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Author:   Daniele Micciancio ,  Shafi Goldwasser
Publisher:   Springer
Imprint:   Springer
Edition:   2002 ed.
Volume:   671
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   1.130kg
ISBN:  

9780792376880

ISBN 10:   0792376889
Pages:   220
Publication Date:   31 March 2002
Audience:   College/higher education ,  Professional and scholarly ,  General/trade ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

1 Basics.- 1 Lattices.- 2 Computational problems.- 3 Notes.- 2. Approximation Algorithms.- 1 Solving SVP in dimension.- 2 Approximating SVP in dimension n.- 3 Approximating CVP in dimension n.- 4 Notes.- 3. Closest Vector Problem.- 1 Decision versus Search.- 2 NP-completeness.- 3 SVP is not harder than CVP.- 4 Inapproximability of CVP.- 5 CVP with preprocessing.- 6 Notes.- 4. Shortest Vector Problem.- 1 Kannan’s homogenization technique.- 2 The Ajtai-Micciancio embedding.- 3 NP-hardnessofSVP.- 4 Notes.- 5. Sphere Packings.- 1 Packing Points in Small Spheres.- 2 The Exponential Sphere Packing.- 3 Integer Lattices.- 4 Deterministic construction.- 5 Notes.- 6. Low-Degree Hypergraphs.- 1 Sauer’s Lemma.- 2 Weak probabilistic construction.- 3 Strong probabilistic construction.- 4 Notes.- 7. Basis Reduction Problems.- 1 Successive minima and Minkowski’s reduction.- 2 Orthogonality defect and KZ reduction.- 3 Small rectangles and the covering radius.- 4 Notes.- 8. Cryptographic Functions.- 1 General techniques.- 2 Collision resistant hash functions.- 3 Encryption Functions.- 4 Notes.- 9. Interactive Proof Systems.- 1 Closest vector problem.- 2 Shortest vector problem.- 3 Treating other norms.- 4 What does it mean?.- 5 Notes.- References.

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