| NSF Org: |
CNS Division Of Computer and Network Systems |
| Recipient: |
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| Initial Amendment Date: | August 11, 2015 |
| Latest Amendment Date: | August 11, 2015 |
| Award Number: | 1526333 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Susanne Wetzel
CNS Division Of Computer and Network Systems CSE Directorate for Computer and Information Science and Engineering |
| Start Date: | August 15, 2015 |
| End Date: | July 31, 2018 (Estimated) |
| Total Intended Award Amount: | $499,522.00 |
| Total Awarded Amount to Date: | $499,522.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
3 RUTGERS PLZ NEW BRUNSWICK NJ US 08901-8559 (848)932-0150 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
3 Rutgers Plaza New Brunswick NJ US 08901-8559 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | Secure &Trustworthy Cyberspace |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.070 |
ABSTRACT
Cryptography is a fundamental part of cybersecurity, both in designing secure applications as well as understanding how truly secure they really are. Traditionally, the mathematical underpinnings of cryptosystems were based on difficult problems involving whole numbers (most famously, the apparent difficulty of factoring a product of two unknown primes back into those prime factors). More recently, several completely new types of cryptography have been proposed using the mathematical properties of lattices. For example, homomorphic encryption offers the possibility of manipulating encrypted data without revealing its contents. The research funded by the project seeks to apply new mathematical techniques to understand difficult properties of lattices and hence of these proposed systems -- properties that are seen as crucial for making them practically fast, in particular.
The projects in the proposal involve using tools from automorphic forms (such as Borel-Harish-Chandra reduction theory, Eisenstein series, and change of base field) to examine concrete questions about short vectors in certain families of lattices. It also includes a study of cryptosystems based on nonabelian generalizations of lattices, and the geometry of BKZ-reduced bases in Coppersmith's method (including the Boneh-Durfee attack on small exponent RSA).
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Intellectual Merit
The PI, in collaboration with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska solved the sphere packing problem in 24-dimensions. Namely, no packing of equal-sized spheres in 24-dimensions can fill more than the proportion pi12/12! (about 0.2%) of space, this being the amount filled using a construction known as the "Leech lattice". In fact, if some finite configuration of spheres is repeated over and over again and achieves this same density of pi12/12!, this packing must actually be identical to the Leech lattice construction. The techniques for this result used the theory of modular forms from number theory in a crucial way. The result also depended on a recent breakthrough of Viazovska in 8-dimensions, and the discovery of certain rational numbers appearing in related calculations that were found by the PI and Henry Cohn as part of this project.
With Noah Stephens-Davidowitz, the PI developed tools to obtain estimates on certain "lattice tail bounds" which appear widely in estimates concerning cryptographic constructions. Lattice-based cryptography currently receives prominent attention as a leading candidate among cryptosystems that can survive attacks by quantum computers.
Together with Bhargav Narayanan and Ramarathnam Venkatesan, the PI developed new methods to attack the RSA cryptostem. The RSA cryptosystem is the most-widely used cryptographic algorithm, and is based on the difficulty of factoring large numbers. It was earlier shown by Coppersmith and Boneh-Durfee that in some instances, the RSA cryptosystem has weaknesses that can be attacked using lattices. The PI's recent joint work shows that these lattices can be cut down in size to improve performance.
Broader Impacts
The PI wrote an expository piece entitled "Cryptanalysis of the NFL schedule", which aims to explain to a general audience how principles used to detect flaws in stream ciphers can be applied to find a flaw in the NFL schedule rotation. This work was featured in the Star Ledger (NJ's largest newspaper) as well as a 25-minute segment on Sirius XM radio's Wharton Moneyball program.
Last Modified: 07/31/2018
Modified by: Stephen D Miller
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