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.

Confirmed Speakers & Participants

Workshop Schedule

Tuesday, April 21, 2015
TimeEventLocationMaterials
8:30 - 8:55Registration: Mathematics of Lattices and Cybersecurity11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 10:00Practical Lattice-Based Cryptography - Joseph Silverman, Brown University11th Floor Lecture Hall
10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:45The 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 - 12:45TBA - Vinod Vaikuntanathan, Massachusetts Institute of Technology11th Floor Lecture Hall 
12:45 - 2:30Break for Lunch   
2:30 - 3:15Graph-Induced Multilinear Maps from Lattices - Shai Halevi, IBM Research11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Privacy as Contextual Integrity: Motivating Science with Politics - Helen Nissenbaum, New York University11th Floor Lecture Hall 
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Wednesday, April 22, 2015
TimeEventLocationMaterials
9:00 - 9:45Computational algebraic number theory tackles lattice-based cryptography - Daniel J. Bernstein, Technische Universiteit Eindhoven11th Floor Lecture Hall 
10:00 - 10:20Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30Faster algorithms for the Shortest Vector Problem - Oded Regev, Courant Institute of Mathematical Sciences, New York University11th Floor Lecture Hall
11:35 - 12:20TBA - Nadia Heninger, University of Pennsylvania 11th Floor Lecture Hall 
12:25 - 12:30Group Photo in Lecture Hall11th Floor Lecture Hall 
12:30 - 1:45Break for Lunch   
1:45 - 2:30The shape of typical LLL reduced bases - Akshay Venkatesh, Stanford University 11th Floor Lecture Hall
2:40 - 3:25The Solovay Kitaev Theorem and Golden Gates - Peter Sarnak, Princeton University11th Floor Lecture Hall
3:40 - 4:25Minitutorial on Mathematical Tools for Lattice Moduli Space - Steve Miller, Rutgers University11th Floor Lecture Hall 
4:30 - 5:30Short Contributed Talks and Coffee Break11th Floor Lecture Hall and Collaborative Space 
Thursday, April 23, 2015
TimeEventLocationMaterials
9:00 - 10:00Ideal Lattices and Ring-LWE- Overview and Open Problems - Chris Peikert, Georgia Institute of Technology 11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15SOLILOQUY -- A cautionary tale - Richard Pinch, HMG 11th Floor Lecture Hall
11:30 - 12:15TBA - Jean-Francois Biasse, University of Calgary11th Floor Lecture Hall 
12:30 - 2:30Break for Lunch   
2:30 - 3:15Recovering Short Generators of Principal Ideals in Cyclotomic Rings - Leo Ducas, Center for Mathematics and Computer Science (CWI)11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Class numbers of cyclotomic fields - John Miller, Rutgers University11th Floor Lecture Hall and Collaborative Space 
Friday, April 24, 2015
TimeEventLocationMaterials
9:00 - 10:00Factoring RSA keys from certified smart cards: Coppersmith in the wild - Tanja Lange, Technische Universiteit Eindhoven 11th Floor Lecture Hall 
10:15 - 11:00Lattices with Symmetry - Alice Silverberg, University of California, Irvine 11th Floor Lecture Hall
11:15 - 12:00Public Key Cryptosystems Based on Subfield Subcodes of Algebraic Geometric Codes - Heeralal Janwa, University of Puerto Rico Rio Piedras 11th Floor Lecture Hall 
12:00 - 5:00Break for Lunch - Afternoon open for collaborations