Current Search: Lattice theory (x)
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 Title
 Deterministic and nondeterministic 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 nondeterministic algorithm for improving basis reduction techniques for NTRU lattices. We show how the nontrivial 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.
Show less  Date Issued
 2002
 PURL
 http://purl.flvc.org/fcla/dt/12933
 Subject Headings
 Cryptography, Lattice theory, Algorithms
 Format
 Document (PDF)
 Title
 Dynamical phase transitions in onedimensional, 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 onedimensional 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)
 Title
 Some topics related to the vibrations of deterministic and nondeterministic 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 substructures, discrete structures with subelements or continuous structures with discrete attached subelements. 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 barchain...
Show moreIn this thesis, we will explore different kinds of metamaterial or architectural structural problems, including structures composed of heterogeneous media with bi periodic substructures, discrete structures with subelements or continuous structures with discrete attached subelements. 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 barchain 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 nondeterministic 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.
Show less  Date Issued
 2023
 PURL
 http://purl.flvc.org/fau/fd/FA00014289
 Subject Headings
 Metamaterials, Hencky barchain model, Lattice theory, Engineering
 Format
 Document (PDF)
 Title
 LATTICE SIGNATURES BASED ON MODULENTRU.
 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 quantumresistant. The NTRU problem, introduced by J. Hoffstein, J. Pipher, and J. H. Silverman in 1996 [16], serves as an important averagecase computational problem in latticebased 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 quantumresistant. The NTRU problem, introduced by J. Hoffstein, J. Pipher, and J. H. Silverman in 1996 [16], serves as an important averagecase computational problem in latticebased 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 ModuleNTRU 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 postquantum Digital Signature Schemes based on the ModuleNTRU problem and its variants.
Show less  Date Issued
 2024
 PURL
 http://purl.flvc.org/fau/fd/FA00014407
 Subject Headings
 Lattice theory, Cryptography, Public key cryptography, Applied mathematics
 Format
 Document (PDF)