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A STUDY OF SOME METHODS FOR FINDING SMALL ZEROS OF POLYNOMIAL CONGRUENCES APPLIED TO RSA
English

2016 Journal of Mathematical Sciences. Advances and Applications  
As an application, we study the security of public key cryptosystems. In particular, we study the RSA public key cryptosystem by making use of these methods.  ...  In this paper, we shall follow Håstad [28] , Coppersmith [16, 17] , and others to describe methods for finding small zeros of polynomial congruences.  ...  Acknowledgements The authors are grateful to the referees and the editors for the careful reading of the manuscript.  ... 
doi:10.18642/jmsaa_7100121630 fatcat:tai75dyztvhzrhmqa6h5p6q7ha

Implicit Factoring with Shared Most Significant and Middle Bits [chapter]

Jean-Charles Faugère, Raphaël Marinier, Guénaël Renault
2010 Lecture Notes in Computer Science  
Note also that the method absolutely requires that the shared bits be the least significant ones.  ...  Our contribution consists of a novel and rigorous lattice-based method that address the implicit factoring problem when p 1 and p 2 share most significant bits.  ... 
doi:10.1007/978-3-642-13013-7_5 fatcat:mt2ky53k4fg6bdzoshvpz2lyhe

On the Structure Analysis by X-Ray Diffraction

S. N. BAGCHI
1983 Zenodo  
theories and the equi­vocal nature of the results obtained by the methodologies usually adopted vis-a-vis the advantages of utilising the concepts and results of Unified Kinematic Theory of Diffrac­tion  ...  5550 Bellerive, Brossard, Quebec, J4Z 3C8, Canada The main purpose of this paper Is to draw the attention of specialists to the problems of structure analysis by pointing out the limitations of conventional  ...  all non-essential factors, (namely, factors depending on the experimental arrangement, Lorentz factors, absorption factor, • For comprehensive discussions and derivations see ref. 1.  ... 
doi:10.5281/zenodo.6348187 fatcat:aqbx7hwowfccjf7wts4ijtk5he

Moments of nucleon generalized parton distributions in lattice QCD

Ph. Hägler, J. W. Negele, D. B. Renner, W. Schroers, Th. Lippert, K. Schilling
2003 Physical Review D, Particles and fields  
constraints on the generalized form factors at a given virtuality, t.  ...  Hence, we present a novel approach that exploits the full information content from a given lattice configuration by measuring an overdetermined set of lattice observables to provide maximal statistical  ...  P.H. and W.S. are grateful for Feodor-Lynen Fellowships from the Alexander von Humboldt Foundation and thank the Center for Theoretical Physics at MIT for its hospitality.  ... 
doi:10.1103/physrevd.68.034505 fatcat:wcka22ktcjgcplu5mayll3bfxy

Page 992 of The Journal of Chemical Physics Vol. 23, Issue 6 [page]

1955 The Journal of Chemical Physics  
are reconstructed to exemplify the method, on the one hand, and to in- vestigate the nature of these combinatory factors from a unified standpoint, on the other.  ...  Hence, Pp > N;=N. 7=0 (B.1) If we denote the probability of appearance of a 7 mole- cule on a lattice point by x;, and that of a j-k pair of molecules on a pair of neighboring lattice points by y,,, we  ... 

Factoring N = p r q for Large r [chapter]

Dan Boneh, Glenn Durfee, Nick Howgrave-Graham
1999 Lecture Notes in Computer Science  
Hence, we obtain a new class of integers that can be efficiently factored. When r ≈ √ log p the algorithm is asymptotically faster than the Elliptic Curve Method.  ...  We present an algorithm for factoring integers of the form N = p r q for large r. Such integers were previously proposed for various cryptographic applications.  ...  Acknowledgments We thank Paul Zimmermann, Peter Montgomery and Bob Silverman for supplying the running times for ECM, and Don Coppersmith for several useful conversations.  ... 
doi:10.1007/3-540-48405-1_21 fatcat:z2uqauha4rcnvhouhqusu5fnkq

Cluster Gutzwiller method for bosonic lattice systems

Dirk-Sören Lühmann
2013 Physical Review A. Atomic, Molecular, and Optical Physics  
A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models.  ...  Due to the exact treatment within a cluster, the method can be effortlessly adapted to more complicated Hamiltonians in the fast progressing field of optical lattice experiments.  ...  by a factor of 8.  ... 
doi:10.1103/physreva.87.043619 fatcat:ogp2qm3jgzhqbmyp7z64jhjlle

Applications of the Feynman-Hellmann theorem in hadron structure [article]

A. J. Chambers, R. Horsley, Y. Nakamura, H. Perlt, D. Pleiter, P. E. L. Rakow, G. Schierholz, A. Schiller, H. Stüben, R. D. Young, J. M. Zanotti
2015 arXiv   pre-print
In particular, a FH-motivated method provides a new approach to calculations of disconnected contributions to matrix elements and high-momentum nucleon and pion form factors.  ...  Extending the FH relation to finite-momentum transfers, we also present calculations of the pion and nucleon electromagnetic form factors up to momentum transfers of around 7-8 GeV^2.  ...  Acknowledgments The numerical configuration generation was performed using the BQCD lattice QCD program, [21] , on the IBM BlueGeneQ using DIRAC 2 resources (EPCC, Edinburgh, UK), the BlueGene P and Q  ... 
arXiv:1511.07090v1 fatcat:rzsdhviusrb47kcewdcngxlw3i

