- The links marked "publisher" point to the electronically
published version of an article. Typically, the publisher will
have an abstract of the article freely available, as well as
links to other articles in the journal or collection. They will
also have links for paid subscribers only, which include
full-text versions of the article in various formats and perhaps
also other information.

- The links marked "xxx" point to a version of an article at the
archive at
`<http://xxx.lanl.gov>`. This archive will have the abstract and full text of the article freely available in various formats.

- The links marked "slideshare" point to a version of a talk
posted at <http://www.slideshare.net>.
This site hosts slideshows which can be freely viewed in
your web browser or downloaded in PDF and/or PowerPoint
versions.

- The links marked "abs" point to a local text-only version of
an abstract, which is typically faster but harder to read than
the other versions.

- The links marked "pdf" (resp. "html") point to a local PDF
(resp. HTML) full-text version of a paper or talk.

- The links marked "web page" point to some other non-local version of the paper or talk.

- 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]

- A Comparison of Cryptography Courses.
*Cryptologia*, 28 (2), 2004. [publisher] [xxx] [abs] [pdf]

- 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]

- 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]

- Some Heuristics and Results for Small Cycles of the Discrete
Logarithm. With Pieter Moree.
*Mathematics of Computation*, 75:419–449, 2006. [publisher] [xxx] [abs]

- 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]

- 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)]]

- 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]

- 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]

- 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]

- Statistics for fixed points of the self-power
map. With Matthew Friedrichsen. Preprint. [xxx]

- 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 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 available)]

- Counting fixed points and two-cycles of the singular map
x ↦x . With Pamela A. Richardson and Margaret M. Robinson. Preprint. [xxx]^{xn}

- Mapping the discrete logarithm. With Daniel R. Cloutier.
ANTS VII, 2006.

- Abstract [pdf (conference web site)]
- Poster [pdf
(conference web site)] [slideshare]

- A statistical look at maps of the discrete logarithm.
With Nathan Lindle. ANTS VIII, 2008.

- Abstract [pdf
(conference web site)] [pdf]
Also published in
*Communications in Computer Algebra*, 42:57–59, 2008. [publisher] - Poster [pdf
(conference web site)] [pdf]
[slideshare]

- Math in Your Hands: Integrating the Use of Maple with
the Collaborative Use of Wireless Tablet PCs. WIPTE, 2008.

- Poster [slideshare] [abs]

- Fixed points and two-cycles of the self-power map. ANTS
X, 2012.

- Abstract [pdf (conference web site)] [pdf]
- Poster [pdf (conference web site)] [pdf] [slideshare]
- Statistics for fixed points of
*x*↦*x*mod^{x}*p.*With Matthew Friedrichsen. ANTS XI, 2014.- Abstract [pdf]
- Poster [pdf] [slideshare]

- Understanding the Magic: Teaching
Cryptography with Just the Right Amount of Mathematics
- Abstract [pdf]
- Slides [pdf] [slideshare]

- Cryptography and Computer Security for Undergraduates (Panel,
SIGCSE 2004)
- Abstract [pdf]
- Moderator (Paul De Palma, Gonzaga University) [html]
- Cryptography and Computer Security for Undergraduates (Suzanne Gladfelter, Penn State York) [html]
- Applied Cryptography (Charles Frank, Northern Kentucky University) [html]
- Mathematical Cryptography (Joshua Holden) [pdf] [slideshare]

- Underwater Hacker Missile Wars: A Multidisciplinary Design
Competition (ASEE 2005. With Richard Layton, Tina Hudson and
Laurence D. Merkle) [html]

- Number Theory, Polynomials, and the Advanced Encryption
Standard

- Slides [pdf] [slideshare]
[abs]

- Handout on S-AES [pdf]

- Slides [pdf] [slideshare]
[abs]
- The Pohlig-Hellman Exponentiation Cipher as a Bridge Between
Classical and Modern Cryptography

- Slides [pdf] [slideshare]
[abs]

