Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an
important discipline that is not only the subject of an enormous amount of research, but …

Public key cryptography is a major interdisciplinary subject with many real-world
applications, such as digital signatures. A strong background in the mathematics underlying …

We report on improved practical algorithms for lattice basis reduction. We propose a
practical floating point version of the L 3-algorithm of Lenstra, Lenstra, Lovász (1982). We …

Abstract At Eurocrypt 2010 van Dijk et al. described a fully homomorphic encryption scheme
over the integers. The main appeal of this scheme (compared to Gentry's) is its conceptual …

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 …

Our objective in writing this book was to produce a general, introductory textbook on the
subject of combinatorial algorithms. Several textbooks on combinatorial algorithms were …

波動方程式 が音響物理の 基礎で あ る こ とは誰で も知って い る. そ の波動方程式 は数の
連続性 を前提 とする数学に属 して い る. 数論 (Number Theory) は整数 (すなわち離散的な数) …

Zero-knowledge proofs were introduced in 1985, in a paper by Goldwasser, Micali and
Rackoff ([6]). Their practical significance was soon demonstrated in the work of Fiat and …

Lattice enumeration algorithms are the most basic algorithms for solving hard lattice
problems such as the shortest vector problem and the closest vector problem, and are often …

We give deterministic~ O (22n+ o (n))-time algorithms to solve all the most important
computational problems on point lattices in NP, including the Shortest Vector Problem …