Skip to main content
SpringerLink
Log in
Book cover

Complexity of Lattice Problems

A Cryptographic Perspective

  • Book
  • © 2002

Overview

Authors:
  1. Daniele Micciancio

    1. University of California, San Diego, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Shafi Goldwasser

    1. The Massachusetts Institute of Technology, Cambridge, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: The Springer International Series in Engineering and Computer Science (SECS, volume 671)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Basics

    • Daniele Micciancio, Shafi Goldwasser
    Pages 1-22

  3. Approximation Algorithms

    • Daniele Micciancio, Shafi Goldwasser
    Pages 23-44

  4. Closest Vector Problem

    • Daniele Micciancio, Shafi Goldwasser
    Pages 45-68

  5. Shortest Vector Problem

    • Daniele Micciancio, Shafi Goldwasser
    Pages 69-90

  6. Sphere Packings

    • Daniele Micciancio, Shafi Goldwasser
    Pages 91-110

  7. Low-Degree Hypergraphs

    • Daniele Micciancio, Shafi Goldwasser
    Pages 111-124

  8. Basis Reduction Problems

    • Daniele Micciancio, Shafi Goldwasser
    Pages 125-142

  9. Cryptographic Functions

    • Daniele Micciancio, Shafi Goldwasser
    Pages 143-194

  10. Interactive Proof Systems

    • Daniele Micciancio, Shafi Goldwasser
    Pages 195-210

  11. Back Matter

    Pages 211-220
    Download chapter PDF
Back to top

Keywords

About this book

Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De­ spite their apparent simplicity, lattices hide a rich combinatorial struc­ ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap­ plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems.

Authors and Affiliations

  • University of California, San Diego, USA

    Daniele Micciancio

  • The Massachusetts Institute of Technology, Cambridge, USA

    Shafi Goldwasser

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation