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Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes [chapter]

N. P. Smart, F. Vercauteren
2010 Lecture Notes in Computer Science  
We present a fully homomorphic encryption scheme which has both relatively small key and ciphertext size.  ...  For the somewhat homomorphic scheme the public and private keys consist of two large integers (one of which is shared by both the public and private key) and the ciphertext consists of one large integer  ...  Introduction A fully homomorphic public key encryption scheme has been a "holy grail" of cryptography for a very long time.  ... 
doi:10.1007/978-3-642-13013-7_25 fatcat:fghljlbbh5bfddhkdk2yr4s7cm

Simulation Study Based on Somewhat Homomorphic Encryption

Jing Yang, Mingyu Fan, Guangwei Wang, Zhiyin Kong
2014 Journal of Computer and Communications  
the relationship between the length of plaintext and ciphertext size.  ...  This paper for the Gentry's Somewhat Homomorphic Encryption scheme for the simulation research, in clear text size within a certain range simulation was Somewhat Homomorphic Encryption scheme, and presents  ...  [6] such as using Gentry fully homomorphic encryption idea, put forward the key and the cipher text with relatively small size of the solution, to improve the efficiency; Stehle and others optimized  ... 
doi:10.4236/jcc.2014.22019 fatcat:ooq223luhjgzfi7vmsu7f4bfny

Privacy-Preserving Oriented Floating-Point Number Fully Homomorphic Encryption Scheme

Shuangjie Bai, Geng Yang, Jingqi Shi, Guoxiu Liu, Zhaoe Min
2018 Security and Communication Networks  
We encrypt a matrix of plaintext bits as a single ciphertext to reduce the ciphertext expansion ratio and reduce the public key size by encrypting with a quadratic form in three types of public key elements  ...  Compared to other schemes, our FFHE scheme is more practical for privacy-preserving in the cloud environment with its low ciphertext expansion ratio and public key size, supporting multiple operation types  ...  ), and Postdoctoral Science Foundation Project of China (2016M601859).  ... 
doi:10.1155/2018/2363928 fatcat:dnf4nm7fbfebvfconueifmidr4

Fully Homomorphic Encryption, Approximate Lattice Problem and LWE

Gu Chunsheng
2012 International Journal of Cloud Computing and Services Science (IJ-CLOSER)  
Then, we construct two new fully homomorphic encryption scheme (FHE) based on respectively approximate principal ideal lattice problem with related modulus (APIP-RM) and approximate lattice problem with  ...  Next, we propose two ALP-based public key encryption schemes.  ...  Smart and Vercauteren [SV10] presented a fully homomorphic encryption scheme with both relatively small key bits , ciphertext size bits and computation per gate at least operations, which is in some  ... 
doi:10.11591/closer.v2i1.1339 fatcat:mh57rvnjq5bxzgnk36vasmfmgu

Generalized Bootstrapping Technique Based on Block Equality Test Algorithm

Xiufeng Zhao, Ailan Wang
2018 Security and Communication Networks  
The key problem of achieving fully homomorphic encryption is how to reduce the increasing noise during the ciphertext evaluation.  ...  Fully homomorphic encryption can be used to protect the privacy of cloud data and solve the trust problem of third party.  ...  In PKC 2010, Smart and Vercauteren [7] proposed a variant of Gentry's scheme with relatively small key and ciphertext sizes.  ... 
doi:10.1155/2018/9325082 fatcat:6kjeirfwqfd5dgdn2ryajz2w64

Homomorphic Encryption [chapter]

Shai Halevi
2017 Tutorials on the Foundations of Cryptography  
Fully homomorphic encryption (FHE) has been called the "Swiss Army knife of cryptography", since it provides a single tool that can be uniformly applied to many cryptographic applications.  ...  In this tutorial we study FHE and describe its different properties, relations with other concepts in cryptography, and constructions.  ...  Homomorphic commitments and signatures.  ... 
doi:10.1007/978-3-319-57048-8_5 fatcat:owa6tq4hl5aafmrrghnn5f6csq

Ciphertext-Only Attack on an Image Homomorphic Encryption Scheme with Small Ciphertext Expansion

Yunyu Li, Jiantao Zhou, Yuanman Li
2015 Proceedings of the 23rd ACM international conference on Multimedia - MM '15  
The paper "An Efficient Image Homomorphic Encryption Scheme with Small Ciphertext Expansion" (In Proc.  ...  ACM MM'13, pp.803-812) presented a novel image homomorphic encryption approach achieving significant reduction of the ciphertext expansion.  ...  CONCLUSIONS In this paper, we have analyzed the security problem of a recently published image homomorphic encryption scheme with small ciphertext expansion.  ... 
doi:10.1145/2733373.2806406 dblp:conf/mm/LiZL15 fatcat:plu47jas5fevriszy4dmwqzlc4

Somewhat homomorphic encryption scheme for arithmetic operations on large integers

Pedro Silveira Pisa, Michel Abdalla, Otto Carlos Muniz Bandeira Duarte
2012 2012 Global Information Infrastructure and Networking Symposium (GIIS)  
ciphertext and plaintext sizes is similar to that of the original scheme.  ...  Homomorphic encryption allows for processing encrypted data without the need to decrypt them. This technique aggregates privacy and security for data processing in unreliable environments.  ...  On the other hand, fully homomorphic encryption schemes allow both addition and multiplication.  ... 
doi:10.1109/giis.2012.6466769 dblp:conf/giis/PisaAD12 fatcat:qd2v53zpijbcdofnfu22s5ft3a

