Research

Malmskog's Lemma!

Malmskog’s Lemma!

I am interested in problems that combine number theory, geometry, combinatorics, and algebra. Though I have worked in graph theory and lattice-based cryptography, the most consistent theme of my work is that of curves over finite fields. These curves are fascinating because they bridges the finite and the infinite, are amenable to both computational exploration and geometric intuition, and present a surprisingly wide variety of intriguing questions.

Here is my current CV.

 

Colin is having this much fun collaborating with me!!

Colin is having this much fun collaborating with me!!

Here is my current publications list.

  • B. Malmskog and C. Rasmussen “Picard curves over Q with good reduction away from 3.”  To appear in LMS Computations.
  • I. Bouw, W. Ho, B. Malmskog, R. Scheidler, P. Srinivasan, and C. Vincent, “Zeta functions of a class of Artin-Scheier curves with many automorphisms.”  Research Directions in Number Theory: Proceedings from the 2014 WIN3 Workshop, Springer Publishing, 2016, pp. 87-124.
  • B. Malmskog and J. Muskat. “Local and Global Zeta Functions of Gauss’ Curve.” Rocky Mountain Journal of Mathematics, volume 45, 2015, pp. 275-285.
  • H. Frielander, D. Garton, B. Malmskog, R. Pries, and C. Weir. “The a-numbers of Jacobians of Suzuki Curves.” Proceedings of the American Mathematical Society,  vol. 141, 2013, pp. 3019–3028. http://arxiv.org/pdf/1110.6898
  • R. Guralnick, B. Malmskog, and R. Pries. “The Automorphism Groups of a Family of Maximal Curves.”  Journal of Algebra, vol. 361, 2012, pp. 92-106. http://arxiv.org/abs/1105.3952
  • B. Malmskog and M. Manes. “Ramified Covers of Graphs and the Ihara Zeta Functions of Certain Ramified Covers.” WIN — Women in Numbers, Fields Institute Communications, vol. 60, Amer. Math. Soc., Providence, RI, 2011, pp. 237–247. preprint fields zeta
  • K. Later, B. Malmskog, M. Naehrig, and V. Vaikuntanathan. “An efficient digital signature scheme based on the learning with errors problem over polynomial rings.”  Patent 20120159179,
  • B. Malmskog and M. Manes. “Almost Divisibility in the Ihara Zeta Functions of Certain Ramified Covers of q+1-regular graphs. Journal of Linear Algebra and Applications, vol. 432, 2010, pp. 2486-2506.

 

Submitted:

In Preparation:

  • Variations of the McEliece cryptosystem 2016, with Jessalyn Bolkema, Heide Gluesing-Luerssen, Christine Kelley, Kristin Lauter, and Joachim Rosenthal.
    In Preparation, expected December 2016

 

Math with friends at the Arizona Winter School–Team F_p!