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Scale-Invariant Fully Homomorphic Encryption over the Integers [chapter]

Jean-Sébastien Coron, Tancrède Lepoint, Mehdi Tibouchi
2014 Lecture Notes in Computer Science  
In this paper we describe a variant of the van Dijk et al. FHE scheme over the integers with the same scale-invariant property.  ...  At Crypto 2012, Brakerski constructed a scale-invariant fully homomorphic encryption scheme based on the LWE problem, in which the same modulus is used throughout the evaluation process, instead of a ladder  ...  The technique was also adapted to the DGHV fully homomorphic encryption scheme over the integers [DGHV10] in [CNT12] .  ... 
doi:10.1007/978-3-642-54631-0_18 fatcat:d5u27xgetvbhjcb6bqorjnqqbq

Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP [chapter]

Zvika Brakerski
2012 Lecture Notes in Computer Science  
We use this technique to construct a scale-invariant fully homomorphic encryption scheme, whose properties only depend on the ratio between the modulus q and the initial noise level B, and not on their  ...  We present a new tensoring technique for LWE-based fully homomorphic encryption.  ...  A Scale Invariant Homomorphic Encryption Scheme We present our scale invariant L-homomorphic scheme as outlined in Section 1.2.  ... 
doi:10.1007/978-3-642-32009-5_50 fatcat:etjkft6ejjbjjpomwl7kd4kzwa

A Comprehensive Study of Fully Homomorphic Encryption Schemes

Majedah Alkharji, Mayyada Al Hammoshi, Hang Liu
2018 Figshare  
Homomorphic encryption schemes using public key algorithms.2. Fully homomorphic encryption (FHE) schemes.This work can be helpful as a guide to principles, properties of FHE  ...  [CLT'14] Coron, Lepoint, and Tibouchi -scale invariant FHE over the integers.  ...  On a broader scale, fully homomorphic encryption enhances the efficiency of protected multiparty computations [3] [18] .  ... 
doi:10.6084/m9.figshare.6667562 fatcat:kaoey2rfkjamddzeni24f5t3dm

A Regev-Type Fully Homomorphic Encryption Scheme Using Modulus Switching

Zhigang Chen, Jian Wang, Liqun Chen, Xinxia Song
2014 The Scientific World Journal  
A critical challenge in a fully homomorphic encryption (FHE) scheme is to manage noise. Modulus switching technique is currently the most efficient noise management technique.  ...  to the existing FHE researches in the literature.  ...  CXLX12 0162), the Fundamental Research Funds for the Central Universities, Ningbo Natural Science Foundation (no. 2012A610067), and the Chinese National Scholarship Fund and also appreciate the benefit  ... 
doi:10.1155/2014/983862 pmid:25093212 pmcid:PMC4100376 fatcat:zl3zfdigc5dstaefxk7ncdpify

A Survey of Homomorphic Encryption for Outsourced Big Data Computation

2016 KSII Transactions on Internet and Information Systems  
In this paper, homomorphic encryption is suggested as a mechanism to protect the confidentiality and privacy of outsourced data, while at the same time allowing third parties to perform computation on  ...  Finally, this paper discusses the current implementation, challenges, and future direction towards a practical homomorphic encryption scheme for securing outsourced Big Data computation.  ...  The author also thanks the anonymous reviewers of the paper for their careful reviews and valuable comments  ... 
doi:10.3837/tiis.2016.08.022 fatcat:plj6fns2l5b6xilzr3kmr3sw4u

Fully Homomophic Encryption over the Integers Revisited [chapter]

Jung Hee Cheon, Damien Stehlé
2015 Lecture Notes in Computer Science  
As a second contribution, we describe a new AGCD-based fully homomorphic encryption scheme, which outperforms all prior AGCD-based proposals: its security does not rely on the presumed hardness of the  ...  Two main computational problems serve as security foundations of current fully homomorphic encryption schemes: Regev's Learning With Errors problem (LWE) and Howgrave-Graham's Approximate Greatest Common  ...  The authors thank Miran Kim, Adeline Langlois, Yongsoo Song and Ron Steinfeld for helpful discussions. We thank Oded Regev for his sketch of the SILWE to ZDLWE reduction [43] .  ... 
doi:10.1007/978-3-662-46800-5_20 fatcat:dxposeaku5hhxpliomj2lsfq7q

Evaluation of homomorphic primitives for computations on encrypted data for CPS systems

Peizhao Hu, Tamalika Mukherjee, Alagu Valliappan, Stanisław Radziszowski
2016 2016 Smart City Security and Privacy Workshop (SCSP-W)  
Homomorphic Encryption (HE) offers a potential solution to safeguard privacy through cryptographic means while allowing the service providers to perform computations on the encrypted data.  ...  Throughout the process, only authorized users have access to the unencrypted data.  ...  One obvious observation is FV has similar or worser performance than the NLV scheme. This indicates that the scale invariants may not provide much of the performance gain over NLV.  ... 
doi:10.1109/scspw.2016.7509556 fatcat:bsmj4lr2lvaoxhll2ly4f7ioze

A quantum approach to homomorphic encryption [article]

Si-Hui Tan, Joshua A. Kettlewell, Yingkai Ouyang, Lin Chen, Joseph F. Fitzsimons
2015 arXiv   pre-print
Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on  ...  This fraction can be made arbitrarily close to unity with overhead scaling only polynomially in the message length.  ...  the encrypted data, thus bringing us closer to the goal of achieving a quantum fully homomorphic encryption scheme.  ... 
arXiv:1411.5254v3 fatcat:yy7pebuhqzdeffl2t5f3k4fhii

