764 research outputs found
The Quantum Frontier
The success of the abstract model of computation, in terms of bits, logical
operations, programming language constructs, and the like, makes it easy to
forget that computation is a physical process. Our cherished notions of
computation and information are grounded in classical mechanics, but the
physics underlying our world is quantum. In the early 80s researchers began to
ask how computation would change if we adopted a quantum mechanical, instead of
a classical mechanical, view of computation. Slowly, a new picture of
computation arose, one that gave rise to a variety of faster algorithms, novel
cryptographic mechanisms, and alternative methods of communication. Small
quantum information processing devices have been built, and efforts are
underway to build larger ones. Even apart from the existence of these devices,
the quantum view on information processing has provided significant insight
into the nature of computation and information, and a deeper understanding of
the physics of our universe and its connections with computation.
We start by describing aspects of quantum mechanics that are at the heart of
a quantum view of information processing. We give our own idiosyncratic view of
a number of these topics in the hopes of correcting common misconceptions and
highlighting aspects that are often overlooked. A number of the phenomena
described were initially viewed as oddities of quantum mechanics. It was
quantum information processing, first quantum cryptography and then, more
dramatically, quantum computing, that turned the tables and showed that these
oddities could be put to practical effect. It is these application we describe
next. We conclude with a section describing some of the many questions left for
future work, especially the mysteries surrounding where the power of quantum
information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information
Technology to Advance Society to be published by CRC Press. Concepts
clarified and style made more uniform in version 2. Many thanks to the
referees for their suggestions for improvement
Fast polynomial arithmetic in homomorphic encryption with cyclo-multiquadratic fields
This work provides refined polynomial upper bounds for the condition number
of the transformation between RLWE/PLWE for cyclotomic number fields with up to
6 primes dividing the conductor. We also provide exact expressions of the
condition number for any cyclotomic field, but under what we call the twisted
power basis. Finally, from a more practical perspective, we discuss the
advantages and limitations of cyclotomic fields to have fast polynomial
arithmetic within homomorphic encryption, for which we also study the RLWE/PLWE
equivalence of a concrete non-cyclotomic family of number fields. We think this
family could be of particular interest due to its arithmetic efficiency
properties
Implementation of Spatial Domain Homomorphic Filtering on Embedded Mobile Devices
This paper describes the analysis of the Homomorphic filtering algorithm, the equivalency between the frequency and spatial-domain methods and the implementation of low-pass and high-pass spatial domain Homomorphic filter in low power embedded devices. It is shown that the Homomorphic filter in the spatial domain combines the sensitivity of local/neighbourhood operations in addition to Laplacian-type edge enhancement, averaging operation of illumination intensity estimation, in addition to dynamic range compression associated with frequency-domain Homomorphic filters. A qualitative and quantitative comparison of the image results confirms the validity of the theoretical approach and advantages for digital hardware implementation. The developed filters are implemented on a Java-enabled mobile phone and form a low cost embedded image processing enhancement system.http://dx.doi.org/10.4314/njt.v34i2.1
Efficiently processing complex-valued data in homomorphic encryption
We introduce a new homomorphic encryption scheme that is natively capable of computing with complex numbers. This is done by generalizing recent work of Chen, Laine, Player and Xia, who modified the Fan–Vercauteren scheme by replacing the integral plaintext modulus t by a linear polynomial X − b. Our generalization studies plaintext moduli of the form Xm + b. Our construction significantly reduces the noise growth in comparison to the original FV scheme, so much deeper arithmetic circuits can be homomorphically executed
SoK: Fully Homomorphic Encryption Accelerators
Fully Homomorphic Encryption~(FHE) is a key technology enabling
privacy-preserving computing. However, the fundamental challenge of FHE is its
inefficiency, due primarily to the underlying polynomial computations with high
computation complexity and extremely time-consuming ciphertext maintenance
operations. To tackle this challenge, various FHE accelerators have recently
been proposed by both research and industrial communities. This paper takes the
first initiative to conduct a systematic study on the 14 FHE accelerators --
cuHE/cuFHE, nuFHE, HEAT, HEAX, HEXL, HEXL-FPGA, 100, F1, CraterLake,
BTS, ARK, Poseidon, FAB and TensorFHE. We first make our observations on the
evolution trajectory of these existing FHE accelerators to establish a
qualitative connection between them. Then, we perform testbed evaluations of
representative open-source FHE accelerators to provide a quantitative
comparison on them. Finally, with the insights learned from both qualitative
and quantitative studies, we discuss potential directions to inform the future
design and implementation for FHE accelerators
Faster Homomorphic Discrete Fourier Transforms and Improved FHE Bootstrapping
In this work, we propose a faster homomorphic linear transform algorithm for structured matrices such as the discrete Fourier transform (DFT) and linear transformations in bootstrapping.
