Complexity of Lattice Problems

A Cryptographic Perspective

[Cover] [Cover (Japanese)]

Authors: Daniele Micciancio and Shafi Goldwasser
Springer International Series in Engineering and Computer Science, vol. 671.
Springer, March 2002, 220 pages
ISBN 0-7923-7688-9

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Also available at [Amazon] and [Barnes&Noble].


Complexity of Lattice Problems: A Cryptographic Perspective is an essential reference for those researching ways in which lattice problems can be used to build cryptographic systems. It will also be of interest to those working in computational complexity, combinatorics, and foundations of cryptography.

The 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 proven 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.

The aim of the authors is to make lattice-based cryptography accessible to a wide audience, ultimately yielding further research and applications. Complexity of Lattice Problems: A Cryptographic Perspective will be valuable to anyone working in this fast-moving field. It serves as an excellent reference, providing insight into some of the most challenging issues being examined today.