On the exact decryption range for Gentry–Halevi's implementation of fully homomorphic encryption

2014 ◽  
Vol 8 (3) ◽  
Author(s):  
Masaya Yasuda ◽  
Kazuhiro Yokoyama ◽  
Takeshi Shimoyama ◽  
Jun Kogure ◽  
Takeshi Koshiba
Keyword(s):  
Upper Bound ◽  
Experimental Evaluation ◽  
Homomorphic Encryption ◽  
Euclidean Norm ◽  
Fully Homomorphic Encryption ◽  
Ideal Lattices ◽  
Noise Density ◽  
Original Scheme ◽  
Somewhat Homomorphic Encryption ◽  
Noise Management

AbstractIn this paper, we revisit the fully homomorphic encryption (FHE) scheme implemented by Gentry and Halevi, which is just an instantiation of Gentry's original scheme based on ideal lattices. Their FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, and its decryption range is deeply related with the FHE construction. Gentry and Halevi gave an experimental evaluation of the decryption range, but theoretical evaluations have not been given so far. Moreover, we give a theoretical upper bound, and reconsider suitable parameters for theoretically obtaining an FHE scheme. In particular, while Gentry and Halevi use the Euclidean norm evaluation in the noise management of ciphertexts, our theoretical bound enables us to use the ∞-norm evaluation, and hence it helps to lower the difficulty of controlling the noise density of ciphertexts.

HOMOMORPHIC OPERATIONS WITHIN IDEAL LATTICE BASED ENCRYPTION SYSTEMS

2020 ◽  
pp. 40-46
Author(s):  
V. Yu. Kadykov ◽  
A. B. Levina
Keyword(s):  
Homomorphic Encryption ◽  
Third Party ◽  
Analysis Method ◽  
Fully Homomorphic Encryption ◽  
Simple Estimate ◽  
Encrypted Data ◽  
Ideal Lattices ◽  
Lattice Space ◽  
Security Properties ◽  
The Ideal

By 2009 the first system of fully homomorphic encryption had been constructed, and it was thought-provoking for many future works based on it. Instead of legacy encryption systems which depend on sharing a key (public or private) among endpoints involved in exchanging en encrypted message the fully homomorphic encryption can keep service without depending on shared keys and does not necessarily need to access the content. Such property allows any third party to operate on the encrypted data without decrypting it in advance. In this work, the possibility of using the ideal lattices for the construction of homomorphic operations is researched with a detailed level of math.The paper represents the analysis method based on the primitive of a union of ideals in lattice space. A segregated analysis between homomorphic and security properties is the advantage of this method. The work will be based on the analysis of generalized operations over ciphertext using the concept of the base reducing element which shares all about the method above. It will be shown how some non-homomorphic encryption systems can be supplemented by homomorphic operations which invoke different parameters choosing. Thus such systems can be decomposed from ciphertext structure to decryption process which will be affected by separately analyzed base reduction elements. Distinct from the encryption scheme the underlying math can be used to analyze only the homomorphic part, particularly under some simplifications. The building of such ideal-based ciphertext is laying on the assumption that ideals can be extracted further. It will be shown that the “remainder theorem” can be one of the principal ways to do this providing a simple estimate of an upper bound security strength of ciphertext structure.

scholarly journals Efficient GSW-Style Fully Homomorphic Encryption over the Integers

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jianan Zhao ◽  
Ruwei Huang ◽  
Bo Yang
Keyword(s):  
Computational Complexity ◽  
Computational Efficiency ◽  
Homomorphic Encryption ◽  
Encryption Scheme ◽  
Prior Work ◽  
Fully Homomorphic Encryption ◽  
Management Method ◽  
Noise Management

We propose a GSW-style fully homomorphic encryption scheme over the integers (FHE-OI) that is more efficient than the prior work by Benarroch et al. (PKC 2017). To reduce the expansion of ciphertexts, our scheme consists of two types of ciphertexts: integers and vectors. Moreover, the computational efficiency in the homomorphic evaluation can be improved by hybrid homomorphic operations between integers and vectors. In particular, when performing vector-integer multiplications, the evaluation has the computational complexity of Ο γ   log   γ and thus outperforms all prior FHE-OI schemes. To slow down the noise growth in homomorphic multiplications, we introduce a new noise management method called sequentialization; therefore, the noise in the resulting ciphertext increases by a factor of l ⋅ poly λ rather than poly λ l in general multiplications, where l is the number of multiplications. As a result, the circuit with larger multiplicative depth can be evaluated under the same parameter settings. Finally, to further reduce the size of ciphertexts, we apply ciphertext truncation and obtain the integer ciphertext of size Ο λ   log   λ , thus additionally reducing the size of the vector ciphertext in Benarroch’s scheme from Ο ˜ λ 4 to Ο λ 2 log 2   λ .

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

A fully homomorphic encryption based on magic number fragmentation and El‐Gamal encryption: Smart healthcare use case

2021 ◽  
Author(s):  
Mostefa Kara ◽  
Abdelkader Laouid ◽  
Mohammed Amine Yagoub ◽  
Reinhardt Euler ◽  
Saci Medileh ◽  
...  
Keyword(s):  
Homomorphic Encryption ◽  
Magic Number ◽  
Use Case ◽  
Healthcare Use ◽  
Fully Homomorphic Encryption ◽  
Smart Healthcare

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.

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