Mathematics of Lattices and Cybersecurity
(April 21-24, 2015)

Picture
Description

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.

Organizing Committee

  • Jeffrey Hoffstein
    (Brown University)
  • Stephen Miller
    (Rutgers University)
  • Ramarathnam Venkatesan
    (Microsoft Research)
  • Therese Avitabile
    (New York University)
  • Boaz Barak
    (Microsoft Research)
  • Daniel J. Bernstein *
    (Technische Universiteit Eindhoven)
  • Jean-Francois Biasse *
    (University of Calgary)
  • Reinier Bröker
    (Worcester Polytechnic Institute)
  • Gizem Cetin
    (Worcester Polytechnic Institute)
  • Cheng Chen
    (MIT)
  • Yilei Chen
    (Boston University)
  • Don Coppersmith
    (Institute for Defense Analyses (IDA))
  • Steven Damelin
    (Mathematical Reviews, American Mathematical Societ)
  • Akshay Degwekar
    (Massachusetts Institute of Technology)
  • Apoorvaa Deshpande
    (Brown University)
  • Yarkin Doroz
    (Worcester Polytechnic Institute)
  • Leo Ducas *
    (Center for Mathematics and Computer Science (CWI))
  • Thomas Eisenbarth
    (Worcester Polytechnic Institute)
  • Lior Eldar
    (Massachusetts Institute of Technology)
  • Venkata Gandikota
    (Purdue University)
  • Farshid Hajir
    (University of Massachusetts)
  • Thomas Hales
    (University of Pittsburgh)
  • Shai Halevi*
    (IBM)
  • Nadia Heninger *
    (University of Pennsylvania)
  • Campbell Hewett
    (Brown University)
  • Jeffrey Hoffstein
    (Brown University)
  • Justin Holmgren
    (MIT)
  • Seyed Kaave Hosseini
    (University of California, San Diego)
  • Ewa Infeld
    (Dartmouth College)
  • Heera Janwa *
    (University of Puerto Rico)
  • Samuel Judge
    (Michigan Technological University)
  • Edmund Karasiewicz
    (Rutgers University)
  • Miran Kim
    (Seoul)
  • Emily Russell
    (Institute for Computational and Experimental Research in Mathematics (ICERM))
  • Peter Sarnak *
    (Princeton University)
  • John Schanck
    (University of Waterloo)
  • Rene Schoof
    (University of Rome Tor Vergata)
  • Adam Sealfon
    (MIT)
  • Alice Silverberg*
    (University of California, Irvine)
  • Joseph Silverman *
    (Brown University)
  • Thomas Silverman
    (Brown University)
  • Eric Sommers
    (University of Massachusetts Amherst)
  • Noah Stephens-Davidowitz
    (New York University)
  • Sophie Stevens
    (University of Bristol)
  • Berk Sunar
    (Worcester Polytechnic Institute)
  • Vladimir Tonchev
    (Michigan Technological University)
  • Ha Tran
    (University of Rome Tor Vergata)
  • Nicholas Triantafillou
    (Massachusetts Institute of Technology)
  • Douglas Ulmer
    (Georgia Institute of Technology)
  • Vinod Vaikuntanathan *
    (Massachusetts Institute of Technology)
  • Luke Valenta
    (University of Pennsylvania)
  • Christine van Vredendaal
    (Technische Universiteit Eindhoven)
  • Prashant Vasudevan
    (MIT)
  • Akshay Venkatesh*
    (Stanford University)
  • Ian Whitehead
    (University of Minnesota)
  • Peter Winkler
    (Dartmouth College)
  • Thomas Wunderer
    (Technische Universtaet Darmstadt)
  • Sophia Yakoubov
    (Boston University)
  • Zijian Yao
    (Brown University)
  • Zhenfei Zhang
    (security innovation)
  • Zhuohui Zhang
    (Rutgers University)
Tuesday April 21, 2015
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration: Mathematics of Lattices and Cybersecurity11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 10:00Practical Lattice-Based CryptographyJoseph Silverman, Brown University11th Floor Lecture Hall
PDF
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 EstimatePhong Nguyen, Inria, France and Tsinghua University, China11th Floor Lecture Hall
12:00 - 12:45TBAVinod Vaikuntanathan, Massachusetts Institute of Technology11th Floor Lecture Hall
12:45 - 2:30Break for Lunch
2:30 - 3:15Graph-Induced Multilinear Maps from LatticesShai Halevi, IBM Research11th Floor Lecture Hall
PDF
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Privacy as Contextual Integrity: Motivating Science with PoliticsHelen Nissenbaum, New York University11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Wednesday April 22, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Computational algebraic number theory tackles lattice-based cryptographyDaniel 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 ProblemOded Regev, Courant Institute of Mathematical Sciences, New York University11th Floor Lecture Hall
PDF
PDF
11:35 - 12:20TBANadia 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 basesAkshay Venkatesh, Stanford University 11th Floor Lecture Hall
PDF
2:40 - 3:25The Solovay Kitaev Theorem and Golden GatesPeter Sarnak, Princeton University11th Floor Lecture Hall
PDF
3:40 - 4:25Minitutorial on Mathematical Tools for Lattice Moduli SpaceSteve 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
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Ideal Lattices and Ring-LWE- Overview and Open ProblemsChris Peikert, Georgia Institute of Technology 11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15SOLILOQUY -- A cautionary taleRichard Pinch, HMG 11th Floor Lecture Hall
PDF
11:30 - 12:15TBAJean-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 RingsLeo Ducas, Center for Mathematics and Computer Science (CWI)11th Floor Lecture Hall
PDF
PDF
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Class numbers of cyclotomic fieldsJohn Miller, Rutgers University11th Floor Lecture Hall and Collaborative Space

Friday April 24, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Factoring RSA keys from certified smart cards: Coppersmith in the wildTanja Lange, Technische Universiteit Eindhoven 11th Floor Lecture Hall
10:15 - 11:00Lattices with SymmetryAlice Silverberg, University of California, Irvine 11th Floor Lecture Hall
11:15 - 12:00Public Key Cryptosystems Based on Subfield Subcodes of Algebraic Geometric CodesHeeralal Janwa, University of Puerto Rico Rio Piedras 11th Floor Lecture Hall
12:00 - 5:00Break for Lunch - Afternoon open for collaborations