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Publications AND Presentations

 


PUBLICATIONS


 

  • L. Babinkostova, A.M. Bowden, A.M. Kimball, K.J. Williams, A simplified and generalized treatment of DES related ciphers Cryptologia 39:1 (2015), 3-24. 
  • L. Babinkostova, K.W. Bombardier, M.C. Cole, T.A. Morrell and C.B. Scott, Algebraic Properties of Generalized Rijndael-like Ciphers, Groups Complexity Cryptology,
    6:1 (2014), 37-54. 
  • L. Babinkostova, K.W. Bombardier, M.C. Cole, T.A. Morrell and C.B. Scott, Elliptic Reciprocity (submitted)  arXiv:1212.198
  • J. Harlander, H.M. Lewis, J.W. Siegel and C. Xu, The Conjugacy Problem in Group Theory manuscript
  • A.N. Earls, J. Harlander,  G.F. Islambouli, R.T. Keller and M. Yang, Labeled oriented trees that are not diagrammatically reducible (in preparation)
  • J.L. Herlin, A.C. Nelson and M. Scheepers, Using ciliate operations to construct chromosome phylogenies, Involve, 9:1 (2016), 1 - 26.   arXiv:1210.0234 
  • C. Anderson, M. Scheepers, M. C. Warner and H. C. Wauck, On permutations optimized for sorting by the ciliate decryptome (in preparation)
  • R.V. Gerecke, J. Harlander, R.J. Manheimer, B.W. Oakley and S. Rahman, Factor groups of Knot and LOT groups arXiv:1505.06364v1
  • A.D. Albertson, L. Babinkostova, H.L. de Kergorlay, A.M. Hegedus, DS.. Nikolov and L.J. Wells, The Round Functions in the Whirlpool Hash Function (in preparation)
  • A.D. Albertson, L. Babinkostova, H.L. de Kergorlay, A.M.. Hegedus, DS.. Nikolov and L.J. Wells, The Cycle Structure of the Discrete Exponential Function (in preparation)
  • C. Jansen, M. Scheepers, S.L. Simon and E.E. Tatum, Context directed reversals and the ciliate decryptome, (submitted) arXiv:1603.06149
  • K.L.M. Adamyk, E.T. Holmes, G. Mayfield, D.J. Moritz, M. Scheepers, B.E. Tenner and H.C. Wauck, Sorting permutations: Games, Genomes and Cycles, Discrete Mathematics, Algorithms and Applications 9:4 (2017), 1750063 (31 pp)
  • C.L. Jansen, M. Scheepers, S.L. Simon and E.E. Tatum, Permutation sorting and a game on graphs, (submitted) arXiv:1411.5429
  • L. Babinkostova, J. Keller, B. Schreiner, J. Schreiner-McGraw and K. Stubbs, Generalization of the Lane Hash Function (in preparation)
  • L. Babinkostova, J. Keller, B. Schreiner, J. Schreiner-McGraw and K. Stubbs, Almost Translation Based Ciphers (in preparation)
  • D. Condon, S. Coskey, L. Serafin and C. Stockdale, On Generalizations of Separating and Splitting Families, Electronic Journal of Combinatorics 23:3 (2016) #P3.36, 19pp arXiv1412.4683
  • H.Q. Li, J. Ramsey, M. Scheepers, H.E. Schilling and C.D. Stanford, Context directed reversals of signed permutations and graphs, (in preparation)
  • L. Babinkostova, J.C. Bahr, Y.H. Kim, E. Neyman and G.K. Taylor, Anomalous primes and the Elliptic Korselt criterion, arXiv1608.02317
  • P. Bernstein, C. Bortner, S. Coskey, S. Li and C. Simpson, The set splittability problem, arXiv:1611.01542
  • M. Gaetz, B. Molokach, M. Scheepers and M. Shanks, Quantifying CDS Sortability of Permutations Using Strategic Piles, (in preparation)
  • L. Babinkostova, A. Hern├índez-Espiet and H.J. Kim, On Types of Elliptic Pseudoprimes, arXiv:1710.05264


