# (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} }

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

### Bootstrapping Fully Homomorphic Encryption with Ring Plaintexts Within Polynomial Noise

- Computer Science, MathematicsProvSec
- 2017

This paper provides a polynomial noise bootstrapping method for the BGV scheme with ring plaintexts that allows users to choose any plaintext modulus \(p>1\) and any modulusPolynomial \(\varPhi (X) for theBGV scheme.

### FDFB: Full Domain Functional Bootstrapping Towards Practical Fully Homomorphic Encryption

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- 2021

A bootstrapping algorithm, which embeds a lookup table and evaluates arbitrary functions of the plaintext while reducing the noise, is shown, which can efficiently convert between arithmetic and boolean plaintexts and extend the plain text space using the Chinese remainder theorem.

### Efficient Bootstrapping for Approximate Homomorphic Encryption with Non-Sparse Keys

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- 2020

This work presents a bootstrapping procedure for the full-RNS variant of the approximate homomorphic-encryption scheme of Cheon et al., CKKS, and proposes a generic algorithm for homomorphic polynomial-evaluation that takes into account the approximate rescaling and is optimal in level consumption.

### Better Bootstrapping in Fully Homomorphic Encryption

- Computer Science, MathematicsPublic 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.

### 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.

### On the Minimal Number of Bootstrappings in Homomorphic Circuits

- Computer Science, MathematicsFinancial Cryptography Workshops
- 2013

A method to compute the exact minimal number of bootstrappings required to homomorphic evaluate any circuit, leading to a 88% faster homomorphic evaluation of AES for any 2-level FHE scheme and an extended algorithm for l max -level encryption with arbitrary l max ≥ 2 to cope with more recent FHE schemes.

### Optimization of Bootstrapping in Circuits

- Computer Science, MathematicsSODA
- 2017

The bootstrapping problem is formally defined, a polynomial-time $L$-approximation algorithm is designed using a novel method of rounding of a linear program, and a matching hardness result is shown: $(L-\epsilon)-inapproximability for any $\ep silon>0$.

### Efficient identity-based leveled fully homomorphic encryption from RLWE

- Mathematics, Computer ScienceSecur. Commun. Networks
- 2016

The security analysis shows that the proposed identity-based leveled FHE scheme is selective-ID secure against chosen-plaintext attacks in the random oracle model and the efficiency analysis and simulation results show that it is much more efficient than Gentry's and Wang's identity- based cryptosystems based on the learning with errors assumption.

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

- Computer Science, MathematicsSIAM J. Comput.
- 2014

It is shown that “somewhat homomorphic” encryption can be based on $\mathsf{LWE}$, using a new relinearization technique, and the security of the scheme is based on the worst-case hardness of “short vector problems” on arbitrary lattices.

### On FHE Without Bootstrapping ( Informal )

- Computer Science, Mathematics
- 2013

This work proposes an IND-CPA secure symmetric key homomorphic encryption scheme using multivariate polynomial ring over finite fields and gives a method of constructing a CPA secure homomorphicryption scheme from another symmetric deterministic CPASecure scheme.

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