Algorithms for the Densest Sub-Lattice Problem

2013 ◽  
Author(s):  
Daniel Dadush ◽  
Daniele Micciancio
Keyword(s):  
Lattice Problem

A Microscopic Theory of a Single Hydrogen Centre in a Magnesium Crystal

1992 ◽  
Vol 47 (6) ◽  
pp. 733-747
Author(s):  
M. Gnirßt ◽  
F. Wahl
Keyword(s):  
Harmonic Approximation ◽  
Microscopic Theory ◽  
Electronic System ◽  
Energy Difference ◽  
Electronic Energy ◽  
Host Lattice ◽  
System A ◽  
Metal Crystal ◽  
Lattice Problem ◽  
Storage Energy

AbstractA microscopic theory of a single hydrogen center embedded in a magnesium crystal is presented. Starting with a many-particle Schrödinger equation, an adiabatic decoupling yields in an electronic system a protonic system and a host lattice system. The storage energy is defined to consist of an electronic part and lattice contributions. The electronic problem is treated with the help of a special energy difference procedure developed by Wahl et al. This procedure is applied in a higher approximation to calculate the electronic energy difference eigenvalue between a metal crystal with and without a hydrogen impurity. The lattice problem is treated in the classical harmonic approximation.

scholarly journals Note on Cumulant Average Used in Random Lattice Problem

1965 ◽  
Vol 34 (5) ◽  
pp. 871-872 ◽  
Author(s):  
Takeo Matsubara ◽  
Fumiko Yonezawa
Keyword(s):  
Random Lattice ◽  
Lattice Problem

scholarly journals On a lattice problem of H. Steinhaus

2002 ◽  
Vol 15 (4) ◽  
pp. 817-856 ◽  
Author(s):  
Steve Jackson ◽  
R. Daniel Mauldin
Keyword(s):  
Lattice Problem

Inverse Lattice Problem and Finnis-Sinclair Model

1995 ◽  
Vol 12 (4) ◽  
pp. 221-224 ◽  
Author(s):  
Xie Qian ◽  
Huang Meichun
Keyword(s):  
Lattice Problem

The Disordered Lattice Problem: A Review

1958 ◽  
Vol 6 (3) ◽  
pp. 302-319 ◽  
Author(s):  
Alexei Maradudin ◽  
George H. Weiss
Keyword(s):  
Disordered Lattice ◽  
Lattice Problem

2345. A Lattice Problem

1953 ◽  
Vol 37 (321) ◽  
pp. 205
Author(s):  
E. V. Newbery
Keyword(s):  
Lattice Problem

BENCHMARKING LATTICE-BASED APPLICATIONS ON PARALLEL ARCHITECTURES

1996 ◽  
Vol 06 (03) ◽  
pp. 309-320
Author(s):  
GIULIO DESTRI ◽  
PAOLO MARENZONI
Keyword(s):  
Message Passing ◽  
Parallel Architecture ◽  
Cellular Neural Network ◽  
General Purpose ◽  
Parallel Architectures ◽  
Lattice Points ◽  
Communication Performance ◽  
Connection Machine ◽  
Lattice Problem ◽  
Overall Performance

The numerical analysis and solution of many physics and engineering problems is based on lattice-oriented algorithms. The Cellular Neural Network (CNN) computational paradigm embodies a wide set of grid problems characterized by locality of information exchanges among lattice points. Performance analysis tests using CNN-based algorithms may provide insights into the performance achievable by a given parallel architecture, with respect to a wide class of lattice problems. In this paper a message passing version of a general CNN-based algorithm is implemented and optimized for three general purpose parallel architectures: Connection Machine CM-5, Cray T3D, and IBM SP2. Separate measurements on computations and communications of the algorithm allow us to evaluate processing node and network communication performance of the machines. Moreover. the overall performance of the full application is analyzed, in order to understand the scalability and the range of applicability of this prototype of lattice problem.

An Improved Multilinear Map and its Applications

2015 ◽  
Vol 10 (3) ◽  
pp. 64-81 ◽  
Author(s):  
Chunsheng Gu
Keyword(s):  
Random Matrix ◽  
Principal Ideal ◽  
Key Exchange ◽  
Ideal Lattice ◽  
Witness Encryption ◽  
Lattice Problem ◽  
Multilinear Maps ◽  
Multilinear Map ◽  
Cover Problem ◽  
Exact Cover

Cryptographic multilinear maps have extensive applications. However, current constructions of multilinear maps suffer from the zeroizing attacks. For a candidate construction of multilinear maps described by Garg, Gentry, and Halevi (GGH13), Hu & Jia recently presented an efficient attack, which broke the GGH13-based applications of multipartite key exchange (MPKE) and witness encryption (WE) based on the hardness of 3-exact cover problem. By introducing random matrix, the author presents an improvement of the GGH13 map, which supports the applications for public tools of encoding in the GGH13 map, such as MPKE and WE. The security of the construction depends upon new hardness assumption. Moreover, the author's improvement destroys the structure of the ring element in the principal ideal lattice problem, and avoids potential attacks using algorithm of solving short principal ideal lattice generator.

Sign in / Sign up

Export Citation Format

Share Document