Cyber defense and cryptography in undergraduate education

Spring Southeastern Sectional Meeting
University of Virginia, Charlottesville, VA
March 13-15, 2020,
Meeting #1143


Lubjana Beshaj
Cyber Fellow of Mathematics,
Army Cyber Institute
West Point, NY
Tony Shaska
Department of Mathematics
Oakland University University


Computing, communications, and storage resources worldwide continue to grow at an exponential rate. Unfortunately, computer security incidents continue to show parallel growth patterns. As the use of the Internet for commercial purposes continues to grow, so do the opportunities for its abuse by criminals.

Today's problems call for research of many kinds, both to understanding better the complexity of systems on which society depends and to lay the foundations for a world in which today's attacks can perhaps be ruled out.

The goal of this session is to bring together people from cyber security as well as cryptography who are involved in undergraduate education, including undergraduate students. We want to highlight the achievements of undergraduate students who are doing research in mathematical cryptography and share experiences among faculty members who have mentored and directed undergraduate projects in cyber security and cryptography.

In order to achieve this goal, a large majority of the talks will fall into the category of “Expository talks with specific open problems”. These talks will be self-contained and undergraduate-accessible. Each talk will provide a short background of the topic, a list of very specific problems and projects for new research, and extensive recommendations for further reading.

We intend to include talks from undergraduate students who have successfully completed research projects in the area. Both the organizers and several of faculty speakers listed below have mentored many undergraduate students in cryptography and related areas. All those students will be invited to participate.

Topics of the session include, but are not limited to:

  • Cyber security
  • Computational number theory. Primality and integer factorization.
  • Schemes based on group theory and algebraic coding theory.
  • Multivariate polynomial cryptosystems. Gröbner Bases. Resultants.
  • Pseudorandom number generators.
  • Lattice Problems
  • Algebraic Curves
  • Divisors and Picard groups
  • Abelian varieties
  • Endomorphisms and isogenies
  • Torsion points and Tate modules
  • l-adic representations and characteristic polynomials
  • Hyperelliptic and superelliptic Jacobians
  • Division polynomials for higher genus
  • Modular polynomials for higher genus
  • Diffie-Hellman Key Exchange on Abelian varieties
  • Index calculus
  • Isogenies of Jacobians via Correspondences
  • Modular correspondences
  • Correspondences via modular groups
  • Elliptic Curve Cryptography
  • Point Counting
  • Supersingular Isogeny Based Cryptography
  • Abelian surfaces
  • Computing isogenies of genus 2 Jacobians
  • Picard groups of curves of genus 3
  • Isogenies via $S_4$ covers
  • Others
  • All speakers in this session will be faculty members, postdocs, and graduate students who have mentored undergraduates in research related to cryptography or undergraduate students who have completed research projects in cryptography or related areas.

    Submitting Abstracts

    Here is the website of the session from the AMS. Click on the left to submit abstracts.

    Special Session on Cyber Defense and Cryptography in Undergraduate Education