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Title: Covering Small Alternating Groups with Proper Subgroups.
Creator: Epstein, Michael, Kappe, Luise-Charlotte, 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: 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 n-dimensional vector space over the field of q elements. By a geometric t-[qn,k,λ] design we mean a collection D of k-dimensional 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 n-dimensional vector space over the field of q elements. By a geometric t-[qn,k,λ] design we mean a collection D of k-dimensional 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 basis-reduction.
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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.
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Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00005827
Format: Document (PDF)

Title: Defeating p-attack in non-abelian discrete logarithm problem.
Creator: Magar, Krishna Thapa, Ilic, Ivana, Magliveras, Spyros S., Graduate College
Date Issued: 2013-04-12
PURL: http://purl.flvc.org/fcla/dt/3361325
Subject Headings: Non-Abelian groups, Logarithms
Format: Document (PDF)

Logarithms (1)	+ -
Non-Abelian groups (1)	+ -

abstract (2)	+ -
poster (2)	+ -

Magar, Krishna Thapa (1)	+ -
Popova, Daniela (1)	+ -

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