# (Leveled) fully homomorphic encryption without bootstrapping

@inproceedings{Brakerski2012LeveledFH,
title={(Leveled) fully homomorphic encryption without bootstrapping},
author={Zvika Brakerski and Craig Gentry and Vinod Vaikuntanathan},
booktitle={Information Technology Convergence and Services},
year={2012}
}
• Published in
Information Technology…
8 January 2012
• Computer Science, Mathematics
We present a novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), without Gentry's bootstrapping procedure. Specifically, we offer a choice of FHE schemes based on the learning with error (LWE) or ring-LWE (RLWE) problems that have 2…
1,792 Citations

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## References

SHOWING 1-10 OF 32 REFERENCES

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

• Computer Science, Mathematics
CRYPTO
• 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.

### Better Bootstrapping in Fully Homomorphic Encryption

• Computer Science, Mathematics
Public Key Cryptography
• 2012
A simpler approach that bypasses the homomorphic modular-reduction bottleneck to some extent, by working with a modulus very close to a power of two, and allows to store the encryption of the secret key as a single ciphertext, thus reducing the size of the public key.

### Fully Homomorphic Encryption without Squashing Using Depth-3 Arithmetic Circuits

• Computer Science, Mathematics
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
• 2011
A new blueprint for FHE is described, showing how to eliminate the squashing step, and thereby eliminate the need to assume that the sparse subset sum problem (SSSP) is hard, as all previous leveled FHE schemes have done.

### Efficient Fully Homomorphic Encryption from (Standard) LWE

• Computer Science, Mathematics
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
• 2011
A new dimension-modulus reduction technique is introduced, which shortens the cipher texts and reduces the decryption complexity of the scheme, showing that somewhat homomorphic'' encryption can be based on LWE, using a new re-linearization technique.

### Fully homomorphic encryption using ideal lattices

This work proposes a fully homomorphic encryption scheme that allows one to evaluate circuits over encrypted data without being able to decrypt, and describes a public key encryption scheme using ideal lattices that is almost bootstrappable.

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

• Computer Science, Mathematics
EUROCRYPT
• 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.

### Fully Homomorphic Encryption over the Integers with Shorter Public Keys

• Mathematics, Computer Science
IACR Cryptol. ePrint Arch.
• 2011
It is shown that fully homomorphic encryption can be implemented using simple arithmetic operations, and some optimizations from the recent Gentry-Halevi implementation of Gentry's scheme are obtained, roughly the same level of efficiency.

### Fully Homomorphic Encryption with Polylog Overhead

• Computer Science, Mathematics
EUROCRYPT
• 2011
This work presents a construction of fully homomorphic encryption schemes that for security parameter λ can evaluate any width-Ω(λ) circuit with t gates in time t· polylog(λ), and introduces permuting/routing techniques to move plaintext elements across these vectors efficiently.

### Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP

A new tensoring technique for LWE-based fully homomorphic encryption that uses the same modulus throughout the evaluation process no need for "modulus switching", and this modulus can take arbitrary form.

### Ring Switching in BGV-Style Homomorphic Encryption

• Mathematics, Computer Science
SCN
• 2012
This work generalizes and extends the basic ring-switching operation used by Brakerski, Gentry and Vaikuntanathan to work over any cyclotomic ring and shows how it can be used not only for bootstrapping but also during the computation itself (in conjunction with the "packed ciphertext" techniques of Gentry, Halevi and Smart).