DATA PRODUCTS at OEIS



  • A249165, Number of cds sortable permutations in Sn
  • A260506, Number of cdr or cds sortable signed permutations of length n
  • A260509, Number of two-rooted graphs in class (a).
  • A260511, Number of cdr sortable signed permutations of length n
  • A260695, Number of permutations in Sn for which minimum number of block swaps sorting the permuatation is maximum in Sn
  • A267323, Number of permutations in Snwith strategic pile of size 3.
  • A267324, Number of permutations in Snwith strategic pile of size 4.
  • A267391, Number of permutations in Snwith strategic pile of size 5.
  • A274351, First terms of proper elliptic 6-cycles
  • A281259, Number of permutations in Sn with strategic pile of size 6.
  • A289472, Number of gcds sortable two-rooted graphs on n vertices
  • A289483, Number of gcds sortable two-rooted Eulerian graphs on n vertices
  • A290338, Euler elliptic Carmichael numbers for the elliptic curve y^2 = x^3 + 80
  • A290339, Strong elliptic Carmichael numbers for the elliptic curve y^2 = x^3 + 80
  • A290560, Generalized Lucas-Carmichael numbers for D = 9697


PRESENTATIONS


 

Shenandoah Undergraduate Mathematics and Statistics Conference 2017
October 07, James Madison University

Colby A. Brown

  1. The Sortability of Permutations under Context Directed Swaps  (oral presentation: 12:10-12:25)
  2. The Sortability of Graphs and Matrices under Context Directed Swaps   (poster presentation: 1-st place award)

Young Mathematician's Conference 2017
August 12, The Ohio State University

Rashmika Goswami, Sorting Matrices with Context Directed Swaps  (oral presentation)

2017 REU MATH Symposium
July 28, Boise State University

B. Bentz, A. Espiet-Hernandez, M. Hassan and H.J. Kim, Relationships among Pseudoprimes and Korselt Criteria  (oral presentation)
C.A. Brown, C.S. Carrillo-Vasquez,R. Goswami and S. Heil, The Mathematical Dynamics of Ciliate Gene Sorting Algorithms  (oral presentation)
C. Chase, O. Dennis, L. Guatelli and J. Modi, Cycle Transformations and cdr - A Unifying Concept   (oral presentation)

2017 Idaho Conference on Undergraduate Research
July 26-27, Boise, ID

L. Babinkostova, B. Bentz, A. Espiet-Hernandez, M. Hassan and H.J. Kim, Anomalous Primes and the Elliptic Korselt Criterion  (poster presentation)
C.A. Brown, C.S. Carrillo-Vasquez,R. Goswami, S. Heil and M. Scheepers, The Sortability of Graphs and Matrices under Context Directed Swaps   (poster presentation)
C. Chase, O. Dennis, L. Guatelli, J. Modi and M. Scheepers, Cycle Transformations and CDR - A Unifying Concept  (poster presentation)

2017 Joint Mathematics Meetings
January 4-7, Atlanta, GA

M. Gaetz, B. Molokach and M. Shanks, Quantifying CDS Sortability of Permutations Using Strategic Piles   (poster presentation: MAA Outstanding Presentation award )
P. Bernstein, C. Bortner, S. Li and C. Simpson, Complexity and Characterization of Set Splitting  (poster presentation)
J. Barr, Y. Kim, E. Neyman and G. Taylor, Anomalous Primes and the Elliptic Korselt Criterion  (poster presentation: MAA Outstanding Presentation award)

2016 MAA MD-DC-VA Sectional Meeting
November 4-5, Johns Hopkins University, Baltimore, Maryland

E. Neyman, Anomalous Primes and the Elliptic Korselt Criterion  (poster presentation)

2016 CUR REU Symposium
October 23-24, Arlington, Virginia

G.K. Taylor, Anomalous Primes and the Elliptic Korselt Criterion  (poster presentation)

2016 Integers Conference
October 6 - 9, University of West Georgia

Y. Kim, Anomalous Primes and the Elliptic Korselt Criterion  (oral presentation)

2016 Shenandoha Undergraduate Mathematics and Statistics Conference (SUMS)
September 24, James Madison University

G.K. Taylor, Anomalous Primes and the Elliptic Korselt Criterion  (oral presentation)

2016 REU MATH Symposium
July 29, Boise State University

J. Bahr, Y. Kim, E. Neyman and G.K. Taylor, Anomalous Primes and Elliptic Carmichael Numbers  (oral presentation)
M. Gaetz, B. Molokach and M. Shanks, Quantifying CDS Sortability of Permutations Using Strategic Piles  (oral presentation)
P. Bernstein, C. Bortner, S. Li and C. Simpson, Complexity & Characterization of Set Splitting   (oral presentation)

