(Leveled) fully homomorphic encryption without bootstrapping

  title={(Leveled) fully homomorphic encryption without bootstrapping},
  author={Zvika Brakerski and Craig Gentry and Vinod Vaikuntanathan},
  booktitle={Information Technology Convergence and Services},
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… 

Bootstrapping Fully Homomorphic Encryption with Ring Plaintexts Within Polynomial Noise

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

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

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

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

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

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

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

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) $\mathsf{LWE}$

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 )

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.



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

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

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

  • Craig GentryS. Halevi
  • 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

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

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

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

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

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).