Gary McGuire



School of Mathematical Sciences


Claude Shannon Institute for Discrete Mathematics, Coding and Cryptography


email: gary dot mcguire at ucd dot ie

Please email me if you would like a copy of any paper.

Recent Preprints:

On the Zeta Functions of an optimal tower of function fields over F4
posted arxiv June 2009 (with Alexey Zaytsev)

Elliptic Curves in Montgomery Form with B=1 and Their Low Order Torsion
posted iacr arxiv May 2009 (with Richard Moloney, Michael Markowitz)

S-Boxes, APN Functions and Related Codes
submitted December 2008, published (with Rafael Alvarez)

Proof of a Conjecture on the Sequence of Exceptional Numbers, Classifying Cyclic Codes and APN functions,
submitted December 2008, posted arxiv (with Fernando Hernando)

On the nonlinearity of the Exponential Welch Costas functions,
submitted December 2008, accepted (with Konstantinos Drakakis, Veronica Requena)

A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem,
accepted ARC2009 conference, December 2008 (with Brian Baldwin, Richard Moloney, Andrew Byrne, William P. Marnane)

CM Construction of Genus 2 Curves with p-rank 1,
posted arxiv November 2008 (with Laura Hitt O'Connor, Michael Naehrig, Marco Streng)

Automorphisms of Some APN Functions and an Inequivalence Result,
submitted October 2008 (with Carl Bracken, Eimear Byrne, Gabriele Nebe)

Division Polynomials for Twisted Edwards Curves,
posted arxiv September 2008 (with Richard Moloney, Laura Hitt)

The Weight Distributions of Cyclic Codes with Two Zeros and Zeta Functions,
submitted August 2008, accepted (with Nigel Boston)

APN Permutations on Zn and Costas Arrays,
Submitted June 2008, accepted (with Konstantinos Drakakis, Rod Gow)

Quadratic Binomial APN Functions and Absolutely Irreducible Polynomials,
Posted Arxiv May 2008 (with Eimear Byrne)

A Few More Quadratic APN Functions,
Submitted April 2008 (with Carl Bracken, Eimear Byrne, Nadya Markin)

Efficient use of cryptographic side channel in Finite Cyclic Groups,
Submitted March 2008 (with Anna Johnston)

Fourier Spectra of Binomial APN Functions,
Submitted February 2008, Accepted (with Carl Bracken, Eimear Byrne, Nadya Markin)

Construction of Bent Functions from Near-Bent Functions,
Submitted February 2008, Accepted, Published (with Gregor Leander)

Cocyclic Hadamard Matrices from Forms over Finite Frobenius Rings,
Submitted February 2008, Accepted (with Harold N. Ward)

Spectra of Boolean Functions, Subspaces of Matrices, and Going Up versus Going Down
Submitted September 2007, Accepted, Published

Construction of Space-Time Codes from Division Algebras with Roots of Unity as Non-Norm Elements
Submitted August 2007, Accepted, Published (with Jyrki Lahtonen, Nadya Markin)

Kasami Bent Functions are not Equivalent to their Duals,
Submitted July 2007, Accepted, Published (with Philippe Langevin, Gregor Leander)

On The Extended Walsh Spectrum of a New APN Function,
Submitted July 2007, Accepted (with Eimear Byrne, Carl Bracken, Nadya Markin)

Determining the Nonlinearity of a New Family of APN Functions,
Submitted June 2007, Accepted (with Eimear Byrne, Carl Bracken, Nadya Markin)

Analysis of Kasami-Welch Functions in Odd Dimension Using Stickelberger's Theorem,
Submitted May 2007, Resubmitted, Accepted (with Philippe Langevin, Gregor Leander, Eugen Zalinescu)

New Families of Quadratic Almost Perfect Nonlinear Trinomials and Multinomials,
Submitted April 2007, Accepted, Published (with Eimear Byrne, Carl Bracken, Nadya Markin)

Near-Bent Functions on a Hyperplane,
Submitted December 2006, Accepted, Published (with John Dillon)

Gold and Kasami-Welch Functions, Quadratic Forms, and Bent Functions,
Submitted December 2006, Accepted, Published (with Jyrki Lahtonen, Harold Ward)

A Counter-Example to a Conjecture of Niho,
Submitted November 2006, Accepted, Published (with Philippe Langevin, Gregor Leander)

Duals of Quasi-3 Designs are Not Necessarily Quasi-3,
Submitted November 2006, Accepted, Published (with Carl Bracken)



ECC 2007 in Dublin



Nicolas Banner



Where is this Fibonacci Chimney ?