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Bootstrappable Identity-Based Fully Homomorphic Encryption [chapter]

Michael Clear, Ciarán McGoldrick
2014 Lecture Notes in Computer Science  
It has been an open problem for a number of years to construct an identity-based fully homomorphic encryption (IBFHE) scheme (first mentioned by Naccache at CHES/CRYPTO 2010).  ...  In fact, a "compiler" was proposed in [7] to transform an LWE-based IBE satisfying certain properties into an identity-based (leveled) fully homomorphic encryption (IBFHE) scheme, and it was noted that  ...  We would like to especially thank one of the reviewers for suggesting an improvement to the attribute-based construction in Section 3.1 in addition to suggesting interesting directions for future work.  ... 
doi:10.1007/978-3-319-12280-9_1 fatcat:sajo7ysvovgvnm5r33hvstwewe

Shift-Type Homomorphic Encryption and Its Application to Fully Homomorphic Encryption [chapter]

Frederik Armknecht, Stefan Katzenbeisser, Andreas Peter
2012 Lecture Notes in Computer Science  
In particular, we are interested in currently existing fully homomorphic encryption (FHE) schemes and their common structures and security.  ...  It generalizes the already known notion of shift-type group homomorphic encryption.  ...  Fully Homomorphic Encryption (FHE) An encryption scheme E = (KeyGen, Enc, Dec, Eval) that is homomorphic for all circuits (in terms of Definition 1) is called fully homomorphic (FHE = Fully Homomorphic  ... 
doi:10.1007/978-3-642-31410-0_15 fatcat:gkpnthelvradddxzysjv6bd4c4

Computing Blindfolded: New Developments in Fully Homomorphic Encryption

Vinod Vaikuntanathan
2011 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science  
A fully homomorphic encryption scheme enables computation of arbitrary functions on encrypted data.  ...  Fully homomorphic encryption has long been regarded as cryptography's prized "holy grail" -extremely useful yet rather elusive.  ...  scheme -called a "bootstrappable" encryption schemeinto a fully homomorphic encryption scheme and finally, to connect the dots, a specialized method of turning the somewhat homomorphic scheme into a bootstrappable  ... 
doi:10.1109/focs.2011.98 dblp:conf/focs/Vaikuntanathan11 fatcat:pqg65eugr5ci7lwov7pgdeusn4

Efficient Fully Homomorphic Encryption from (Standard) LWE

Zvika Brakerski, Vinod Vaikuntanathan
2011 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science  
We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption.  ...  We show that "somewhat homomorphic" encryption can be based on LWE, using a new relinearization technique.  ...  fully homomorphic encryption based on Theorem 4.1 and Lemma 4.6.  ... 
doi:10.1109/focs.2011.12 dblp:conf/focs/BrakerskiV11 fatcat:tv5ku2ylmfcwlatnfrrgok5pre

Faster Fully Homomorphic Encryption [chapter]

Damien Stehlé, Ron Steinfeld
2010 Lecture Notes in Computer Science  
Gentry's Somewhat Homomorphic Encryption Scheme SomHom.  ...  Keywords: fully homomorphic encryption, ideal lattices, SSSP. and (π 1 + i 1 ) × (π 2 + i 2 ) are not larger than r Dec . This limits the degree of polynomials that can be evaluated homomorphically.  ...  Fully homomorphic encryption over the integers In [7] , van Dijk et al. describe another fully homomorphic scheme, whose security relies on the hardness of the Approximate Greatest Common Divisor Problem  ... 
doi:10.1007/978-3-642-17373-8_22 fatcat:aj5rnp2qj5dvjge5dktnqtpjri

Efficient Fully Homomorphic Encryption from (Standard) $\mathsf{LWE}$

Zvika Brakerski, Vinod Vaikuntanathan
2014 SIAM journal on computing (Print)  
A fully homomorphic encryption (FHE) scheme allows anyone to transform an encryption of a message, m, into an encryption of any (efficient) function of that message, f (m), without knowing the secret key  ...  We show that "somewhat homomorphic" encryption can be based on LWE, using a new relinearization technique.  ...  This allows them to implement our outline above to achieve fully homomorphic identity-based encryption, as well as fully homomorphic attribute-based encryption.  ... 
doi:10.1137/120868669 fatcat:dfegiyoylndyjnynxy5rwejzoa

More Practical Fully Homomorphic Encryption

Gu Chunsheng
2012 International Journal of Cloud Computing and Services Science (IJ-CLOSER)  
In this paper, we first modify the Smart-Vercauteren's fully homomorphic encryption scheme [1] by applying self-loop bootstrappable technique.  ...  The securities of our improving FHE's are respectively based on the hardness of factoring integer problem, solving Diophantine equation problem, and finding approximate greatest common divisor problem.  ...  Fully Homomorphic Encryption (FHE) In this section, we firstly construct a self-loop FHE based on the Smart-Vercauteren's SHE, and simply analyze the security of our scheme.  ... 
doi:10.11591/closer.v1i4.1438 fatcat:owzgmmyrmjgyfefskwh43ntmbq