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  ...  Vercauteren, "Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes", In Proceedings of PKC'10 the 13th international conference on Practice and Theory in Public Key Cryptography,  ...  work, and the complexity of these cryptosystems. 1 st Improvement of Gentry's scheme with a small key and ciphertext size, using "principalideal lattices."  ... 
doi:10.6084/m9.figshare.6667562 fatcat:kaoey2rfkjamddzeni24f5t3dm

Challenges of Fully Homomorphic Encryptions for the Internet of Things

Licheng WANG, Jing LI, Haseeb AHMAD
2016 IEICE transactions on information and systems  
most of them suffer from the problems of inefficient key size and noisy restraining.  ...  of the so-called fully homomorphic encryption (FHE).  ...  At PKC 2010, Smart and Vercauteren [46] proposed an FHE scheme, which offers the both relatively small key and ciphertext size.  ... 
doi:10.1587/transinf.2015ini0003 fatcat:zx3mj3425fbb5exactwj4sm3fm

Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based [chapter]

Craig Gentry, Amit Sahai, Brent Waters
2013 Lecture Notes in Computer Science  
We describe a comparatively simple fully homomorphic encryption (FHE) scheme based on the learning with errors (LWE) problem.  ...  In previous schemes, the homomorphic evaluator needs to obtain the user's "evaluation key", which consists of a chain of encrypted secret keys. Our scheme has no evaluation key.  ...  We also thank Boaz Barak and the anonymous CRYPTO reviewers for their many helpful comments.  ... 
doi:10.1007/978-3-642-40041-4_5 fatcat:fqwzglav2fhy7olktxlob536jq

Batch Fully Homomorphic Encryption over the Integers [chapter]

Jung Hee Cheon, Jean-Sébastien Coron, Jinsu Kim, Moon Sung Lee, Tancrède Lepoint, Mehdi Tibouchi, Aaram Yun
2013 Lecture Notes in Computer Science  
(DGHV) into a batch fully homomorphic encryption scheme, i.e. to a scheme that supports encrypting and homomorphically processing a vector of plaintexts as a single ciphertext.  ...  We extend the fully homomorphic encryption scheme over the integers of van Dijk et al.  ...  We would like to thank Taekyoung Kwon and Hyung Tae Lee for valuable comments. The first, third, and fourth authors were  ... 
doi:10.1007/978-3-642-38348-9_20 fatcat:gwhzg2zjezghheitk3hkbucmvy

Homomorphic encryption algorithms and schemes for secure computations in the cloud

Majedah Alkharji, Hang Liu
2018 Figshare  
A detailed survey of homomorphic encryption (HE) using public key algorithms such as RSA, El-Gamal, and Paillier algorithms.2.  ...  Fully homomorphic encryption (FHE) schemes.This work can be helpful as a guide to principles, properties of FHE as researchers believe in the possibility of advancement in the FHE area.  ...  small key and ciphertext size.  ... 
doi:10.6084/m9.figshare.5996759.v1 fatcat:kunl4v6rynawjneutyvtttptpa

Exploring the Application of Homomorphic Encryption to a Cross Domain Solution

Cody Tinker, Kevin Millar, Alan Kaminsky, Michael Kurdziel, Marcin Lukowiak, Stanislaw Radziszowski
2019 MILCOM 2019 - 2019 IEEE Military Communications Conference (MILCOM)  
Other fully homomorphic encryption schemes and techniques should be explored. The YASHE scheme is designed in a way to keep ciphertext and key elements small.  ...  Fully Homomorphic Encryption Schemes Preliminaries and Notation Both the message space and ciphertext space of the schemes are defined with some relation to the ring R.  ...  The trade-off in both systems compared to the original is that the metadata must now be encrypted and transferred under YASHE  ... 
doi:10.1109/milcom47813.2019.9021015 dblp:conf/milcom/TinkerMKKLR19 fatcat:bl7lqxfxhbbk7p565eoawahbpu

Toward Scalable Fully Homomorphic Encryption Through Light Trusted Computing Assistance [article]

Wenhao Wang, Yichen Jiang, Qintao Shen, Weihao Huang, Hao Chen, Shuang Wang, XiaoFeng Wang, Haixu Tang, Kai Chen, Kristin Lauter, Dongdai Lin
2019 arXiv   pre-print
TEEFHE, the hybrid system we designed, makes it possible for homomorphic computations to be performed on smaller ciphertext and secret key, providing better performance and lower memory consumption.  ...  While fully homomorphic encryption (FHE) is a promising technique that allows computations performed on the encrypted data, it suffers from a significant slow down to the computation.  ...  TEEFHE not only offers a speed-up to the bootstrapping operation, but also enables the somewhat homomorphic encryption to be bootstrappable with small secret key and ciphertext (and thus accelerates basic  ... 
arXiv:1905.07766v1 fatcat:e5h56qsfoneyzlob2wlzg4j6fi
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