◽

Homomorphic Encryption ◽

Security Model ◽

Storage Efficiency ◽

Complex Matrix ◽

Fully Homomorphic Encryption ◽

Multiple Data ◽

Learning With Errors ◽

Matrix Vector ◽

And Storage

Fully homomorphic encryption (FHE) supports arbitrary computations on ciphertexts without decryption to protect users’ privacy. However, currently, there are still some shortcomings in research studies on FHE. For example, the NTRU-based FHE scheme constructed using the approximate eigenvector method requires complex matrix multiplications, and the power-of-two cyclotomic ring cannot prevent subfield attacks. To address these problems, this paper proposed a NTRU-based FHE scheme constructed based on the power-of-prime cyclotomic ring and made the following improvements: (1) the power-of-prime cyclotomic ring is immune to subfield attacks; (2) complex matrix multiplications are replaced with matrix-vector multiplications to modify the ciphertext forms and decryption structures, so as to gain advantages in storage, transportation, and computations; (3) the single instruction multiple data (SIMD) technology is introduced, and homomorphic operations are executed through the Chinese remainder theorem, further improving the scheme computation and storage efficiency. The ciphertext of the scheme is in a form of a vector, and no key exchange is required for homomorphic operations. In addition, this scheme can eliminate the decisional small polynomial ratio (DSPR) assumption under certain conditions and only relies on the ring learning with errors (RLWE) assumption. The standard security model can prove that this scheme is secure against chosen-plaintext (IND-CPA) attacks. Compared with similar schemes, the proposed scheme improves the efficiency at least by a factor of l φ x / d + 1 and quadratically decreases the noise growth rate.

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