The Springer International Series in Engineering and Compute ...

Daniele Micciancio

• 31 maart 2002
• 9780792376880

Samenvatting:

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.



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.