Homomorphic Evaluation of Database Queries [article]

Sudharaka Palamakumbura, Hamid Usefi
2016 arXiv   pre-print
We propose a new database search technique that can be used with the ring-based fully homomorphic encryption scheme proposed by Braserski.  ...  Homomorphic encryption is an encryption method that enables computing over encrypted data.  ...  For example, using our Homomorphic Query Processing technique with the more recent ring based fully homomorphic encryption scheme proposed by Braserski et al.  ... 
arXiv:1606.03304v1 fatcat:gbhnf7j7sfe65kwkqa6lfkimaa

Homomorphic Encryption: Theory & Applications [article]

Jaydip Sen
2013 arXiv   pre-print
A significant number of propositions on fully homomorphic encryption is then discussed.  ...  The chapter then introduces the most important and recent research direction in the filed - fully homomorphic encryption.  ...  All known fully homomorphic encryption schemes are based on hardness of lattice problems.  ... 
arXiv:1305.5886v1 fatcat:agzyco4ehnfajiamrbp7qobo2a

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.  ...  The GSW cryptosystem was presented by Gentry et al. in [48] , together with some extensions such as identity-based FHE.  ...  Homomorphic commitments and signatures.  ... 
doi:10.1007/978-3-319-57048-8_5 fatcat:owa6tq4hl5aafmrrghnn5f6csq

STUDY OF LATTICE BASED FHE FOR CLOUD DATA SECURITY

Aarti Dadheech
2017 International Journal of Advanced Research in Computer Science  
In order to solve the problem of data security in cloud computing system, lattice-based cryptographic schemes implements the so called "Fully Homomorphic Encryption (FHE) scheme", which allows processing  ...  Fully homomorphic encryption is a good solution to enhance security measures of cloud system that handles critical data. This makes cloud computing more stable and solid.  ...  The other lattice based fully homomorphic encryption schemes are listed in Table 1 [10]. V.  ... 
doi:10.26483/ijarcs.v8i7.4573 fatcat:kk33lqjcdnbp7gh7uhrleowwym

Homomorphic encryption algorithms and schemes for secure computations in the cloud

Majedah Alkharji, Hang Liu
2018 Figshare  
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.  ...  A detailed survey of homomorphic encryption (HE) using public key algorithms such as RSA, El-Gamal, and Paillier algorithms.2.  ...  Gentry (2009) In late 2009, Craig Gentry, an employee of IBM invented the first encryption scheme that is fully homomorphic [3] , [18] based on ideal lattices.  ... 
doi:10.6084/m9.figshare.5996759.v1 fatcat:kunl4v6rynawjneutyvtttptpa

Fully Homomorphic Encryption over the Integers [chapter]

Marten van Dijk, Craig Gentry, Shai Halevi, Vinod Vaikuntanathan
2010 Lecture Notes in Computer Science  
We describe a very simple "somewhat homomorphic" encryption scheme using only elementary modular arithmetic, and use Gentry's techniques to convert it into a fully homomorphic scheme.  ...  over encrypted data.  ...  Making the Scheme Fully Homomorphic We follow Gentry's approach [7] for constructing a fully homomorphic encryption scheme from a somewhat homomorphic scheme E that is bootstrappable as per Definition  ... 
doi:10.1007/978-3-642-13190-5_2 fatcat:esp5ueyd35esvc5otyxnoxllyi

Lattice-based FHE as secure as PKE

Zvika Brakerski, Vinod Vaikuntanathan
2014 Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14  
We show that (leveled) fully homomorphic encryption (FHE) can be based on the hardness of O(n 1.5+ )-approximation for lattice problems (such as GapSVP) under quantum reductions for any > 0 (or O(n 2+  ...  This matches the best known hardness for "regular" (non-homomorphic) lattice based public-key encryption up to the factor.  ...  For all > 0, there exist: • A bootstrappable homomorphic encryption scheme based on the worst-case quantum hardness of solving GapSVP O(n 1.5+ ) and SIVP O(n 1.5+ ) . • A bootstrappable homomorphic encryption  ... 
doi:10.1145/2554797.2554799 dblp:conf/innovations/BrakerskiV14 fatcat:n5awft54cnewjigr6ymmyqqhjm

Homomorphic Encryption — Theory and Application [chapter]

Jaydip Sen
2013 Theory and Practice of Cryptography and Network Security Protocols and Technologies  
Toward Basing Fully Homomorphic Encryption on Worst-Case Hardness.  ...  Fully Secure Functional Encryption: Attribute-Based Encryption and (Hierarchical) Inner Product Encryption.  ... 
doi:10.5772/56687 fatcat:amgaohpdbnal3ly6nsx4nvasmm
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