Complexity of Lattice Problems: A Cryptographic Perspective

Micciancio (U. of California, San Diego) and Goldwasser (Massachusetts Institute of Technology) introduce lattices, deceptively simple geometric objects that can be pictorially depicted as the set of intersection points of an infinite, regular n-dimensional grid. Their rich combinatoratorial structure has attracted mathematicians and computer scientists working on diverse applications from number theory to cryptography. Following Atjai's lead, the authors focus on designing cryptographic functions that are as difficult to break as solving a computationally hard lattice problem. After introducing the basics of point lattices, complexity theory, and Minkowski's theorems, they venture into specific types of algorithmic problems (e.g., shortest vector, closest vector, and basis reduction problems). The final chapters delve into cryptographic functions and interactive proof systems. Annotation c. Book News, Inc., Portland, OR (booknews.com)