2016 Idaho Conference on Undergraduate Research
July 27-28, Boise, ID

L. Babinkostova, J. Bahr, Y. Kim, E. Neyman and G.K. Taylor, Anomalous Primes and the Elliptic Korselt Criterion  (poster presentation)
P. Bernstein, C. Bortner, S. Coskey, S. Li and C. Simpson, Complexity and Characterization of Set Splitting  (poster presentation)
M. Gaetz, B. Molokach, M. Scheepers and M. Shanks, Quantifying CDS Sortability of Permutations Using Strategic Piles   (poster presentation)

Szego Seminar
April 13 2016, Washington University of St. Louis, MO

C. Stockdale, The Minimum Sizes of Separating and Splitting Families.  (oral presentation)

2016 Joint Mathematics Meetings
January 6-9, Seattle, WA

H.Q. Li, J. Ramsey, H. Schilling and C. Stanford, Context Directed Reversals of Signed Permutations  (poster presentation: MAA Outstanding Presentation award )
G. Currier and C. Okasaki, Minimality of Uniform Splitting Families  (poster presentation)
M. Mastrianni, N. Lacasse, B. Lin and D. Khripkov, Sums of Permutations in Cryptographic Hash Functions   (poster presentation)
D. Kondryatuk and S. Potter, A study of Games over Finite Groups   (poster presentation)

Mathematics Club Seminar
November 2015, University of Massachusetts-Amherst, MA

H. Schilling, Context Directed Reversals of Permutations and Graphs.  (oral presentation)  

2015 CUR REU Symposium
October 25-26, Arlington, VA

H.Q. Li, Context Directed Reversals of Signed Permutations  (poster presentation)

COPLAC Northeast Regional Undergraduate Research, Scholarly, and Creative Activity Conference
October 23-24 2015, Ramapo College, NJ

N. Lacasse, Sums of Permutations in Cryptographic Hash Functions

2015 REU MATH Symposium
July 31, Boise State University

H.Q. Li, J. Ramsey, H. Schilling and C. Stanford, Context Directed Reversals of Signed Permutations  (oral presentation)
G. Currier and C. Okasaki, Minimality of Uniform Splitting Families  (oral presentation)
M. Mastrianni, N. Lacasse, B. Lin and D. Khripkov, Sums of Permutations in Cryptographic Hash Functions
  (oral presentation)

2015 Idaho Conference on Undergraduate Research
July 29-30, Boise, ID

H.Q. Li, J. Ramsey, H. Schilling and C. Stanford, Context Directed Reversals of Signed Permutations  (poster presentation)
G. Currier and C. Okasaki, Minimality of Uniform Splitting Families  (poster presentation)
M. Mastrianni, N. Lacasse, B. Lin and D. Khripkov, Sums of Permutations in Cryptographic Hash Functions
  (poster presentation)
D. Kondryatuk and S. Potter, A study of Games over Finite Groups   (poster presentation)

2015 Joint Mathematics Meetings
January 10-13, San Antonio, TX

K. Stubbs, Generalized AES-based Hash Functions  (poster presentation)
C.L. Jansen, S.L. Simon, E. Tatum, Games and Genomes  (poster presentation)
D. Condon, L. Serafin, C. Stockdale, Graphs, Probability and Separating Families
  (poster presentation)

2014 CUR REU Symposium
October 15-18, Arlington, VA

K. Stubbs, Generalized AES-based Ciphers 

2014 Student Seminar
October 6, Wellesley College

B. Schreiner, Hash Functions 

2014 REU MATH Symposium
August 1, Boise State University

J. Keller, B. Schreiner, J. Schreiner-McGraw and K. Stubbs, Generalized AES-based Ciphers  
C. Jansen, S. Simon, E. Tatum, Games and Genomes 
D. Condon, L. Serafin, C. Stockdale, Graphs, Probability and Separating Families
 

2014 Idaho Conference on Undergraduate Research
July 30-31, Boise, ID

J. Keller, B. Schreiner, J. Schreiner-McGraw and K. Stubbs, Generalized AES-based Hash Functions  (poster presentation)
C. Jansen, S. Simon, E. Tatum, Games and Genomes (poster presentation)
D. Condon, L. Serafin, C. Stockdale, Graphs, Probability and Separating Families
 (poster presentation)

2014 REU Mathematics
June 26, Boise State University
T. Morrell, Elliptic Curves and Elliptic Reciprocity

2014 Undergraduate Research Symposium - Gordon College
May 7, Gordon College, Wenham, Massachusetts

K.L.M. Adamyk, Games, Genomes, and Graphs: A Mathematical Investigation of DNA Decryption in Ciliates (poster presentation)