A Simple Improvement for Integer Factorizations with Implicit Hints

Ryuichi HARASAWA, Heiwa RYUTO, Yutaka SUEYOSHI
2016 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
In this paper, we improve their method by increasing the determinant of the lattice obtained from the k RSA moduli. We see that, after our improvement, May et al.'  ...  May et al. reduced this problem to finding a shortest (or a relatively short) vector in the lattice of dimension k obtained from a given system of k RSA moduli, for which they applied Gaussian reduction  ...  Acknowledgments The authors thank the reviewers for their valuable comments which make this paper more valuable.  ... 
doi:10.1587/transfun.e99.a.1090 fatcat:fcpab2sw55ewhl7zrxmogitcr4

Extraction of the isovector magnetic form factor of the nucleon at zero momentum [article]

Constantia Alexandrou, Martha Constantinou, Giannis Koutsou, Konstantin Ottnad, Marcus Petschlies
2015 arXiv   pre-print
We present position space methods that rely on taking the derivative of relevant correlators to extract directly the magnetic form factor at zero momentum without the need to assume a functional form for  ...  These methods are explored on one ensemble using N_f=2+1+1 Wilson twisted mass fermions.  ...  Numerical calculations have used HPC resources from John von Neumann-Institute for Computing on the JUQUEEN and JUROPA systems at the research center in Jülich.  ... 
arXiv:1410.8818v2 fatcat:xjd3p6w6ijbgne64i4evenwlsi

Arbitrary Accuracy Integration Scheme for the Subsonic Doublet Lattice Method

Louw H. van Zyl
1998 Journal of Aircraft  
The approximation in the unsteady component places a restriction on the doublet lattice method in terms of box aspect ratio, which does not apply to the vortex lattice method.  ...  The downwash factors are calculated as the sum of the steady component, identical to that of the vortex lattice method, and an unsteady component.  ... 
doi:10.2514/2.2397 fatcat:2vii7osszbfb7h7dpxqflctybi

NPR determination of quark masses from the HISQ action [article]

Andrew T. Lytle, for the HPQCD Collaboration
2015 arXiv   pre-print
I report on a calculation of bilinear Z-factors needed for determining Z_m using non-perturbative renormalization (NPR) on n_f=2+1+1 HISQ ensembles. RI/MOM and RI/SMOM schemes are studied.  ...  These will provide an independent determination of quark masses in addition to other methods being used by the HPQCD collaboration.  ...  NPR method The MS renormalized quark mass is related to the bare lattice input mass m 0 , m MS (µ) = Z MS m (µ, 1/a) m 0 . (2.1) In practice it is difficult to compute the factor Z MS m (µ, 1/a) beyond  ... 
arXiv:1511.06547v1 fatcat:g65dn3eiwvgpdlwynicvs636pq

Calculation of Tracer and Chemical Diffusion Coefficients in the Intermetallic Compound β-AgMg

Irina V. Belova, Graeme E. Murch
2003 Defect and Diffusion Forum  
The method is demonstrated for the simple cubic one component lattice gas with nearest neighbour interactions.  ...  The new method gives results in good agreement with a Monte Carlo method based on Einsteinian expressions for the phenomenological coefficients.  ...  One of us (I.V.B.) wishes to thank the Australian Research Council for the award of a Professorial Fellowship.  ... 
doi:10.4028/www.scientific.net/ddf.224-225.45 fatcat:syaykvo32zhrlj2735ooyitvhq

AN IMPROVED MONTE CARLO METHOD APPLIED TO THE HEAT CONDUCTION ANALYSIS OF A PEBBLE WITH DISPERSED FUEL PARTICLES

Jae-Hoon Song, Nam-Zin Cho
2009 Nuclear Engineering and Technology  
A large scaling factor plays the additional role of reducing the extrapolation distance to a minimum, since the extrapolation distance is on the order of a mean free path.  ...  Based on the results in the previous section, temperature distributions were calculated using a scaling factor of 50.  ... 
doi:10.5516/net.2009.41.3.279 fatcat:rqqq6ws22nffhbgq6lw3dmotoe

|V_cd| and |V_cs| from Semileptonic and Leptonic decays using lattice QCD methods [article]

Heechang Na
2013 arXiv   pre-print
In this paper, we review recent calculations of the CKM matrix elements |V_cd| and |V_cs| from semileptonic and leptonic decays of D and D_s mesons using lattice QCD methods.  ...  lattice QCD is the only successful non-perturbative method.  ...  Current deviation is about 1.5 σ; however, if the errors on the leptonic determinations of |V cs | are reduced by a factor of two while the middle value stays as the current number, then the deviation  ... 
arXiv:1301.4515v1 fatcat:3rwgymx7enfgncdribaxe3iao4
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