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Deterministic and non-deterministic basis reduction techniques for NTRU lattices
Title
Deterministic and non-deterministic basis reduction techniques for NTRU lattices.
Creator
Socek, Daniel, Florida Atlantic University, Magliveras, Spyros S.
Abstract/Description
Finding the shortest or a "short enough" vector in an integral lattice of substantial dimension is a difficult problem. The problem is not known to be but most people believe it is [7]. The security of the newly proposed NTRU cryptosystem depends solely on this fact. However, by the definition NTRU lattices possess a certain symmetry. This suggests that there may be a way of taking advantage of this symmetry to enable a new cryptanalytical approach in combination with existing good lattice...
Show moreFinding the shortest or a "short enough" vector in an integral lattice of substantial dimension is a difficult problem. The problem is not known to be but most people believe it is [7]. The security of the newly proposed NTRU cryptosystem depends solely on this fact. However, by the definition NTRU lattices possess a certain symmetry. This suggests that there may be a way of taking advantage of this symmetry to enable a new cryptanalytical approach in combination with existing good lattice reduction algorithms. The aim of this work is to exploit the symmetry inherent in NTRU lattices to design a non-deterministic algorithm for improving basis reduction techniques for NTRU lattices. We show how the non-trivial cyclic automorphism of an NTRU lattice enables further reduction. Our approach combines the recently published versions of the famous LLL algorithm for lattice basis reduction with our automorphism utilization techniques.
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Date Issued
2002
PURL
http://purl.flvc.org/fcla/dt/12933
Subject Headings
Cryptography, Lattice theory, Algorithms
Format
Document (PDF)
Dynamical phase transitions in one-dimensional, annealed cellular automata
Title
Dynamical phase transitions in one-dimensional, annealed cellular automata.
Creator
Blagoev, Krastan Blagoev., Florida Atlantic University, Wille, Luc T.
Abstract/Description
A dynamical phase transition between a frozen and a chaotic state has been found in one-dimensional lattice systems with annealed disorder. An exponential decay to a homogeneous state is observed below the transition point. Above the transition point damage spreading and damage decaying phases are observed. A time dependent order parameter is suggested for describing the observed behavior.
Date Issued
1992
PURL
http://purl.flvc.org/fcla/dt/14820
Subject Headings
Lattice theory, Thermodynamics, Statistical mechanics
Format
Document (PDF)
Some topics related to the vibrations of deterministic and non-deterministic metamaterial structures
Title
Some topics related to the vibrations of deterministic and non-deterministic metamaterial structures.
Creator
Li, Yuchen, Elishakoff, Isaac, Challamel, Noël, Florida Atlantic University, Department of Ocean and Mechanical Engineering, College of Engineering and Computer Science
Abstract/Description
In this thesis, we will explore different kinds of metamaterial or architectural structural problems, including structures composed of heterogeneous media with bi periodic sub-structures, discrete structures with sub-elements or continuous structures with discrete attached sub-elements. The thesis is composed of seven parts. After having introduced the specificities of metamaterial mechanics, the second chapter is devoted to the vibration of discrete beam problems called Hencky bar-chain...
Show moreIn this thesis, we will explore different kinds of metamaterial or architectural structural problems, including structures composed of heterogeneous media with bi periodic sub-structures, discrete structures with sub-elements or continuous structures with discrete attached sub-elements. The thesis is composed of seven parts. After having introduced the specificities of metamaterial mechanics, the second chapter is devoted to the vibration of discrete beam problems called Hencky bar-chain model in a stochastic framework. It is shown that the lattice beam behaves as a nonlocal continuous beam problem, both in the deterministic and the non-deterministic analyses. The third chapter considers the vibration of continuous beams with the introduction of shear effects and attached periodically oscillators. A discussion on beam modelling, for example Timoshenko beam models or truncated Timoshenko beam models is included. It is shown that the bandgap phenomenon observed for metamaterial beams can be accurately captured by a truncated Timoshenko beam model which means the last term in the Timoshenko equation is not that important.
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Date Issued
2023
PURL
http://purl.flvc.org/fau/fd/FA00014289
Subject Headings
Metamaterials, Hencky bar-chain model, Lattice theory, Engineering
Format
Document (PDF)
LATTICE SIGNATURES BASED ON MODULE-NTRU
Title
LATTICE SIGNATURES BASED ON MODULE-NTRU.
Creator
Kottal, Sulani Thakshila Baddhe Vidhanalage, Bai, Shi, Karabina, Koray, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description
Euclidean lattices have attracted considerable research interest as they can be used to construct efficient cryptographic schemes that are believed to be quantum-resistant. The NTRU problem, introduced by J. Hoffstein, J. Pipher, and J. H. Silverman in 1996 [16], serves as an important average-case computational problem in lattice-based cryptography. Following their pioneer work, the NTRU assumption and its variants have been used widely in modern cryptographic constructions such as...
Show moreEuclidean lattices have attracted considerable research interest as they can be used to construct efficient cryptographic schemes that are believed to be quantum-resistant. The NTRU problem, introduced by J. Hoffstein, J. Pipher, and J. H. Silverman in 1996 [16], serves as an important average-case computational problem in lattice-based cryptography. Following their pioneer work, the NTRU assumption and its variants have been used widely in modern cryptographic constructions such as encryption, signature, etc. Let Rq = Zq[x]/ (xn + 1) be a quotient polynomial ring. The standard NTRU problem asks to recover short polynomials f, g E Rq such that h - g/ f (mod q), given a public key h and the promise that such elements exist. In practice, the degree n is often a power of two. As a generalization of NTRU, the Module-NTRU problems were introduced by Cheon, Kim, Kim, and Son (IACR ePrint 2019/1468), and Chuengsatiansup, Prest, Stehle, Wallet, and Xagawa (ASIACCS '20). In this thesis, we presented two post-quantum Digital Signature Schemes based on the Module-NTRU problem and its variants.
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Date Issued
2024
PURL
http://purl.flvc.org/fau/fd/FA00014407
Subject Headings
Lattice theory, Cryptography, Public key cryptography, Applied mathematics
Format
Document (PDF)