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Project Information

SATC: CORE: SMALL: NUMBER-THEORETIC ASPECTS OF LATTICE CRYPTOLOGY

Agency:
NSF

National Science Foundation

Project Number:
1815562
Contact PI / Project Leader:
MILLER, STEPHEN D
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
This award supports research in the mathematical underpinnings of cryptography. Since the late 1970s, widely-used cryptosystems have been developed based on the perceived difficulty of certain mathematical problems. New applications, as well as improvements in attacks on existing cryptosystems, call for a better understanding of these underlying mathematical problems. In particular, the potential to develop quantum computers (and new techniques they would be able to execute) puts many existing cryptosystems, such as the well known Rivest-Shamir-Adleman (RSA) system and Elliptic Curve Cryptography, at possible long-term risk. For this reason, it is important to study post-quantum alternatives, such as lattice-based cryptology (which is the focus of this project). Lattices also offer other potential benefits, including new types of functionalities such as the ability to perform some operations on encrypted data (which would strengthen cloud security).The project centers on the cryptographic strength of special types of lattices (such as ideal lattices or integer lattices) that are used in numerous recent proposed cryptographic schemes. The investigator and collaborators intend to study the distribution of these special lattices amongst larger natural families, to see whether or not they are distinguished by presently-unknown geometric features that might make attacks possible. They plan to use techniques from automorphic forms and algebraic number theory. Tail bounds (such as Banaszczyk's tail bound for Gaussian mass) will be studied for more general regions and functions appropriate to these lattices. From a different, computational perspective, the project will explore lattice-reduction algorithms tailored for these special types of lattices, and analyze how challenging bases of these lattices can be generated.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
Project Terms:
Algebra; Algorithms; Award; base; cryptography; Data; Evaluation; Family; Foundations; Gaussian model; Mathematics; Mission; Names; number theory; operation; quantum; quantum computer; Research Personnel; Research Support; Risk; Scheme; Security; System; Tail; Techniques

Details

Contact PI / Project Leader Information:
Name:  MILLER, STEPHEN D
Other PI Information:
Not Applicable
Awardee Organization:
Name:  RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK
City:  PISCATAWAY    
Country:  UNITED STATES
Congressional District:
State Code:  NJ
District:  06
Other Information:
Fiscal Year: 2018
Award Notice Date: 30-Aug-2018
DUNS Number: 001912864
Project Start Date: 01-Sep-2018
Budget Start Date:
CFDA Code: 47.070
Project End Date: 31-Aug-2021
Budget End Date:
Agency: ?

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National Science Foundation
Project Funding Information for 2018:
Year Agency

Agency: The entity responsible for the administering of a research grant, project, or contract. This may represent a federal department, agency, or sub-agency (institute or center). Details on agencies in Federal RePORTER can be found in the FAQ page.

FY Total Cost
2018 NSF

National Science Foundation

$300,000

Results

i

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