Comparative Analysis of Homomorphic Encryption Algorithms Based on Learning with Errors

Mikhail Babenko, Elena Golimblevskaia, Egor Shiriaev
2020 Proceedings of the Institute for System Programming of RAS  
Homomorphic encryption allows performing of arithmetic operations over encrypted text and obtaining an encrypted result that corresponds to the result of operations performed over plaintext.  ...  Homomorphic encryption is used for processing confidential data.  ...  Thus, the task is to find the most productive scheme of fully homomorphic encryption (FHE) [1] [2] .  ... 
doi:10.15514/ispras-2020-32(2)-4 fatcat:uk42jlsegfbybpgkqfzlctlwta

Adaptive Key Recovery Attacks on NTRU-Based Somewhat Homomorphic Encryption Schemes [chapter]

Ricardo Dahab, Steven Galbraith, Eduardo Morais
2015 Lecture Notes in Computer Science  
Such attacks show that one must be very careful about the use of homomorphic encryption in practice. The existence of a key recovery attack means that the scheme is not CCA1-secure.  ...  In this paper we present adaptive key recovery attacks on NTRU-based somewhat homomorphic encryption schemes. Among such schemes, we study the proposal by Bos et al [BLLN13] in 2013.  ...  Acknowledgements We thank Qiang Tang and the anonymous referees for helpful comments.  ... 
doi:10.1007/978-3-319-17470-9_17 fatcat:pw2ibfw5ubabrd5ldlo3jxubmu

Comprehensive Introduction to Fully Homomorphic Encryption for Dynamic Feedback Controller via LWE-based Cryptosystem [article]

Junsoo Kim and Hyungbo Shim and Kyoohyung Han
2019 arXiv   pre-print
Moreover, the LWE-based cryptosystem allows fully homomorphic arithmetics so that two encrypted variables can be added and multiplied without decrypting them.  ...  A key to the security of the LWE-based cryptosystem is the injection of random errors in the ciphertexts, which however hinders unlimited recursive operation of homomorphic arithmetics on ciphertexts due  ...  Acknowledgement The authors are grateful to Prof. Jung Hee Cheon and Dr. Yongsoo Song, Department of Mathematical Sciences, Seoul National University, for helpful discussions.  ... 
arXiv:1904.08025v1 fatcat:wrgosjc7njelxcyb7bxnxy73ta

Notes on non-interactive secure comparison in "image feature extraction in the encrypted domain with privacy-preserving SIFT"

Matthias Schneider, Thomas Schneider
2014 Proceedings of the 2nd ACM workshop on Information hiding and multimedia security - IH&MMSec '14  
(IEEE Transactions on Image Processing 2012) propose protocols for privacy-preserving computation of the scale-invariant feature transform (SIFT) in the encrypted domain.  ...  As alternatives we propose to use either interactive comparison protocols or non-interactive somewhat or fully homomorphic encryption.  ...  Acknowledgments We thank the anonymous reviewers of IH&MMSec'14 for their helpful comments. The second author was supported by the Ger-  ... 
doi:10.1145/2600918.2600927 dblp:conf/ih/SchneiderS14 fatcat:hifivsismre4law5jn6hpmmrp4

Input-Output History Feedback Controller for Encrypted Control with Leveled Fully Homomorphic Encryption [article]

Kaoru Teranishi, Tomonori Sadamoto, Kiminao Kogiso
2021 arXiv   pre-print
Although a fully homomorphic encryption scheme allows the evaluation of controller operations with encrypted data, an encrypted dynamic controller with the encryption scheme destabilizes a closed-loop  ...  A numerical simulation demonstrates the feasibility of the proposed encrypted control scheme, which inherits the control performance of the original controller at a sufficient level.  ...  Thus, encrypted dynamic controllers can be implemented using fully homomorphic encryption because the accumulation of scaling parameters can be removed by division over a ciphertext space.  ... 
arXiv:2109.10718v1 fatcat:ba3dzdydu5d7rooyqk44fde7py

Efficient Evaluation of Low Degree Multivariate Polynomials in Ring-LWE Homomorphic Encryption Schemes [chapter]

Sergiu Carpov, Oana Stan
2018 Lecture Notes in Computer Science  
Homomorphic encryption schemes allow to perform computations over encrypted data. In schemes based on RLWE assumption the plaintext data is a ring polynomial.  ...  In many use cases of homomorphic encryption only the degree-0 coefficient of this polynomial is used to encrypt data. In this context any computation on encrypted data can be performed.  ...  In [4] a notion of scale-invariance for leveled SHE schemes is introduced. In scale-invariant schemes a single modulus, q, is used for ciphertexts during the whole homomorphic evaluation.  ... 
doi:10.1007/978-3-319-99807-7_16 fatcat:u4owko7xqvc75oiadkq257e6eu

A Comparison of the Homomorphic Encryption Schemes FV and YASHE [chapter]

Tancrède Lepoint, Michael Naehrig
2014 Lecture Notes in Computer Science  
(resp. over lattices and over the integers).  ...  At Crypto 2012, Brakerski proposed the new notion of scale-invariance [Bra12] for leveled homomorphic encryption schemes.  ...  We thank the Africacrypt 2013 referees for their interesting reviews, and Frederik Vercauteren for insightful comments on batching.  ... 
doi:10.1007/978-3-319-06734-6_20 fatcat:emiit62dcbdsrnc46bc2wgk6wm
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