2014 Northwest Undergraduate Mathematics Symposium
April 12, Oregon State University, Corvallis, Oregon

G. Mayfield, Game Theory and Algebraic Structures (AWM Award For Presentation)

2014 Joint Mathematics Meetings
January 15-18, Baltimore, MD

D. Albertson, H. de Kergorlay and A. Hegedus, Generalizations of the Whirlpool Hash Function  (poster presentation)
K. Adamyk, E. Holmes and D. Moritz, Games, Genomes and Graphs (poster presentation)
R. Gerecke and B. Oakley, Factor Groups of Knot and LOT Groups
 (poster presentation)

2013 MAA Northeastern Sectional Meeting
November 22, Wheaton College

K. Adamyk, Games, Genomes and Graphs

2013 Algebra, Geometry and Cryptology Seminar
November 12, Boise State University

D. Albertson, Generalizations of the Whirlpool Hash Function

CUR Conference of Research Experiences for Undergraduates Student Scholarship
October 27-28, 2013 Arlington, Virginia

H. de Kergorlay, Generalizations of the Whirlpool Hash Function

2013 Southeastern Conference for Undergraduate Women in Mathematics
October 26-27, Clemson University, South Carolina

R. Gerecke, Factor Groups of Knot and LOT Groups

2013 Mathematics REU Seminar
October 22, The College of New York

Ryan Manheimer, Factor Groups of LOT and Knot Groups

Claremont Topology Seminar
October 15, Pomona College

R. Gerecke, Factor Groups of Knot and LOT Groups

2013 MATH FORUM
September 26, Gordon College

K. Adamyk, Games, Genomes and Graphs

2013 Summer Undergraduate Research Conference [Proceedings]
August 1, Boise State University
D. Albertson, H. de Kergorlay, A. Hegedus, D. Nikolov and L. Wells, Generalizations of the Whirlpool Hash Function  (poster presentation)
K. Adamyk, E. Holmes, G. Mayfield and D. Moritz, Games, Genomes and Graphs  (poster presentation)
R. Gerecke, R. Manheimer, S. Rahman and B. Oakley, Factor Groups of Knots and Lots
 (poster presentation)

2013 REU Symposium in Mathematics [Proceedings]
July 31, Boise State University
D. Albertson, H. de Kergorlay, A. Hegedus, D. Nikolov and L. Wells, Generalizations of the Whirlpool Hash Function
K. Adamyk, E. Holmes, G. Mayfield and D. Moritz, Games, Genomes and Graphs
R. Gerecke, R. Manheimer, S. Rahman and B. Oakley, Factor Groups of Knots and Lots

2013 AMS Spring Western Sectional Meeting
April 13-14, University of Colorado, Boulder, CO
C. Anderson, Biological Implications of the Mathematical Properties of Cilliate Genome Decryption

K. Bombardier, Algebraic Properties of Generalized Rijndael-like Ciphers
C. Scott,  Elliptic Reciprocity
H. Wauck, Mathematical Representations of Ciliate Genome Decryption

2013 AMS Spring Eastern Sectional Meeting
April 5-6, Boston College, Chestnut Hill, MA
T. Morrell, Elliptic Reciprocity
M. Cole, AES-like Ciphers over any Finite Field

2013 MAA Spring SoCal-Nev Section Meeting
April 14, California State University, Fullerton, CA
A. Earls and G. Islambouili, Labeled Oriented Intervals That Are Not Diagrammatically Reducible (poster presentation)

2013 Northwest Undergraduate Mathematics Symposium
April 6, Tacoma, WA
C. Anderson, Biological Implications of the Mathematical Properties of Cilliate Genome Decryption

2013 Mathematics Seminar
February 28, Gustavus Adolphus College
H. Wauck, Mathematical Representations of Cilliate Genome Decryption

2012 Northfield Undergraduate Mathematics Symposium
September 25, Carlton College
A. Earls, Labeled Oriented Intervals that are not Diagrammatically Reducible


2012 Summer Undergraduate Research Conference [Proceedings]
July 29, Boise State University
C. Anderson, M. Warner, and H. Wauck, Ciliate Genome Remodeling (poster presentation)
K. Bombardier, M. Cole, T. Morrell and C. Scott, Elliptic Pairs and Elliptic Reciprocity
(poster presentation)
K. Bombardier, M. Cole, T. Morrell and C. Scot,
Generalizations of Advanced Encryption Standard
(poster presentation)
A. Earls, G. Islambouili, R. Keller, and M. Yang, Labeled Oriented Intervals That Are Not Diagrammatically Reducible
(poster presentation)  


