PPT-Lattice Sparsification and the Approximate Closest Vector Problem

Author : aaron | Published Date : 2018-09-22

Daniel Dadush Centrum Wiskunde en Informatica Joint work with Gabor Kun Renyi Institute Outline Norms Lattices and Lattice Problems Shortest amp Closest Vector

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Lattice Sparsification and the Approximate Closest Vector Problem: Transcript

Daniel Dadush Centrum Wiskunde en Informatica Joint work with Gabor Kun Renyi Institute Outline Norms Lattices and Lattice Problems Shortest amp Closest Vector Problems SVP CVP. Band structure. Content. Lattice structure. Lattice symmetry. Reciprocal lattice. Brillouin. zone. Schrodinger equation . Bloch theorem. Tight-binding method. Lattice structure. Solid state has lattice structure.. We show how randomized rounding can be applied to finding the closest lattice vector. Given the basis of a lattice, and given a vector x not in the lattice, the heuristic will with high probability fi Determinantal. Assignment Problem. John . Leventides. . City University London. &. University of Athens. Tensor . Approximations (1). Rank 1 approximation of . tensors. An object of . parameters . Voronoi. Graph. and the. Closest Vector Problem with Preprocessing. Daniel . Dadush. Centrum . Wiskunde. . en. . Informatica. Joint . work with . Nicolas . Bonifas. (. École. . Polytechnique. . Can We Solve Ideal Lattice Problems Efficiently?. Craig Gentry. IBM T.J. Watson. Workshop on Lattices with Symmetry. Can we efficiently break lattices with certain types of symmetry?. If a lattice has an orthonormal basis, can we find it?. 4.2 Written Algorithms For Whole-Number Operations. An Overview of the Topics . Define what an algorithm is.. Discuss the importance of place value and . distributivity. in whole number operations.. China Summer School on Lattices and Cryptography, June 2014. Starting Point: Linear Equations. Easy to solve a linear system of equations. Given . A. , . b. , find . s. S. olved using Gaussian elimination, Cramer rule, etc.. Robert Krauthgamer, . Weizmann Institute of Science. WorKer. 2015, . Nordfjordeid. TexPoint. fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. Graph . Sparsification. time. via Discrete Gaussian Sampling. . Divesh. Aggarwal. École . Polytechnique Fédérale . de . Lausanne (. EPFL). Daniel . Dadush. Centrum . Wiskunde. . en. . Informatica. (CWI). Noah Stephens-. China Summer School on Lattices and Cryptography, June 2014. Starting Point: Linear Equations. Easy to solve a linear system of equations. Given . A. , . b. , find . s. S. olved using Gaussian elimination, Cramer rule, etc.. Craig Gentry. IBM T.J. Watson. Workshop on Lattices with Symmetry. Can we efficiently break lattices with certain types of symmetry?. If a lattice has an orthonormal basis, can we find it?. Can we break “ideal lattices” – lattices for ideals in number fields – by combining geometry with algebra?. . Lyubashevsky. INRIA / ENS, Paris. Outline. LLL sketch. Application to Subset Sum. Application to SIS. Application to LWE. Lattice Reduction in Practice. Small Integer Solution. Problem (SIS). Learning With Errors. Bravais lattice, real lattice vector . R. , reciprocal lattice vector . K. , point group, space group, group representations, Bloch theorem. Discrete lattices. 1D. 2D. 3D. a. Bravais lattice: each unit cell has only one atom (5 types in 2D). MENA 3100: . Diff. Linear defects. https://. www.ndeed.org/EducationResources/CommunityCollege/Materials/Structure/linear_defects.htm. Dislocations are areas were the atoms are out of position in the crystal structure. .

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