Organizing Committee
  • Jeffrey Hoffstein
    Brown University
  • Stephen Miller
    Rutgers University
  • Ramarathnam Venkatesan
    Microsoft Research India
Abstract

Lattices are abstractly very simple objects, yet their concrete realizations contain beautifully intricate problems that are stubbornly difficult even in low dimensions. For example, our present day understandings of densest lattice packings and reduction theory are still plagued with large gaps.

In the 1970's and 1980's lattices entered the world of cryptography as tools used to break certain crypto systems, particularly those based on the subset sum problem, and since the 1990's they have become increasingly important in the building of other types of crypto systems (thanks to the difficulty in the underlying mathematics). Their significance has recently been bolstered by average-case complexity bounds and their present resistance to quantum computing attacks.

Currently the theory of lattices is a lively research topic among mathematicians, computer scientists, and experts in cybersecurity. However, to this date, there has been little to no interaction between these communities. The goal of this workshop is to stimulate activity between these different groups interested in lattice problems. Topics to be covered include, but are not restricted to, recent results on densest lattice packings, the geometry of lattice moduli space and its connections with automorphic forms and algebraic number theory, cryptographic applications of lattices, and the state of the art of lattice reduction in high dimensions.

Image for "Mathematics of Lattices and Cybersecurity"

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Tuesday, April 21, 2015
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration: Mathematics of Lattices and Cybersecurity11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 10:00am EDTPractical Lattice-Based Cryptography - Joseph Silverman, Brown University11th Floor Lecture Hall
10:15 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:45am EDTThe Hardness of Lattice Problems: Worst-case to Average-case Reductions and Security Estimate - Phong Nguyen, Inria, France and Tsinghua University, China11th Floor Lecture Hall 
12:00 - 12:45pm EDTTBA - Vinod Vaikuntanathan, Massachusetts Institute of Technology11th Floor Lecture Hall 
12:45 - 2:30pm EDTBreak for Lunch   
2:30 - 3:15pm EDTGraph-Induced Multilinear Maps from Lattices - Shai Halevi, IBM Research11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTPrivacy as Contextual Integrity: Motivating Science with Politics - Helen Nissenbaum, New York University11th Floor Lecture Hall 
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Wednesday, April 22, 2015
TimeEventLocationMaterials
9:00 - 9:45am EDTComputational algebraic number theory tackles lattice-based cryptography - Daniel J. Bernstein, Technische Universiteit Eindhoven11th Floor Lecture Hall 
10:00 - 10:20am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30am EDTFaster algorithms for the Shortest Vector Problem - Oded Regev, Courant Institute of Mathematical Sciences, New York University11th Floor Lecture Hall
11:35 - 12:20pm EDTTBA - Nadia Heninger, University of Pennsylvania 11th Floor Lecture Hall 
12:25 - 12:30pm EDTGroup Photo in Lecture Hall11th Floor Lecture Hall 
12:30 - 1:45pm EDTBreak for Lunch   
1:45 - 2:30pm EDTThe shape of typical LLL reduced bases - Akshay Venkatesh, Stanford University 11th Floor Lecture Hall
2:40 - 3:25pm EDTThe Solovay Kitaev Theorem and Golden Gates - Peter Sarnak, Princeton University11th Floor Lecture Hall
3:40 - 4:25pm EDTMinitutorial on Mathematical Tools for Lattice Moduli Space - Steve Miller, Rutgers University11th Floor Lecture Hall 
4:30 - 5:30pm EDTShort Contributed Talks and Coffee Break11th Floor Lecture Hall and Collaborative Space 
Thursday, April 23, 2015
TimeEventLocationMaterials
9:00 - 10:00am EDTIdeal Lattices and Ring-LWE- Overview and Open Problems - Chris Peikert, Georgia Institute of Technology 11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTSOLILOQUY -- A cautionary tale - Richard Pinch, HMG 11th Floor Lecture Hall
11:30 - 12:15pm EDTTBA - Jean-Francois Biasse, University of Calgary11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch   
2:30 - 3:15pm EDTRecovering Short Generators of Principal Ideals in Cyclotomic Rings - Leo Ducas, Center for Mathematics and Computer Science (CWI)11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTClass numbers of cyclotomic fields - John Miller, Rutgers University11th Floor Lecture Hall and Collaborative Space 
Friday, April 24, 2015
TimeEventLocationMaterials
9:00 - 10:00am EDTFactoring RSA keys from certified smart cards: Coppersmith in the wild - Tanja Lange, Technische Universiteit Eindhoven 11th Floor Lecture Hall 
10:15 - 11:00am EDTLattices with Symmetry - Alice Silverberg, University of California, Irvine 11th Floor Lecture Hall
11:15 - 12:00pm EDTPublic Key Cryptosystems Based on Subfield Subcodes of Algebraic Geometric Codes - Heeralal Janwa, University of Puerto Rico Rio Piedras 11th Floor Lecture Hall 
12:00 - 5:00pm EDTBreak for Lunch - Afternoon open for collaborations  

Lecture Videos

Public Key Cryptosystems Based on Subfield Subcodes of Algebraic Geometric Codes

Heera Janwa
University of Puerto Rico
April 24, 2015
Mathematics of Lattices and Cybersecurity
Play

Recovering Short Generators of Principal Ideals in Cyclotomic Rings

Leo Ducas
Centrum Wiskunde & Informatica
April 23, 2015
Mathematics of Lattices and Cybersecurity
Play     Abstract     Slides

Ideal Lattices and Ring-LWE: Overview and Open Problems

Chris Peikert
Georgia Institute of Technology
April 23, 2015
Mathematics of Lattices and Cybersecurity
Play     Slides

Minitutorial on Mathematical Tools for Lattice Moduli Space

Stephen Miller
Rutgers University
April 22, 2015
Mathematics of Lattices and Cybersecurity
Play

Faster algorithms for the Shortest Vector Problem

Oded Regev
New York University, Courant Institut
April 22, 2015
Mathematics of Lattices and Cybersecurity
Play     Abstract     Slides

Graph-Induced Multilinear Maps from Lattices

Shai Halevi
IBM
April 21, 2015
Mathematics of Lattices and Cybersecurity
Play     Abstract