scholarly journals An Effective NTRU-Based Fully Homomorphic Encryption Scheme

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.

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.

scholarly journals Algorithms for CRT-variant of Approximate Greatest Common Divisor Problem

2020 ◽  
Vol 14 (1) ◽  
pp. 397-413
Author(s):  
Jung Hee Cheon ◽  
Wonhee Cho ◽  
Minki Hhan ◽  
Jiseung Kim ◽  
Changmin Lee
Keyword(s):  
Time Complexity ◽  
Chinese Remainder Theorem ◽  
Homomorphic Encryption ◽  
Divisor Problem ◽  
Greatest Common Divisor ◽  
Fully Homomorphic Encryption ◽  
Cryptographic Primitives ◽  
Multiple Messages ◽  
Polynomial Factor ◽  
Parameter Condition

AbstractThe approximate greatest common divisor problem (ACD) and its variants have been used to construct many cryptographic primitives. In particular, the variants of the ACD problem based on Chinese remainder theorem (CRT) are being used in the constructions of a batch fully homomorphic encryption to encrypt multiple messages in one ciphertext. Despite the utility of the CRT-variant scheme, the algorithms that secures its security foundation have not been probed well enough.In this paper, we propose two algorithms and the results of experiments in which the proposed algorithms were used to solve the variant problem. Both algorithms take the same time complexity $\begin{array}{} \displaystyle 2^{\tilde{O}(\frac{\gamma}{(\eta-\rho)^2})} \end{array}$ up to a polynomial factor to solve the variant problem for the bit size of samples γ, secret primes η, and error bound ρ. Our algorithm gives the first parameter condition related to η and γ size. From the results of the experiments, it has been proved that the proposed algorithms work well both in theoretical and experimental terms.

scholarly journals Two-Party Secure Computation for Any Polynomial Function on Ciphertexts under Different Secret Keys

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Bingbing Jiang
Keyword(s):  
Polynomial Function ◽  
Homomorphic Encryption ◽  
Auxiliary Information ◽  
Secure Computation ◽  
Encryption Algorithm ◽  
Fully Homomorphic Encryption ◽  
Simple Scheme ◽  
Secret Keys ◽  
Learning With Errors ◽  
Multiple Keys

Multikey fully homomorphic encryption proposed by Lopez-Alt et al. (STOC12) is a significant primitive that allows one to perform computation on the ciphertexts encrypted by multiple different keys independently. Then, several schemes were constructed based on decisional small polynomial ratio or learning with errors. These schemes all require an expansion algorithm to transform a ciphertext under a single key into an encryption of the same message under a set of keys. To achieve the expansion algorithm without interaction with these key-keepers, their encryption algorithm not only outputs a ciphertext of a plaintext but also exports auxiliary information generated from the randomness used in the former encryption process. Beyond that, the size of the ciphertext encrypted by multiple keys increases linearly or quadratically in the number of participants. In this paper, we studied the problem whether someone can directly perform arbitrary computation on ciphertexts encrypted by different keys without any auxiliary information in the output of the encryption algorithm and an increase in the size of the ciphertext in the expansion algorithm. To this end, we proposed a novel and simple scheme of secure computation on ciphertexts under two different keys directly without any auxiliary information. In other words, each party just provides its own ciphertexts encrypted by the GSW scheme (CRYPTO13). In the procedure of executing evaluation on these ciphertexts, the size of the new ciphertext remains the same as that of the GSW ciphertext.

Research perspectives on fully homomorphic encryption models for cloud sector

2021 ◽  
pp. 1-26
Author(s):  
Sonam Mittal ◽  
K.R. Ramkumar
Keyword(s):  
Cloud Computing ◽  
Big Data ◽  
Homomorphic Encryption ◽  
Data Encryption ◽  
Cloud Services ◽  
Future Research ◽  
Public Cloud ◽  
Fully Homomorphic Encryption ◽  
Research Perspectives ◽  
Learning With Errors

