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.

scholarly journals A Password Meter without Password Exposure

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 345
Author(s):  
Pyung Kim ◽  
Younho Lee ◽  
Youn-Sik Hong ◽  
Taekyoung Kwon
Keyword(s):  
Performance Enhancement ◽  
Homomorphic Encryption ◽  
Optimization Techniques ◽  
Third Party ◽  
Fully Homomorphic Encryption ◽  
Performance Achievement ◽  
Server Side ◽  
On Line ◽  
Internal Mechanism ◽  
High Chance

To meet password selection criteria of a server, a user occasionally needs to provide multiple choices of password candidates to an on-line password meter, but such user-chosen candidates tend to be derived from the user’s previous passwords—the meter may have a high chance to acquire information about a user’s passwords employed for various purposes. A third party password metering service may worsen this threat. In this paper, we first explore a new on-line password meter concept that does not necessitate the exposure of user’s passwords for evaluating user-chosen password candidates in the server side. Our basic idea is straightforward; to adapt fully homomorphic encryption (FHE) schemes to build such a system but its performance achievement is greatly challenging. Optimization techniques are necessary for performance achievement in practice. We employ various performance enhancement techniques and implement the NIST (National Institute of Standards and Technology) metering method as seminal work in this field. Our experiment results demonstrate that the running time of the proposed meter is around 60 s in a conventional desktop server, expecting better performance in high-end hardware, with an FHE scheme in HElib library where parameters support at least 80-bit security. We believe the proposed method can be further explored and used for a password metering in case that password secrecy is very important—the user’s password candidates should not be exposed to the meter and also an internal mechanism of password metering should not be disclosed to users and any other third parties.

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 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 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.

An Improvement for Fully Homomorphic Encryption over Integers with Shorter Public Keys

2014 ◽  
Vol 989-994 ◽  
pp. 4326-4331
Author(s):  
Ze Tao Jiang ◽  
Xiao Te Huang
Keyword(s):  
Quadratic Form ◽  
Homomorphic Encryption ◽  
Public Key ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
The Public ◽  
Cubic Form ◽  
Public Keys ◽  
Subset Sum ◽  
Approximate Gcd

This paper puts forward a more efficient fully homomorphic encryption scheme with a view to improving the oversized public key based on the Dijk’s scheme.Encrypted with a cubic form in the public key elements instead of quadratic form by adopting Gentry’s fully homomorphic techonology.The results show that the public key size reduce from to compared to the Coron’s scheme.The security of the proposed scheme is based on both the approximate GCD problem and the sparse-subset sum problem.

A Key Management Scheme for Smart Grid Wireless Terminals

2013 ◽  
Vol 442 ◽  
pp. 501-506
Author(s):  
Bo Zhang ◽  
Yu Fei Wang ◽  
Tao Zhang ◽  
Yuan Yuan Ma
Keyword(s):  
Smart Grid ◽  
Power Systems ◽  
Key Management ◽  
Large Scale ◽  
Homomorphic Encryption ◽  
Symmetric Polynomial ◽  
Encryption Algorithm ◽  
Fully Homomorphic Encryption ◽  
Management Scheme ◽  
Key Management Scheme

With the large-scale construction of smart grid, smart grid terminals widely using wireless access technology to communicate to the power systems. For ensuring the communication security, pair-wise key pre-distribution scheme is widely used, however, which introduces the complexity of key management, and insufficient security problems. According to the smart grid terminals wireless communication features, proposes an intelligent grid wireless terminal online key management scheme, which is based on the t rank binary symmetric polynomial and fully homomorphic encryption algorithm. This scheme make the communication key could be established with a few parameters between the communicating parties, which reduces the complexity of key predistribution and the amount of calculation. Moreover, the whole process of the key generation is encrypted by fully homomorphic encryption algorithm, effectively enhances the security of the scheme.

scholarly journals Public key cryptosystem based on multiple chaotic maps for image encryption

2021 ◽  
Vol 22 (3) ◽  
pp. 1457
Author(s):  
Yousif S. Najaf ◽  
Maher K. Mahmood Al-Azawi
Keyword(s):  
Chaotic Maps ◽  
Third Party ◽  
Public Key ◽  
Secret Key ◽  
Chebyshev Map ◽  
Key Space ◽  
Public Keys ◽  
Secret Keys ◽  
Shared Secret ◽  
Multiple Chaotic Maps

Image is one of the most important forms of information. In this paper, two public key encryption systems are proposed to protect images from various attacks. Both systems depend on generating a chaotic matrix (<em>I</em>) using multiple chaotic maps. The parameters for these maps are taken from the shared secret keys generated from Chebyshev map using public keys for Alice and secret key for Bob or vice versa. The second system has the feature of deceiving the third party for searching for fake keys. Analysis and tests showed that the two proposed systems resist various attacks and have very large key space. The results are compared with other chaos based systems to show the superiority of these two proposed systems.

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