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.

Practical private-key fully homomorphic encryption in rings

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexey Gribov ◽  
Delaram Kahrobaei ◽  
Vladimir Shpilrain
Keyword(s):  
Homomorphic Encryption ◽  
Public Information ◽  
Third Party ◽  
Efficient Computation ◽  
Fully Homomorphic Encryption ◽  
Encrypted Data ◽  
Private Key

Abstract We describe a practical fully homomorphic encryption (FHE) scheme based on homomorphisms between rings and show that it enables very efficient computation on encrypted data. Our encryption though is private-key; public information is only used to operate on encrypted data without decrypting it. Still, we show that our method allows for a third party search on encrypted data.

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.

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.

An Efficient Fully Homomorphic Encryption Scheme for Private Information Retrieval in the Cloud

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.

Statistical learning based fully homomorphic encryption on encrypted data

2016 ◽  
Vol 21 (24) ◽  
pp. 7473-7483 ◽  
Author(s):  
Linzhi Jiang ◽  
Chunxiang Xu ◽  
Xiaofang Wang ◽  
Chao Lin
Keyword(s):  
Statistical Learning ◽  
Homomorphic Encryption ◽  
Fully Homomorphic Encryption ◽  
Encrypted Data

scholarly journals Oblivious Lookup-Tables

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.

scholarly journals A Proposed Fully Homomorphic for Securing Cloud Banking Data at Rest

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.

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.

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