First, we proposed new method to evaluate the DFT homomorphically for a given packed ciphertext from the Cooley-Tukey fast Fourier transform algorithm. While the previous method requires rotations and constant vector multiplications, our method only needs rotations/multiplications by consuming depth for the length of input vector .
Second, we apply the same method to the linear transform of bootstrapping for . To achieve this, we construct a recursive relation of matrices in those linear transformations. Accordingly, we can highly accelerate the linear transformation part of bootstrapping: the number of homomorphic operations becomes logarithmic to the number of slots, as in homomorphic DFT.
We also implement both algorithms. Our homomorphic DFT with length only takes about 8 seconds which is about 150 times faster result than previous one. The bootstrapping for with our linear transform algorithm takes about 2 minutes for plaintext space with 8 bit precision, which takes 26 hours using the previous method
Accelerating Number Theoretic Transformations for Bootstrappable Homomorphic Encryption on GPUs
Homomorphic encryption (HE) draws huge attention as it provides a way of
privacy-preserving computations on encrypted messages. Number Theoretic
Transform (NTT), a specialized form of Discrete Fourier Transform (DFT) in the
finite field of integers, is the key algorithm that enables fast computation on
encrypted ciphertexts in HE. Prior works have accelerated NTT and its inverse
transformation on a popular parallel processing platform, GPU, by leveraging
DFT optimization techniques. However, these GPU-based studies lack a
comprehensive analysis of the primary differences between NTT and DFT or only
consider small HE parameters that have tight constraints in the number of
arithmetic operations that can be performed without decryption. In this paper,
we analyze the algorithmic characteristics of NTT and DFT and assess the
performance of NTT when we apply the optimizations that are commonly applicable
to both DFT and NTT on modern GPUs. From the analysis, we identify that NTT
suffers from severe main-memory bandwidth bottleneck on large HE parameter
sets. To tackle the main-memory bandwidth issue, we propose a novel
NTT-specific on-the-fly root generation scheme dubbed on-the-fly twiddling
(OT). Compared to the baseline radix-2 NTT implementation, after applying all
the optimizations, including OT, we achieve 4.2x speedup on a modern GPU.Comment: 12 pages, 13 figures, to appear in IISWC 202
A Homomorphic Interpretation of the Complex Fm Expansion
A Complex Frequency Modulation (FM) signal is one whose instantaneous phase is time-varying according to a
complicated dynamic function. This paper commences with the standard expansion for the spectrum of a Complex FM
signal. It then explains how this can be interpreted in terms of a series of convolutions. The Homomorphic processing framework, in essence, provides a means by which a convolution operation can be related to a product operation which can then be transformed into an addition. This is very useful as it offers an approach for the fast computation of the theoretical spectra of complex FM signals, and further then leads to a cepstrum-like representation that will only display the modulation indices of the FM components. ‘Liftering’ of this representation can be carried out to alter the
proportion of modulation components in the FM signal. Examples of the various stages of this processing will be given to illustrate its usefulness in the analysis and synthesis Complex FM signals
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