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Complexity of Lattice Problems: A Cryptographic Perspective(671 The Springer International Series in Engineering and Computer Science)

Complexity of Lattice Problems: A Cryptographic Perspective(671 The Springer International Series in Engineering and Computer Science)


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About the Book

This book presents a self-contained overview of the state of the art in the complexity of lattice problems, with particular emphasis on problems that are related to the construction of cryptographic functions. Specific topics covered are the strongest known inapproximability result for the shortest vector problem; the relations between this and other computational lattice problems; an exposition of how cryptographic functions can be built and prove secure based on worst-case hardness assumptions about lattice problems; and a study of the limits of non-approximability of lattice problems. Some background in complexity theory, but no prior knowledge about lattices, is assumed. This is a useful reference for those researching ways in which lattice problems can be used to build cryptographic systems. It could also be of interest to those working in computational complexity, combinatorics, and foundations of cryptography.

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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Product Details
  • ISBN-13: 9780792376880
  • Publisher: Kluwer Academic Publishers
  • Publisher Imprint: Kluwer Academic Publishers
  • Height: 235 mm
  • No of Pages: 220
  • Returnable: Y
  • Sub Title: A Cryptographic Perspective
  • ISBN-10: 0792376889
  • Publisher Date: 31 Mar 2002
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 671 The Springer International Series in Engineering and Computer Science
  • Width: 155 mm


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Complexity of Lattice Problems: A Cryptographic Perspective(671 The Springer International Series in Engineering and Computer Science)
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Complexity of Lattice Problems: A Cryptographic Perspective(671 The Springer International Series in Engineering and Computer Science)
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