Dr. Joshua Holden specializes in number theory, cryptography, and algebra. He has led National Science Foundation-funded research projects exploring discrete logarithms, has led the campus committee on integrating classroom technology, and also advised several student projects and theses. Dr. Holden held post-doctoral positions at the University of Massachusetts and Duke University and has industry experience as a cryptography consultant for Vadium Technology, Inc. He also advises the Jewish culture and juggling clubs. Check out his personal web page

Academic Degrees

  • PhD, Brown University, Mathematics, 1998
  • AM, Brown University, Mathematics, 1994
  • AB, Harvard University, Mathematics, 1992

Awards & Honors

  • Honorary Member, Upsilon Pi Epsilon, 2008
  • Best Paper, Mechanical Engineering Division, ASEE Annual Conference, 2005

Research Interests

  • Computational number theory
  • Discrete logarithms
  • Algebraic number theory
  • Applications of number theory to cryptography
  • Cryptography consultant, Vadium Technology, Inc., 2003

Select Publications & Presentations

  • “Modeling Braids, Cables, and Weaves with Stranded Cellular Automata,” Proceedings of Bridges: Mathematics, Music, Art, Architecture, Culture, Tessellations Publishing, 2016
  • “A Good Hash Function is Hard to Find, and Vice Versa,” Cryptologia, 37:107-119, 2013
  • “Demitasse: A ‘Small’ Version of the Tiny Encryption Algorithm and its Use in a Classroom Setting,”Cryptologia, 37:74-83, 2013
  • “An Interactive Tour of Public Key Cryptography (and of Number Theory)'', Illinois Mathematical Association of America Section Meeting, 2012; Indiana Mathematical Association of American Section Meeting, 2014
  • Holden, J. and Robinson, M. M., “Counting Fixed Points, Two-Cycles, and Collisions of the Discrete Exponential Function using p-adic Methods,” Journal of the Australian Mathematical Society, 92, 163-178, 2012
  • “Braids, Cables, and Cells: Modeling Art and Craft with Mathematics and Computer Science,” Illinois Mathematical Association of America Section Meeting, 2012
  • Holden, J., Sexton, S., and Williams, J., “Math in Your Hands: Integrating the Use of Maple with the Collaborative Use of Wireless Tablet PCs,” The Impact of Tablet PCs and Pen-based Technology: New Horizons, Purdue University Press, 2009 

Teaching Interests

  • Calculus
  • Discrete mathematics
  • Number theory
  • Cryptography
  • Abstract algebra
  • Theoretical computer science
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