5,065 research outputs found
Optimization of Bootstrapping in Circuits
In 2009, Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme, an extremely powerful cryptographic primitive that enables to perform computations, i.e., to evaluate circuits, on encrypted data without decrypting them first. This has many applications, in particular in cloud computing.
In all currently known FHE schemes, encryptions are associated to some (non-negative integer) noise level, and at each evaluation of an AND gate, the noise level increases. This is problematic because decryption can only work if the noise level stays below some maximum level at every gate of the circuit. To ensure that property, it is possible to perform an operation called _bootstrapping_ to reduce the noise level. However, bootstrapping is time-consuming and has been identified as a critical operation. This motivates a new problem in discrete optimization, that of choosing where in the circuit to perform bootstrapping operations so as to control the noise level; the goal is to minimize the number of bootstrappings in circuits.
In this paper, we formally define the _bootstrap problem_, we design a polynomial-time -approximation algorithm using a novel method of rounding of a linear program, and we show a matching hardness result: -inapproximability for any
Readiness of Quantum Optimization Machines for Industrial Applications
There have been multiple attempts to demonstrate that quantum annealing and,
in particular, quantum annealing on quantum annealing machines, has the
potential to outperform current classical optimization algorithms implemented
on CMOS technologies. The benchmarking of these devices has been controversial.
Initially, random spin-glass problems were used, however, these were quickly
shown to be not well suited to detect any quantum speedup. Subsequently,
benchmarking shifted to carefully crafted synthetic problems designed to
highlight the quantum nature of the hardware while (often) ensuring that
classical optimization techniques do not perform well on them. Even worse, to
date a true sign of improved scaling with the number of problem variables
remains elusive when compared to classical optimization techniques. Here, we
analyze the readiness of quantum annealing machines for real-world application
problems. These are typically not random and have an underlying structure that
is hard to capture in synthetic benchmarks, thus posing unexpected challenges
for optimization techniques, both classical and quantum alike. We present a
comprehensive computational scaling analysis of fault diagnosis in digital
circuits, considering architectures beyond D-wave quantum annealers. We find
that the instances generated from real data in multiplier circuits are harder
than other representative random spin-glass benchmarks with a comparable number
of variables. Although our results show that transverse-field quantum annealing
is outperformed by state-of-the-art classical optimization algorithms, these
benchmark instances are hard and small in the size of the input, therefore
representing the first industrial application ideally suited for testing
near-term quantum annealers and other quantum algorithmic strategies for
optimization problems.Comment: 22 pages, 12 figures. Content updated according to Phys. Rev. Applied
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Enabling Secure Database as a Service using Fully Homomorphic Encryption: Challenges and Opportunities
The database community, at least for the last decade, has been grappling with
querying encrypted data, which would enable secure database as a service
solutions. A recent breakthrough in the cryptographic community (in 2009)
related to fully homomorphic encryption (FHE) showed that arbitrary computation
on encrypted data is possible. Successful adoption of FHE for query processing
is, however, still a distant dream, and numerous challenges have to be
addressed. One challenge is how to perform algebraic query processing of
encrypted data, where we produce encrypted intermediate results and operations
on encrypted data can be composed. In this paper, we describe our solution for
algebraic query processing of encrypted data, and also outline several other
challenges that need to be addressed, while also describing the lessons that
can be learnt from a decade of work by the database community in querying
encrypted data
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
Array-based architecture for FET-based, nanoscale electronics
Advances in our basic scientific understanding at the molecular and atomic level place us on the verge of engineering designer structures with key features at the single nanometer scale. This offers us the opportunity to design computing systems at what may be the ultimate limits on device size. At this scale, we are faced with new challenges and a new cost structure which motivates different computing architectures than we found efficient and appropriate in conventional very large scale integration (VLSI). We sketch a basic architecture for nanoscale electronics based on carbon nanotubes, silicon nanowires, and nano-scale FETs. This architecture can provide universal logic functionality with all logic and signal restoration operating at the nanoscale. The key properties of this architecture are its minimalism, defect tolerance, and compatibility with emerging bottom-up nanoscale fabrication techniques. The architecture further supports micro-to-nanoscale interfacing for communication with conventional integrated circuits and bootstrap loading
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