Lattice problem

Applied sciences
Computer engineering
Computer security
Post-quantum cryptography

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Polynomially Solvable Instances of the Shortest and Closest Vector Problems With Applications to Compute-and-Forward

Michael Christoph Gastpar, Saeid Sahraei

A particular instance of the shortest vector problem (SVP) appears in the context of compute-and-forward. Despite the NP-hardness of the SVP, we will show that this certain instance can be solved in complexity order O(nψlog(nψ)) , where ψ=sqrt(P ||h||^2+1) ...

Institute of Electrical and Electronics Engineers2017

LPN in Cryptography : an Algorithmic Study

Sonia Mihaela Bogos

The security of public-key cryptography relies on well-studied hard problems, problems for which we do not have efficient algorithms. Factorization and discrete logarithm are the two most known and used hard problems. Unfortunately, they can be easily solv ...

EPFL2017

Short Stickelberger Class Relations and Application to Ideal-SVP

Benjamin Pierre Charles Wesolowski

The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and t ...

Springer International Publishing Ag2017

Avalanches in dry and saturated disordered media at fracture in shear and mixed mode scenarios

Jean-François Molinari, Enrico Milanese, Okan Yilmaz

We investigate shear and mixed mode fracture scenarios in inhomogeneous dry and fully saturated porous media with a 2D central force lattice model. For the fully saturated case we adopt the extended Biot's theory. The bars of the lattice break only under t ...

Elsevier2017

Improved hardness results for unique shortest vector problem

Divesh Aggarwal

The unique shortest vector problem on a rational lattice is the problem of finding the shortest non-zero vector under the promise that it is unique (up to multiplication by -1). We give several incremental improvements on the known hardness of the unique s ...

Elsevier2016

Multilevel Design Understanding: From Specification to Logic Invited Paper

Mathias Soeken

We present an outline of the field of Multilevel Design Understanding by first defining and motivating the related problems, and then describing the key issues which must be addressed in future research. ...

Assoc Computing Machinery2016

On lattice codes for Gaussian interference channels

Michael Christoph Gastpar, Jingge Zhu

The usefulness of lattice codes is investigated for two-user Gaussian interference channels (IC). A coding scheme based on the compute-and-forward technique is shown to achieve the capacity region of the Gaussian IC under strong interference. The proposed ...

2015

A sieve algorithm based on overlattices

Anja Annemone Becker

In this paper, we present a heuristic algorithm for solving exact, as well as approximate, shortest vector and closest vector problems on lattices. The algorithm can be seen as a modified sieving algorithm for which the vectors of the intermediate sets lie ...

Cambridge Univ Press2014

A Lattice Reduction-Aided MIMO Channel Equalizer in 90 nm CMOS Achieving 720 Mb/s

Andreas Peter Burg, Carl Christian Sten Dominic Senning

In this paper, a VLSI implementation of a complete MIMO channel equalization ASIC based on lattice reduction-aided linear detection is presented. The architecture performs preprocessing steps at channel rate and low-complexity linear data detection at symb ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Compute-and-Forward: Finding the Best Equation

Michael Christoph Gastpar, Saeid Sahraei

Compute-and-Forward is an emerging technique to deal with interference. It allows the receiver to decode a suitably chosen integer linear combination of the transmitted messages. The integer coefficients should be adapted to the channel fading state. Optim ...

2014

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