# 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…

## 147 Citations

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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.

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- 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.

### Fully homomorphic encryption must be fat or ugly?

- 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.

### On the IND-CCA1 Security of FHE Schemes

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2021

This paper grouped the SHE schemes into broad categories based on their similarities and underlying hardness problems, and concluded that none of the proposed schemes were IND-CCA1-secure and that the known general constructions all had their shortcomings.

### Accelerating Homomorphic Computations on Rational Numbers

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This work has shown that not only the FHE schemes themselves contribute to the slowdown, but also the choice of data encoding, so there is a huge interest in improving the performance of applying FHE to concrete use cases.

### 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.

## References

SHOWING 1-10 OF 67 REFERENCES

### FHEW: Bootstrapping Homomorphic Encryption in Less Than a Second

- Computer Science, MathematicsEUROCRYPT
- 2015

A new method to homomorphically compute simple bit operations, and refresh (bootstrap) the resulting output, which runs on a personal computer in just about half a second, and is presented on the performance of the prototype implementation.

### Fully Homomorphic Encryption without bootstrapping

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2015

This book provides the new fully homomorphic encryption scheme without “bootstrapping” which runs fast for practical use and is immune from the attacks by the quantum computers.

### Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages

- Computer Science, MathematicsCRYPTO
- 2011

A somewhat homomorphic encryption scheme that is both very simple to describe and analyze, and whose security reduces to the worst-case hardness of problems on ideal lattices using the RLWE assumption, which allows us to completely abstract out the lattice interpretation.

### On the Relationship between Functional Encryption, Obfuscation, and Fully Homomorphic Encryption

- Computer Science, MathematicsIMACC
- 2013

It is shown that RFEs constructed in this way can be used to construct FHE schemes thereby establishing a relation between the FHE and FE primitives.

### Can homomorphic encryption be practical?

- Computer Science, MathematicsCCSW '11
- 2011

A proof-of-concept implementation of the recent somewhat homomorphic encryption scheme of Brakerski and Vaikuntanathan, whose security relies on the "ring learning with errors" (Ring LWE) problem, and a number of application-specific optimizations to the encryption scheme, including the ability to convert between different message encodings in a ciphertext.

### Practical applications of homomorphic encryption

- Computer Science, MathematicsCCSW '12
- 2012

This talk will survey the current state of the art and the trade-offs when using homomorphic encryption, and highlight scenarios and functionality where homomorphic encrypted data can be used to enable private versions of some basic machine learning algorithms.

### Faster Fully Homomorphic Encryption

- Computer Science, MathematicsASIACRYPT
- 2010

Two improvements to Gentry’s fully homomorphic scheme based on ideal lattices are described: a more aggressive analysis of one of the hardness assumptions and a probabilistic decryption algorithm that can be implemented with an algebraic circuit of low multiplicative degree.

### Homomorphic Encryption with Access Policies: Characterization and New Constructions

- Mathematics, Computer ScienceAFRICACRYPT
- 2013

The main construction is an XOR-homomorphic IBE scheme based on the quadratic residuosity problem (variant of the Cocks’ scheme), which is shown to be strongly homomorphic and achieved anonymity for a weaker notion of homomorphic encryption, which is called non-universal.

### Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers

- Mathematics, Computer ScienceEUROCRYPT
- 2012

A compression technique that reduces the public key size of van Dijk, Gentry, Halevi and Vaikuntanathan's (DGHV) fully homomorphic scheme over the integers from O(λ7) to O( λ5) remains semantically secure, but in the random oracle model.

### Implementing Gentry's Fully-Homomorphic Encryption Scheme

- Computer Science, MathematicsEUROCRYPT
- 2011

A working implementation of a variant of Gentry's fully homomorphic encryption scheme, similar to the variant used in an earlier implementation effort by Smart and Vercauteren (PKC 2010), with a number of optimizations that allow it to implement all aspects of the scheme, including the bootstrapping functionality.