Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 3
CVP Algorithm
Lecturer: Oded Regev
Scribe: Eyal Kaplan
In this lecture, we describe an approximation algorithm to the Closest Vector Problem (CVP).
This algorithm, known as the Nearest
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 8
2O(n) -time algorithm for SVP
Lecturer: Oded Regev
Scribe: Michael Khanevsky
In this lecture we present the fastest known algorithm for solving the shortest vector problem, due to
Ajtai
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 5
Some basic complexity results
Lecturer: Oded Regev
Scribe: Ishay Haviv
In this lecture we present some basic computational complexity results related to lattice problems. We
focus mainl
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 5
Integer Programming
Lecturer: Oded Regev
Scribe: Ishay Haviv
In this lecture we present another application of the LLL algorithm, namely, integer programming in
xed dimension.
1
Integer
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 7
Limits on inapproximability
Lecturer: Oded Regev
Scribe: Michael Khanevsky
Let us recall the promise problem GapCVP .
D EFINITION 1 GapCVP
YES instances: triples (B, v, d) such that dis
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 8
Dual Lattices
Lecturer: Oded Regev
Scribe: Gillat Kol
In this lecture we dene the notion of the dual of a lattice and see some if its applications.
D EFINITION 1 For a full-rank lattice
Lecture 11
Transference Theorems
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecturer: Oded Regev
Scribe: Elad Verbin
In the last two lectures we have seen the concept of a dual lattice and Fourier analysis on lattices. In
this lecture we
Lecture 9
Fourier Transform
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecturer: Oded Regev
Scribe: Gillat Kol
In this lecture we describe some basic facts of Fourier analysis that will be needed later. The rst section
discusses the Fouri
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 4
Attack on RSA with
Low Public Exponent
Lecturer: Oded Regev
Scribe: Ishay Haviv
The well-known RSA public key cryptosystem is nowadays used in a wide variety of applications ranging fro
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 12
Average-case Hardness
Lecturer: Oded Regev
Scribe: Elad Verbin
Traditionally, lattices were used as tools in cryptanalysis, that is, as tools in breaking cryptographic
schemes. We have
Tel Aviv University, Fall 2004
Lattices in Computer Science
Lecture 1
Introduction
Lecturer: Oded Regev
Scribe: D. Sieradzki, V. Bronstein
In this course we will consider mathematical objects known as lattices. What is a lattice? It is a set
of points in
Tel Aviv University, Fall 2004
Lecture 2
Lecturer: Oded Regev
Lattices in Computer Science
LLL Algorithm
Scribe: Eyal Kaplan
1 we describe an approximation algorithm to the Shortest Vector Problem (SVP).
In this lecture
This algorithm, developed in 1982 b