- Slides [pdf] [slideshare]
[abs]

- Teaching the Group Theory of Permutation Ciphers [slideshare]
[abs]

- ``How Do You Say 'Cryptography' in Romanian?'' Learning About
Integers from Ciphers in Different Languages [slideshare]
[abs]

- A Good Hash Function is Hard to Find, and Vice Versa [slideshare] [abs]

- Modular Arithmetic and Trap Door Ciphers (RSA)

- Newest version [pdf] [slideshare] [abs]
- Older version (uglier, but longer) [html]

- A Tour of Public Key Cryptography (and of Number Theory) (Merkle's Puzzles, Diffie-Hellman, RSA, Massey-Omura, etc.) [html] [abs]
- AMS Special Session on Mathematics and Mathematics Education
in Fiber Arts (January 2005 Joint Mathematics Meetings) [web page]
- The graph theory of Blackwork embroidery (joint work with Lana Holden) [slideshare] [abs] [web page 1] [web page 2] [web page 3]
- Exhibit [web page]
- AMS "Highlights of the 2005 Joint Mathematics Meetings" [web page]

- Blackwork Embroidery and Algorithms for Maze Traversals
(joint work with Lana Holden) [slideshare]
[abs]

- How to Paint Your Way out of a Maze (joint work with Lana
Holden) [slideshare]
[abs]

- Two versions of a talk on math and art (joint work with Lana
Holden):

- Braids, Cables, and Cells: An Interesting Intersection of Mathematics, Computer Science, and Art (more general examples) [slideshare] [abs]
- Braids, Cables, and Cells: An Intersection of
Mathematics, Computer Science, and Fiber Arts (knitting and
crochet examples) [slideshare]
[abs]

- Braids, Cables, and Cells II: Representing Art and Craft with
Mathematics and Computer Science (joint work with Lana Holden)
[slideshare]
[abs]

- Stitching Graphs and Painting Mazes: Problems in
Generalizations of Eulerian Walks (joint work with Lana Holden)
[slideshare] [abs]

- Granny’s Not So Square, After All: Hyperbolic Tilings with
Truly Hyperbolic Crochet Motifs (joint work with Lana Holden) [slideshare]
[abs]

- Senior Thesis on ``Mapping the
Discrete Logarithm'', Daniel Cloutier, Computer Science
and Software Engineering department, 2004-2005.

- Senior Thesis on ``A
Statistical Look at Maps of the Discrete Logarithm'',
Nathaniel W. Lindle, Computer Science and Software
Engineering department, 2007-2008.

- Senior Thesis on ``Algebraic
Solutions to Overdefined Systems with Applications to
Cryptanalysis'', Eric Crockett, Computer Science and
Software Engineering department, 2010-2011.

- Senior Thesis on ``Counting
Solutions to Discrete Non-Algebraic Equations Modulo Prime
Powers'',
Abigail Mann, Mathematics Department, 2015-2016.

- Senior Thesis on ``Statistical
Analysis of Binary Functional Graphs of the Discrete Logarithm'',
Mitchell Orzech, Mathematics Department, 2015-2016.

- Research Experience for Undergraduates (REU) Projects:
- Mapping the Discrete Logarithm talk notes

- Announcing the Data Encryption Standard, Federal Information
Processing Standards Publication 46 (FIPS PUB 46), 1977 January
15. [pdf]

(No, I certainly didn't write this! But for some reason, there does not seem to be copy of this version of FIPS PUB 46 anywhere I can find on the web. So, here it is.)

- I did an email interview about cryptography with some very
nice students who were participating in a 2008 international
educational website design competition sponsored by
Oracle. Turns out they placed second in their division
("19 and under") and came up with a very nice site! Here
are links to the students'
site and my
interview.

- I was interviewed by Maplesoft for a User Case Study entitled
"Rose-Hulman Institute of Technology Uses Maple to Improve
Learning for Two Thousand Students". It was published in a
booklet entitled
*Bring Learning to Life*and also online.