Summer 2022

Summer Cluster: Lattices and Beyond

May 23Jun. 24, 2022

This extended reunion is for long-term participants in the program Lattices: Algorithms, Complexity, and Cryptography, held in the spring 2020 semester. It will provide an opportunity to meet old and new friends. Moreover, we hope that it will give everyone a chance to reflect on the progress made during the semester and since, and sketch in which directions the field should go in the future. In an effort to keep things informal and to encourage open discussion, none of the activities will be recorded. Participation in the reunion is by invitation only.

The study of integer lattices serves as a bridge between number theory and geometry and has for centuries received the attention of illustrious mathematicians, including Lagrange, Gauss, Dirichlet, Hermite, and Minkowski. In computer science, lattices made a grand appearance in 1982 with the celebrated work of Lenstra, Lenstra, and Lovász, who developed the celebrated LLL algorithm to find short vectors in integer lattices. The role of lattices in cryptography has been equally, if not more, revolutionary and dramatic, with lattices first playing a destructive role as a potent tool for breaking cryptosystems and later serving as a new way to realize powerful and game-changing notions such as fully homomorphic encryption. These exciting developments over the last two decades have taken us on a journey through such diverse areas as quantum computation, learning theory, Fourier analysis, and algebraic number theory. 

The promise of practical lattice-based cryptosystems, together with their apparent quantum resistance, is generating a tremendous amount of interest in deploying these schemes at internet scale. However, before lattice cryptography goes live, we need major advances in understanding the hardness of lattice problems that underlie the security of these cryptosystems. Significant, groundbreaking progress on these questions requires a concerted effort by researchers from many areas: (algebraic) number theory, (quantum) algorithms, optimization, cryptography, and coding theory.
The goal of this extended reunion for the Lattices: Algorithms, Complexity, and Cryptography program is to bring back together experts in these areas to review progress, to continue to attack outstanding open questions, and to continue the exploration of connections among lattices, computer science, and mathematics. The need to thoroughly understand the computational landscape and cryptographic capabilities of lattice problems is greater now than ever, given the possibility that secure communication on the internet and secure collaboration on the cloud might soon be powered by lattices.

The program Lattices: Algorithms, Complexity, and Cryptography was supported in part by the Alfred P. Sloan Foundation.



Shafi Goldwasser (UC Berkeley; co-chair), Vinod Vaikuntanathan (Massachusetts Institute of Technology; co-chair), Daniele Micciancio (UC San Diego), Oded Regev (Courant Institute, NYU)

Long-Term Participants (including Organizers):

Divesh Aggarwal (NUS), Martin Albrecht (Royal Holloway, University of London), Prabhanjan Ananth (UC Santa Barbara), Huck Bennett (Oregon State University), Jean-Francois Biasse (University of South Florida), Elette Boyle (IDC Herzliya), Zvika Brakerski (Weizmann Institute of Science), Sanjam Garg (UC Berkeley), Rishab Goyal (Massachusetts Institute of Technology), Nadia Heninger (UCSD), Justin Holmgren (Princeton University), Yuval Ishai (Technion - Israel Institute of Technology), Abhishek Jain (Johns Hopkins University), Dakshita Khurana (University of Illinois Urbana-Champaign), Tanja Lange (Eindhoven University of Technology and Academia Sinica), Rachel Lin (University of Washington), Vadim Lyubashevsky (IBM Research- Zurich), Raluca Popa (UC Berkeley), Amit Sahai (UCLA), Fang Song (Portland State University), Damien Stehlé (ENS de Lyon), Noah Stephens-Davidowitz (Cornell University), Stefano Tessaro (University of Washington), Umesh Vazirani (UC Berkeley), Hoeteck Wee (CNRS and ENS), Daniel Wichs (Northeastern University)

Visiting Graduate Students and Postdocs:

Yael Eisenberg (Cornell University), Thomas Espitau (Rennes University), Alexis Korb (UCLA), Rajendra Kumar (National University of Singapore), Thijs Laarhoven (Eindhoven University of Technology), Jiahui Liu (University of Texas Austin), Qipeng Liu (Simons Institute, UC Berkeley), Paul Lou (UCLA), Chuhan Lu (Portland State University), Spencer Peters (Cornell University), Willy Quach (Northeastern University), Adam Suhl (UC San Diego), Neekon Vafa (MIT)


Monday, Jun. 13Friday, Jun. 17, 2022


Shafi Goldwasser (UC Berkeley), Urmila Mahadev (California Institute of Technology), Vinod Vaikuntanathan (Massachusetts Institute of Technology), Umesh Vazirani (UC Berkeley), Henry Yuen (Columbia University)

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