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Fully homomorphic encryption using ideal lattices
 In Proc. STOC
, 2009
"... We propose a fully homomorphic encryption scheme – i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result – that, to construct an encryption scheme that permits evaluation of arbitra ..."
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Cited by 663 (17 self)
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that is represented as a lattice), as needed to evaluate general circuits. Unfortunately, our initial scheme is not quite bootstrappable – i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than
Closest Point Search in Lattices
 IEEE TRANS. INFORM. THEORY
, 2000
"... In this semitutorial paper, a comprehensive survey of closestpoint search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closestpoint search algorithm, ba ..."
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Cited by 333 (2 self)
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theoretical comparison with the Kannan algorithm and an experimental comparison with the Pohst algorithm and its variants, such as the recent ViterboBoutros decoder. The improvement increases with the dimension of the lattice. Modifications of the algorithm are developed to solve a number of related search
Experimental verification of a negative index of refraction,”
 Science,
, 2001
"... Abstract: We studied a twodimensional squarelattice photonic crystal with allangle negative refraction at its first band. Using this photonic crystal, we designed and fabricated a flat lens functioning as a cylindrical lens by increasing the vertical dimension of the photonic crystal. Twodimensi ..."
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Cited by 377 (9 self)
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Abstract: We studied a twodimensional squarelattice photonic crystal with allangle negative refraction at its first band. Using this photonic crystal, we designed and fabricated a flat lens functioning as a cylindrical lens by increasing the vertical dimension of the photonic crystal
The Optimal Lattice Quantizer in Three Dimensions
, 1983
"... The bodycentered cubic lattice is shown to have the smallest mean squared error of any lattice quantizer in three dimensions, assuming that the input to the quantizer has a uniform distribution. ..."
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Cited by 33 (7 self)
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The bodycentered cubic lattice is shown to have the smallest mean squared error of any lattice quantizer in three dimensions, assuming that the input to the quantizer has a uniform distribution.
Image Representation Using 2D Gabor Wavelets
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1996
"... This paper extends to two dimensions the frame criterion developed by Daubechies for onedimensional wavelets, and it computes the frame bounds for the particular case of 2D Gabor wavelets. Completeness criteria for 2D Gabor image representations are important because of their increasing role in man ..."
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Cited by 375 (4 self)
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This paper extends to two dimensions the frame criterion developed by Daubechies for onedimensional wavelets, and it computes the frame bounds for the particular case of 2D Gabor wavelets. Completeness criteria for 2D Gabor image representations are important because of their increasing role
SCALING DIMENSIONS OF LATTICE QUANTIZED GRAVITY
, 2001
"... I discuss a model for quantized gravitation based on the simplicial lattice discretization. It has been studied in detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are consistent with a value for the universal critical exponent for gr ..."
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I discuss a model for quantized gravitation based on the simplicial lattice discretization. It has been studied in detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are consistent with a value for the universal critical exponent
Quantization of Fourform Fluxes and Dynamical Neutralization Of The Cosmological Constant
, 2000
"... A fourform gauge flux makes a variable contribution to the cosmological constant. This has often been assumed to take continuous values, but we argue that it has a generalized Dirac quantization condition. For a single flux the steps are much larger than the observational limit, but we show that wi ..."
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Cited by 274 (21 self)
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A fourform gauge flux makes a variable contribution to the cosmological constant. This has often been assumed to take continuous values, but we argue that it has a generalized Dirac quantization condition. For a single flux the steps are much larger than the observational limit, but we show
Optimization of Lattices for Quantization
 IEEE Trans. Inform. Theory
, 1998
"... A training algorithm for the design of lattices for vector quantization is presented. The algorithm uses a steepest descent method to adjust a generator matrix, in the search for a lattice whose Voronoi regions have minimal normalized second moment. The numerical elements of the found generator matr ..."
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Cited by 12 (2 self)
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A training algorithm for the design of lattices for vector quantization is presented. The algorithm uses a steepest descent method to adjust a generator matrix, in the search for a lattice whose Voronoi regions have minimal normalized second moment. The numerical elements of the found generator
The Optimal Isodual Lattice Quantizer in Three Dimensions
, 2006
"... The meancentered cuboidal (or m.c.c.) lattice is known to be the optimal packing and covering among all isodual threedimensional lattices. In this note we show that it is also the best quantizer. It thus joins the isodual lattices Z, A2 and (presumably) D4, E8 and the Leech lattice in being simult ..."
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The meancentered cuboidal (or m.c.c.) lattice is known to be the optimal packing and covering among all isodual threedimensional lattices. In this note we show that it is also the best quantizer. It thus joins the isodual lattices Z, A2 and (presumably) D4, E8 and the Leech lattice in being
Asymptotic Analysis Of LatticeBased Quantization
, 1998
"... this paper, we find asymptotic expressions for aN and DN for a class of generalized Gaussian sources. Past work on the optimal support of uniform scalar quantization, which is lattice quantization in one dimension, has included numerical optimization [3, 4] and curve fitting [5][8]. Nonlinear equat ..."
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Cited by 2 (0 self)
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this paper, we find asymptotic expressions for aN and DN for a class of generalized Gaussian sources. Past work on the optimal support of uniform scalar quantization, which is lattice quantization in one dimension, has included numerical optimization [3, 4] and curve fitting [5][8]. Nonlinear
Results 1  10
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5,715