As there is a continuous delivery of big data, the researchers are showing interest in the applications of cloud computing concerning privacy, and security. On the other hand, many researchers and experts of cybersecurity have commenced on a quest for improving the data encryption to the models of big data and applications of cloud computing. Since many users of the cloud become public cloud services, confidentiality turns out to be a more compound problem. To solve the confidentiality problem, cloud clients maintain the data on the public cloud. Under this circumstance, Homomorphic Encryption (HE) appears as a probable solution, in which the information of the client is encrypted on the cloud in such a process that it permits few manipulation operations without decryption. The main intent of this paper is to present the systematic review of research papers published in the field of Fully Homomorphic Encryption (FHE) over the past 10 years. The encryption scheme is considered full when it consists of plaintext, a ciphertext, a keyspace, an encryption algorithm, and a decryption algorithm. Hence, the review mostly concentrates on reviewing more powerful and recent FHE. The contributions using different algorithms in FHE like Lattice-based, integer-based, Learning With Errors (LWE), Ring Learning With Errors (RLWE), and Nth degree Truncated polynomial Ring Units (NTRU) are also discussed. Finally, it highlights the challenges and gaps to be addressed in modeling and learning about competent, effectual, and vigorous FHE for the cloud sector and pays attention to directions for better future research.

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

2019 ◽  
Vol 2019 (3) ◽  
pp. 87-107 ◽  
Author(s):  
Adi Akavia ◽  
Craig Gentry ◽  
Shai Halevi ◽  
Max Leibovich
Keyword(s):  
Homomorphic Encryption ◽  
Success Probability ◽  
Post Processing ◽  
Fully Homomorphic Encryption ◽  
Matching Criterion ◽  
Encrypted Data ◽  
Multiple Data ◽  
Secure Search ◽  
Order Of Magnitude ◽  
Factor C

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.

scholarly journals Compressible Multikey and Multi-Identity Fully Homomorphic Encryption

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Tongchen Shen ◽  
Fuqun Wang ◽  
Kefei Chen ◽  
Zhonghua Shen ◽  
Renjun Zhang
Keyword(s):  
Key Management ◽  
Homomorphic Encryption ◽  
Third Party ◽  
Secret Key ◽  
Fully Homomorphic Encryption ◽  
Expansion Technique ◽  
Public Keys ◽  
Learning With Errors ◽  
Computable Functions ◽  
Computing Models

With the development of new computing models such as cloud computing, user’s data are at the risk of being leaked. Fully homomorphic encryption (FHE) provides a possible way to fundamentally solve the problem. It enables a third party who does not know anything about the secret key and plaintexts to homomorphically perform any computable functions on the corresponding ciphertexts. In 2009, Gentry proposed the first FHE scheme. After that, its inefficiency has always been a bottleneck of the development of practical schemes and applications. At TCC 2019, Gentry and Halevi proposed the first compressible FHE scheme that enables the ratio of plaintext size to the ciphertext size (i.e., the compression rate) to reach 1 − ε for any small ε > 0 under the standard learning with errors (LWE) assumption. However, it is only a single-key one, where the homomorphic evaluation can only be performed over ciphertexts encrypted under the same key. Compared with single-key FHE, multikey FHE is more practical. Multikey FHE enables ciphertexts encrypted under different public keys to be homomorphically computed without having to decrypt these ciphertexts using their own private keys. In addition, in a multi-identity FHE scheme, only identity information and public parameters are required when encrypting, which simplifies certificate-based key management in public key infrastructure. In this paper, a new compressible ciphertext expansion technique is proposed. Then, we use this technique to construct a compressible multikey FHE scheme and a compressible multi-identity FHE scheme to overcome the bottleneck of bandwidth inefficiency in the multikey and multi-identity settings. The two schemes proposed in this paper make it possible that the objects of homomorphic operation can be the ciphertexts encrypted under different keys or different identities before compression, thus solving the single-key defect of the work of Gentry and Halevi.

A Neural Network Application of Fully Homomorphic Encryption for Cloud Computing

2020 ◽  
Author(s):  
Megha Kolhekar ◽  
Ashish Pandey ◽  
Ayushi Raina ◽  
Rijin Thomas ◽  
Vaibhav Tiwari ◽  
...  
Keyword(s):  
Neural Network ◽  
Cloud Computing ◽  
Homomorphic Encryption ◽  
Fully Homomorphic Encryption ◽  
Network Application
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