# A Guide to Fully Homomorphic Encryption

@article{Armknecht2015AGT, title={A Guide to Fully Homomorphic Encryption}, author={Frederik Armknecht and Colin Boyd and Christopher Carr and Kristian Gj{\o}steen and Angela J{\"a}schke and Christian A. Reuter and Martin Strand}, journal={IACR Cryptol. ePrint Arch.}, year={2015}, volume={2015}, pages={1192} }

Fully homomorphic encryption (FHE) has been dubbed the holy grail of cryptography, an elusive goal which could solve the IT world’s problems of security and trust. Research in the area exploded after 2009 when Craig Gentry showed that FHE can be realised in principle. Since that time considerable progress has been made in finding more practical and more efficient solutions. Whilst research quickly developed, terminology and concepts became diverse and confusing so that today it can be difficult…

## 143 Citations

Fully homomorphic encryption with applications to electronic voting

- Computer Science
- 2018

Fully homomorphic encryption (FHE) has been dubbed the holy grail of cryptography, an elusive goal which could solve the IT world’s problems of security and trust. Research in the area exploded after…

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- Computer Science, MathematicsICETE
- 2018

This work shows how to construct a distributed fully homomorphic identity-based encryption secure in the continual auxiliary input model based on the fully Homomorphic scheme of Gentry, Sahai and Waters and relies merely on the learning with errors assumption, which is conjectured being resistant against quantum attacks.

Key-Recovery Attacks Against Somewhat Homomorphic Encryption Schemes

- Computer Science, Mathematics
- 2017

In 1978, Rivest, Adleman and Dertouzos introduced the concept of privacy homomorphism and Gentry gave a positive answer in his seminal paper at STOC 2009, by proposing an ingenious approach to construct fully homomorphic encryption (FHE) schemes.

An Overview on Homomorphic Encryption Algorithms

- Computer Science, Mathematics
- 2019

The concepts that support modern homomorphic encryption schemes, together with the description of some FHE schemes, are presented and some practical applications for processing sensitive data are presented.

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- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2016

It is proved that fully homomorphic schemes are impossible for several algebraic structures, and a conjecture stating that secure FHE schemes must either have a significant ciphertext expansion or use unusual algebraic structure is proposed.

A Survey on Homomorphic Encryption Schemes: Theory and Implementation

- Computer Science, Mathematics
- 2017

The basics of HE and the details of the well-known Partially Homomorphic Encryption and Somewhat HomomorphicEncryption, which are important pillars of achieving FHE, are presented and the main FHE families, which have become the base for the other follow-up FHE schemes are presented.

Verifiable Computing from Fully Homomorphic Encryption

- Computer Science, Mathematics
- 2017

This chapter discusses approaches to verifiable computing that use fully homomorphic encryption (FHE) as a building block and describes the verifiable Computing schemes using this primitive, i.e. the client encrypts the data before it outsources it to the server.

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- Computer Science2020 IEEE International Conference on Big Data (Big Data)
- 2020

This article focuses on how HE and data science can be leveraged to design and develop privacy-preserving enterprise applications and proposes a survey of main Homomorphic Encryption techniques and recent advances in the conubium between data science and HE.

Privacypreservingdistributed optimizationusing homomorphic encryption ?

- Computer Science, Mathematics
- 2018

Novel algorithms are proposed which can achieve secure multiparty computation with perfect correctness and the correctness and computational efficiency are verified by two case studies of power systems, one on a demand response problem and the other on an optimal power flow problem.

The Handling of Noise and Security of Two Fully Homomorphic Encryption Schemes

- Computer Science, Mathematics
- 2017

Noise is introduced as a means to ensure security of encryption schemes in general, and fully homomorphic encryption schemes in particular. Strategies to control the growth of this and thereby…

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