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Four dimensional GallantLambertVanstone scalar multiplication
, 2001
"... The GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) computes any multiple kP of a point P of prime order n lying on an elliptic curve with a lowdegree endomorphism Φ (called GLV curve) over Fp as kP = k1P + k2Φ(P), with max{k1, k2} ≤ C1 n for some explicit constant C1> 0. Recent ..."
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Cited by 22 (4 self)
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The GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) computes any multiple kP of a point P of prime order n lying on an elliptic curve with a lowdegree endomorphism Φ (called GLV curve) over Fp as kP = k1P + k2Φ(P), with max{k1, k2} ≤ C1 n for some explicit constant C1> 0
Sica F.: Fourdimensional GallantLambertVanstone scalar multiplication. ArXiv:1106.5149
, 2011
"... Abstract. The GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) computes any multiple kP of a point P of prime order n lying on an elliptic curve with a lowdegree endomorphism Φ (called GLV curve) over Fp as kP = k1P + k2Φ(P), with max{k1, k2} ≤ C1 n for some explicit constant C1> 0 ..."
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Cited by 2 (0 self)
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Abstract. The GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) computes any multiple kP of a point P of prime order n lying on an elliptic curve with a lowdegree endomorphism Φ (called GLV curve) over Fp as kP = k1P + k2Φ(P), with max{k1, k2} ≤ C1 n for some explicit constant C1>
Analysis of the GallantLambertVanstone Method based on Efficient Endomorphisms: Elliptic and Hyperelliptic Curves
, 2002
"... In this work we analyse the GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) which uses a fast endomorphism # with minimal polynomial X + rX + s to compute any multiple kP of a point P of order n lying on an elliptic curve. First we ..."
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Cited by 11 (3 self)
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In this work we analyse the GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) which uses a fast endomorphism # with minimal polynomial X + rX + s to compute any multiple kP of a point P of order n lying on an elliptic curve. First we
Analysis of the GallantLambertVanstone Method based on Efficient Endomorphisms: Elliptic and Hyperelliptic Curves Francesco Sica?, Mathieu Ciet?, and JeanJacques Quisquater
"... kP = k1P + k2\Phi (P), with max{k1, k2} < = p1 + r  + spn. Next we improve on this bound and give the best constant in the given examples for the quantity supk,n max{k1, k2}/pn. Independently Park, Jeong, Kim, and Lim (PKC 2002) have given similar but slightly weaker bounds. Finally we ..."
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kP = k1P + k2\Phi (P), with max{k1, k2} < = p1 + r  + spn. Next we improve on this bound and give the best constant in the given examples for the quantity supk,n max{k1, k2}/pn. Independently Park, Jeong, Kim, and Lim (PKC 2002) have given similar but slightly weaker bounds. Finally we provide the first explicit bounds for the GLV method generalised to hyperelliptic curves as described in Park, Jeong and Lim (EUROCRYPT 2002).
Liouville Correlation Functions from Fourdimensional Gauge Theories
 SIMONS CENTER FOR GEOMETRY AND PHYSICS, STONY BROOK UNIVERSITY
, 2009
"... We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N = 2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture ..."
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Cited by 394 (22 self)
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We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N = 2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0, 1.
The string dual of a confining fourdimensional gauge theory
, 2000
"... We study N = 1 gauge theories obtained by adding finite mass terms to N = 4 YangMills theory. The Maldacena dual is nonsingular: in each of the many vacua, there is an extended brane source, arising from Myers’ dielectric effect. The source consists of one or more (p,q) 5branes. In particular, the ..."
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Cited by 359 (8 self)
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We study N = 1 gauge theories obtained by adding finite mass terms to N = 4 YangMills theory. The Maldacena dual is nonsingular: in each of the many vacua, there is an extended brane source, arising from Myers’ dielectric effect. The source consists of one or more (p,q) 5branes. In particular, the confining vacuum contains an NS5brane; the confining flux tube is a fundamental string bound to the 5brane. The system admits a simple quantitative description as a perturbation of a state on the N = 4 Coulomb branch. Various nonperturbative phenomena, including flux tubes, baryon vertices, domain walls, condensates and instantons, have new, quantitatively precise, dual descriptions. We also briefly consider two QCDlike theories. Our method extends to the nonsupersymmetric case. As expected, the N = 4 matter cannot be decoupled within the supergravity regime.
FourDimensional GLV via the Weil Restriction
"... The GallantLambertVanstone (GLV) algorithm uses efficiently computable endomorphisms to accelerate the computation of scalar multiplication of points on an abelian variety. Freeman and Satoh proposed for cryptographic use two families of genus 2 curves defined over Fp which have the property that ..."
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Cited by 5 (0 self)
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The GallantLambertVanstone (GLV) algorithm uses efficiently computable endomorphisms to accelerate the computation of scalar multiplication of points on an abelian variety. Freeman and Satoh proposed for cryptographic use two families of genus 2 curves defined over Fp which have the property
Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE TRANS IMAGE PROCESSING
, 2003
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 514 (17 self)
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vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each
Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization
, 1993
"... The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to a ..."
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Cited by 610 (15 self)
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The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified
Recovering High Dynamic Range Radiance Maps from Photographs
"... We present a method of recovering high dynamic range radiance maps from photographs taken with conventional imaging equipment. In our method, multiple photographs of the scene are taken with different amounts of exposure. Our algorithm uses these differently exposed photographs to recover the respon ..."
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Cited by 856 (15 self)
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We present a method of recovering high dynamic range radiance maps from photographs taken with conventional imaging equipment. In our method, multiple photographs of the scene are taken with different amounts of exposure. Our algorithm uses these differently exposed photographs to recover
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