Current Search: FAU Graduate Student Research (x) » Magliveras, Spyros S. (x)


Title

Covering Small Alternating Groups with Proper Subgroups.

Creator

Epstein, Michael, Kappe, LuiseCharlotte, Magliveras, Spyros S., Graduate College, Popova, Daniela

Abstract/Description

Any group with a finite noncyclic homomorphic image is a finite union of proper subgroups. Given such a group G, we define the covering number of G to be the least positive integer m such that G is the union of m proper subgroups. We present recent results on the determination of the covering numbers of the alternating groups on nine and eleven letters.

Date Issued

2015

PURL

http://purl.flvc.org/fau/fd/FA00005874

Format

Document (PDF)


Title

Defeating pattack in nonabelian discrete logarithm problem.

Creator

Magar, Krishna Thapa, Ilic, Ivana, Magliveras, Spyros S., Graduate College

Date Issued

20130412

PURL

http://purl.flvc.org/fcla/dt/3361325

Subject Headings

NonAbelian groups, Logarithms

Format

Document (PDF)


Title

New LS[3][2,3,2^8] Geometric Large Sets.

Creator

Hurley, Michael Robert, Khadka, Bal K., Magliveras, Spyros S., Graduate College

Abstract/Description

Let V be an ndimensional vector space over the field of q elements. By a geometric t[qn,k,λ] design we mean a collection D of kdimensional subspaces if V, called blocks, such that every tdimensional subspace T of V appears in exactly λ blocks in D. In a recent paper Braun, Kohnert, Ӧstergård, and Wassermann constructed the first ever known large set LS[N][2,k,qn], namely an LS[3][2,3,28] under a cyclic group G of order 255. In this work we construct an additional 8 large sets with the same...
Show moreLet V be an ndimensional vector space over the field of q elements. By a geometric t[qn,k,λ] design we mean a collection D of kdimensional subspaces if V, called blocks, such that every tdimensional subspace T of V appears in exactly λ blocks in D. In a recent paper Braun, Kohnert, Ӧstergård, and Wassermann constructed the first ever known large set LS[N][2,k,qn], namely an LS[3][2,3,28] under a cyclic group G of order 255. In this work we construct an additional 8 large sets with the same parameters, using the L3 algorithm for lattice basisreduction.
Show less

Date Issued

2015

PURL

http://purl.flvc.org/fau/fd/FA00005885

Format

Document (PDF)


Title

Solving approximate SVP in an Ideal Lattice using a cluster.

Creator

Khadka, Bal K., Magliveras, Spyros S., Graduate College

Abstract/Description

The shortest vector problem SVP is de ned as follows: For a given basis B of an integral lattice L fi nd a vector v in L whose length is minimal. Here we present the result of our experiments based on a hill climbing algorithm using a computer cluster and a number of parallel executions of a standard basis reduction technique, such as LLL, to successfully reduce an initial basis of L. We begin by reducing ideal lattices of relatively small dimension and progressively reduce ideal lattices of...
Show moreThe shortest vector problem SVP is de ned as follows: For a given basis B of an integral lattice L fi nd a vector v in L whose length is minimal. Here we present the result of our experiments based on a hill climbing algorithm using a computer cluster and a number of parallel executions of a standard basis reduction technique, such as LLL, to successfully reduce an initial basis of L. We begin by reducing ideal lattices of relatively small dimension and progressively reduce ideal lattices of higher dimension, beating several earlier published solutions to the approximate SVP problem.
Show less

Date Issued

2014

PURL

http://purl.flvc.org/fau/fd/FA00005827

Format

Document (PDF)