Partially Homomorphic Encryption Schemes over Finite Fields

2016 ◽  
pp. 109-123 ◽  
Author(s):  
Jian Liu ◽  
Sihem Mesnager ◽  
Lusheng Chen
Keyword(s):  
Finite Fields ◽  
Homomorphic Encryption ◽  
Encryption Schemes

Revisiting Homomorphic Encryption Schemes for Finite Fields

2021 ◽  
pp. 608-639
Author(s):  
Andrey Kim ◽  
Yuriy Polyakov ◽  
Vincent Zucca
Keyword(s):  
Finite Fields ◽  
Homomorphic Encryption ◽  
Encryption Schemes

Candidate iO from Homomorphic Encryption Schemes

2020 ◽  
pp. 79-109 ◽  
Author(s):  
Zvika Brakerski ◽  
Nico Döttling ◽  
Sanjam Garg ◽  
Giulio Malavolta
Keyword(s):  
Homomorphic Encryption ◽  
Encryption Schemes

scholarly journals A Survey on Homomorphic Encryption Schemes

2018 ◽  
Vol 51 (4) ◽  
pp. 1-35 ◽  
Author(s):  
Abbas Acar ◽  
Hidayet Aksu ◽  
A. Selcuk Uluagac ◽  
Mauro Conti
Keyword(s):  
Homomorphic Encryption ◽  
Encryption Schemes

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.

Sign in / Sign up

Export Citation Format

Share Document