2012 REU Symposium in Mathematics [Proceedings]

July 28, Boise State University
C. Anderson, M. Warner, and H. Wauck, Cilliate Genome Remodeling
K. Bombardier, M. Cole, T. Morrell and C. Scott, Elliptic Reciprocity and Generalizations of the Advanced Encryption Standard
A. Earls, G. Islambouili, R. Keller, and M. Yang, Labeled Oriented Intervals that are not Diagrammatically Reducible


93rd Annual Meeting of the AAAS Pacific Division[Proceedings]
June 24-27, 2012
Boise, Idaho

C. Anderson, Genome Remodeling in Developmental Time: Algorithms for Ciliates (part I)
M. Warner,
Genome Remodeling in Developmental Time: Algorithms for Ciliates (part II)
H. Wauck,
Genome Remodeling in Developmental Time: Algorithms for Ciliates (part III)
A. Earls, Geometry, Topology, and Complexity of Virtual Knots (part I)
G. Islambouili,
Geometry, Topology, and Complexity of Virtual Knots (part II)
R. Keller,
Geometry, Topology, and Complexity of Virtual Knots (part III)
M. Yang,
Geometry, Topology, and Complexity of Virtual Knots (part IV)
K. Bombardier, Computability and Complexity in Elliptic Curves and Cryptography: Parity of s-round Generalized AES - Best Presentation (3rd place)
M. Cole, Computability and Complexity in Elliptic Curves and Cryptography: SubBytes, MixColumns, and one round Generalized AES
T. Morell, Computability and Complexity in Elliptic Curves and Cryptography: An Algorithm for Finding Elliptic Curves of Prime Order
A. Nelson, Exploring Phylogenetic Relationships in Drosophila with Ciliate Operations - Best Presentation (2nd place)
K. Williams,
Symmetric key cryptography over non-binary algebraic structures - Best Presentation (3rd place)

2012 Boise State Undergraduate Research Conference
April 16, Boise State University

A. Nelson, Exploring Phylogenetic Relationships in Drosophila using Ciliate Operations
K. Williams, Luby-Rackoff Variants over Finite Groups

2012 NCUR meeting
March 29 - 31, Weber University, Utah

A. Nelson,
Exploring Phylogenetic Relationships in Drosophila using Ciliate Operations
A. Bowden, Elliptic Curves, Feistel Networks and the Design of E-DES
K. Williams, Luby - Rackoff Variants over Finite Groups
A. Kimball, Security Properties of Elliptic Curve DES

2012 Loyola Marymount Undergraduate Research Symposium
March 23, Loyola
Marymount University
A. Bowden, The Data Encryption Standard Over Elliptic Curves


2012 AMS Southeastern Section Meeting
March 9-10, Clayton State University, Georgia

A. Kimball, On the Design of Simplified DES Based on Elliptic Curves (Award for Best Presentation)


2012 Seminar Talk
February 24, Department of Mathematics, University of Northern Colorado
J. Herlin, Exploring Phylogenetic Relationships in Drosophilia with Cilliate Operations

2012 Joint Mathematics Meetings
January 4-7, 2012, Boston, MA
J. Herlin and A. Nelson, Mathematics and Genome Remodeling (poster presentation)
J. Siegel and C. Xu, Conjugacy Problem - Theory and applications (poster presentation)


CUR Conference for Undergraduates Student Scholarship

October 16-17, 2011, Arlington, Virginia

K. Williams, DES and Luby - Rackoff over Finite groups


2011 Summer Undergraduate Research Conference

July 28, Boise State University

H. Brown, J. Siegel and C. Xu, Conjugacy Problem - Theory and Applications (poster presentation)
J. Herlin and A. Nelson, Mathematics and Genome Remodeling (poster presentation)
A. Bowden, A. Kimball and K. Williams, DES over Finite Groups
(poster presentation)

2011 REU Symposium in Mathematics
July 27, Boise State University

H. Brown, Conjugacy Problem - Theory and Applications I
J. Siegel
Conjugacy Problem - Theory and Applications II
C. Xu
Conjugacy Problem - Theory and applications III
J. Herlin and A. Nelson Mathematics and Genome Remodeling 
A. Bowden, A. Kimball and K. Williams
DES over Finite Groups