5 research outputs found
A Survey on Homomorphic Encryption Schemes: Theory and Implementation
Legacy encryption systems depend on sharing a key (public or private) among
the peers involved in exchanging an encrypted message. However, this approach
poses privacy concerns. Especially with popular cloud services, the control
over the privacy of the sensitive data is lost. Even when the keys are not
shared, the encrypted material is shared with a third party that does not
necessarily need to access the content. Moreover, untrusted servers, providers,
and cloud operators can keep identifying elements of users long after users end
the relationship with the services. Indeed, Homomorphic Encryption (HE), a
special kind of encryption scheme, can address these concerns as it allows any
third party to operate on the encrypted data without decrypting it in advance.
Although this extremely useful feature of the HE scheme has been known for over
30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE)
scheme, which allows any computable function to perform on the encrypted data,
was introduced by Craig Gentry in 2009. Even though this was a major
achievement, different implementations so far demonstrated that FHE still needs
to be improved significantly to be practical on every platform. First, we
present the basics of HE and the details of the well-known Partially
Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which
are important pillars of achieving FHE. Then, the main FHE families, which have
become the base for the other follow-up FHE schemes are presented. Furthermore,
the implementations and recent improvements in Gentry-type FHE schemes are also
surveyed. Finally, further research directions are discussed. This survey is
intended to give a clear knowledge and foundation to researchers and
practitioners interested in knowing, applying, as well as extending the state
of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the
survey that is being submitted to ACM CSUR and has been uploaded to arXiv for
feedback from stakeholder
cuHE: A Homomorphic Encryption Accelerator Library
We introduce a CUDA GPU library to accelerate evaluations with homomorphic schemes defined over polynomial rings enabled with a number of optimizations including algebraic techniques for efficient evaluation, memory minimization techniques, memory and thread scheduling and low level CUDA hand-tuned assembly optimizations to take full advantage of the mass parallelism and high memory bandwidth GPUs offer. The arithmetic functions constructed to handle very large polynomial operands using number-theoretic transform (NTT) and Chinese remainder theorem (CRT) based methods are then extended to implement the primitives of the leveled homomorphic encryption scheme proposed by Löpez-Alt, Tromer and Vaikuntanathan. To compare the performance of the proposed CUDA library we implemented two applications: the Prince block cipher and homomorphic sorting algorithms on two GPU platforms in single GPU and multiple GPU configurations. We observed a speedup of 25 times and 51 times over the best previous GPU implementation for Prince with single and triple GPUs, respectively. Similarly for homomorphic sorting we obtained 12-41 times speedup depending on the number and size of the sorted elements
Blind Web Search: How far are we from a privacy preserving search engine?
Recent rapid progress in fully homomorphic encryption (FHE) and somewhat homomorphic encryption (SHE) has catalyzed renewed efforts to develop efficient privacy preserving protocols. Several works have already appeared in the literature that provide solutions to these problems by employing FHE or SHE techniques.
In this work, we focus on a natural application where privacy is a major concern: web search. An estimated 5 billion web queries are processed by the world\u27s leading search engines each day. It is no surprise, then, that
privacy-preserving web search was proposed as the paragon FHE application in Gentry\u27s seminal FHE paper.
Indeed, numerous proposals have emerged in the intervening years that attack various privatized search problems over encrypted user data, e.g. private information retrieval (PIR). Yet, there is no known work that focuses on implementing a completely blind web search engine using an FHE/SHE construction. In this work, we focus first
on single keyword queries with exact matches, aiming toward real-world viability. We then discuss multiple-keyword
searches and tackle a number of issues currently hindering practical implementation,
such as communication and computational efficiency
Flattening NTRU for Evaluation Key Free Homomorphic Encryption
We propose a new FHE scheme {\sf F-NTRU} that adopts the flattening technique proposed in GSW to derive an NTRU based scheme that (similar to GSW) does not require evaluation keys or key switching. Our scheme eliminates the decision small polynomial ratio (DSPR) assumption but relies only on the standard R-LWE assumption. It uses wide key distributions, and hence is immune to the Subfield Lattice Attack. In practice, our scheme achieves competitive timings compared to the existing schemes. We are able to compute a homomorphic multiplication in ~msec and ~msec for and levels, respectively, without amortization. Furthermore, our scheme features small ciphertexts, e.g. ~KB for levels, and eliminates the need for storing and managing costly evaluation keys.
In addition, we present a slightly modified version of F-NTRU that is capable to support integer operations with a very large message space along with noise analysis for all cases. The assurance gained by using wide key distributions along with the message space flexibility of the scheme, i.e. bits, binary polynomials, and integers with a large message space, allows the use of the proposed scheme in a wide array of applications
Comparison between Subfield and Straightforward Attacks on NTRU
Recently in two independent papers, Albrecht, Bai and Ducas and Cheon, Jeong and Lee presented two
very similar attacks, that allow to break NTRU with larger parameters and GGH Multinear Map without
zero encodings. They proposed an algorithm for recovering the NTRU secret key given the public key
which apply for large NTRU modulus, in particular to Fully Homomorphic Encryption schemes based on
NTRU. Hopefully, these attacks do not endanger the security of the NTRUE NCRYPT scheme, but shed new
light on the hardness of this problem. The basic idea of both attacks relies on decreasing the dimension
of the NTRU lattice using the multiplication matrix by the norm (resp. trace) of the public key in some
subfield instead of the public key itself. Since the dimension of the subfield is smaller, the dimension of
the lattice decreases, and lattice reduction algorithm will perform better.
Here, we revisit the attacks on NTRU and propose another variant that is simpler and outperforms both
of these attacks in practice. It allows to break several concrete instances of YASHE, a NTRU-based FHE
scheme, but it is not as efficient as the hybrid method of Howgrave-Graham on concrete parameters of
NTRU. Instead of using the norm and trace, we propose to use the multiplication by the public key in
some subring and show that this choice leads to better attacks. We
√ can then show that for power of two
cyclotomic fields, the time complexity is polynomialFinally, we show that, under
heuristics, straightforward lattice reduction is even more efficient, allowing to extend this result to fields
without non-trivial subfields, such as NTRU Prime. We insist that the improvement on the analysis applies
even for relatively small modulus ; though if the secret is sparse, it may not be the fastest attack. We also
derive a tight estimation of security for (Ring-)LWE and NTRU assumptions. when