Number Theory and Cryptography:

• Irregularity of prime numbers over real quadratic fields. In: Algorithmic number theory: third international symposium; proceedings, no. 1423 in Springer Lecture Notes in Computer Science, Springer-Verlag, 1998. [publisher] [abs] [pdf]
• Comparison of Algorithms to Calculate “Quadratic Irregularity” of Prime Numbers: Extended Abstract. In: Proceedings of the Conference on The Mathematics of Public-Key Cryptography, June 12–17, 1999, Fields Institute, Toronto. [abs] [pdf]
• On the Fontaine-Mazur Conjecture for number fields and an analogue for function fields. Journal of Number Theory, 81:16–47, 2000. [publisher] [abs] [pdf]
• Comparison of algorithms to calculate quadratic irregularity of prime numbers. Mathematics of Computation, 71:863–871, 2002. [publisher] [xxx] [abs] [pdf]
• Fixed Points and Two-Cycles of the Discrete Logarithm. In: Algorithmic number theory: 5th international symposium; proceedings, no. 2369 in Springer Lecture Notes in Computer Science, Springer-Verlag, 2002. [publisher] [abs] [pdf] [addenda/corrigenda from xxx]
• Notes on an analogue of the Fontaine-Mazur conjecture. With Jeffrey D. Achter. Journal de Théorie des Nombres de Bordeaux, 15:627–637, 2003. [publisher] [xxx] [abs]
• First-hit analysis of algorithms for computing quadratic irregularity. Mathematics of Computation, 73:939–948, 2004. [publisher] [xxx] [abs]
• Distribution of Values of Real Quadratic Zeta Functions. In: Unusual Applications of Number Theory, no. 64 in DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, AMS, 2004. [xxx] [abs]
• New Conjectures and Results for Small Cycles of the Discrete Logarithm. With Pieter Moree. In: High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, no. 41 in Fields Institute Communications, AMS, 2004. [xxx] [abs]
• Abelian varieties over finite fields with a specified characteristic polynomial modulo ℓ. Journal de Théorie des Nombres de Bordeaux, 16:173–178, 2004. [publisher] [xxx] [abs]
• Distribution of the Error in Estimated Numbers of Fixed Points of the Discrete Logarithm. Communications in Computer Algebra, 38:111–118, 2004. [publisher or publisher] [xxx] [abs]
• Some Heuristics and Results for Small Cycles of the Discrete Logarithm. With Pieter Moree. Mathematics of Computation, 75:419–449, 2006. [publisher] [xxx] [abs]
• Mapping the discrete logarithm.  With Daniel R. Cloutier. Involve, 3:197–213, 2010.  [publisher] [pdf (for screen)]  [pdf (for printing)]
• Counting Fixed Points, Two-Cycles, and Collisions of the Discrete Exponential Function using p-adic Methods. With Margaret M. Robinson.   Journal of the Australian Mathematical Society, 92: 163-178, 2012. (Special issue in memory of Alf van der Poorten) [publisher] [xxx]
• Counting fixed points and rooted closed walks of the singular map x ↦ x^xn.  With Pamela A. Richardson and Margaret M. Robinson.  p-Adic Numbers, Ultrametric Analysis and Applications, 12: 12–28, 2020. [publisher] [xxx]

Mathematics of Arts and Crafts:

• The Graph Theory of Blackwork Embroidery. In:  Making Mathematics with Needlework: Ten Papers and Ten Projects, edited by sarah-marie belcastro and Carolyn Yackel.  A.K. Peters, 2007.  [book web page] [abs] [pdf (preprint, not complete)]]
• Hyperbolic Tilings with Truly Hyperbolic Crochet Motifs. With Lana Holden. In: Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, Tessellations Publishing, 2014.  [publisher (full-text freely available)]
• Modeling Braids, Cables, and Weaves with Stranded Cellular Automata. With Lana Holden. In: Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Culture, Tessellations Publishing, 2016.  [publisher (full-text freely available)]
• The Complexity of Braids, Cables, and Weaves Modeled with Stranded Cellular Automata. In: Proceedings of Bridges 2017: Mathematics, Music, Art, Architecture, Education, Culture, Tessellations Publishing, 2017.  [publisher (full-text freely available)]
• Rock Me Fibonacci: Using Recurrence Relations and State-Transition Matrices to Count Rock Drum Fill Patterns. In: Proceedings of Bridges 2018: Mathematics, Music, Art, Architecture, Education, Culture, Tessellations Publishing, 2018.  [publisher (full-text freely available)]
• A Survey of Cellular Automata in Fiber Arts. With Lana Holden.  In:  Handbook of the Mathematics of the Arts and Sciences, Springer, 2019. [publisher]

Teaching:

• A Comparison of Cryptography Courses. Cryptologia, 28 (2), 2004. [publisher] [xxx] [abs] [pdf]
• Underwater Model Rockets: An Innovative Design Problem and Competition for Undergraduate Students in Engineering, Math and Science. With Richard Layton, Tina Hudson and Laurence D. Merkle. In: Proceedings of the 2005 American Society for Engineering Education Annual Conference and Exposition, 2005. [publisher] [abs] [pdf]
• Underwater Hacker Missile Wars: A Cryptography and Engineering Contest. With Richard Layton, Laurence Merkle, and Tina Hudson. Cryptologia, 30:69–77, 2006. [publisher] [xxx] [abs]
• Review of Complexity and Cryptography: An Introduction by John Talbot and Dominic Welsh Cryptologia, 32:92–97, 2008. [publisher]
• Math in Your Hands: Integrating the Use of Maple with the Collaborative Use of Wireless Tablet PCs. With Shannon Sexton and Julia Williams. In: The Impact of Tablet PCs and Pen-based Technology: New Horizons, Purdue University Press, 2009.  [book web page] [abs]
• A Good Hash Function is Hard to Find, and Vice Versa. Cryptologia, 37:107-119, 2013.  [pdf]
  Acknowledgement:  This is an Author’s Accepted Manuscript of an article published in Cryptologia, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/01611194.2012.687429. [publisher]
• Demitasse: A “Small” Version of the Tiny Encryption Algorithm and its Use in a Classroom Setting.   Cryptologia, 37:74-83, 2013.  [pdf]
  Acknowledgement:  This is an Author’s Accepted Manuscript of an article published in Cryptologia, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/01611194.2012.660237. [publisher]