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1 Dembowski-Ostrom Polynomials and Linearised Polynomials Let p be a prime and q = p e. Let F q denote the finite field of order q and F * q represent the set of non-zero elements of F q. The ring of polynomials in the indeterminate X with coefficients from F q will be represented by F q [X]. A polynomial f ∈ F q [X] which permutes F q under evaluation is… (More)

- Robert S. Coulter, Marie Henderson, Rex W. Matthews
- Finite Fields and Their Applications
- 2009

Let H be a subgroup of the multiplicative group of a finite field. In this note we give a method for constructing permutation polynomials over the field using a bi-jective map from H to a coset of H. A similar, but inequivalent, method for lifting permutation behaviour of a polynomial to an extension field is also given.

- Robert S. Coulter, Marie Henderson, Pamela Kosick
- Des. Codes Cryptography
- 2007

We consider the implications of the equivalence of commutative semifields of odd order and planar Dembowski-Ostrom polynomials. This equivalence was outlined recently by Coulter and Henderson. In particular, following a more general statement concerning semifields we identify a form of planar Dembowski-Ostrom polynomial which must define a commutative… (More)

- Marie Henderson, Robert S. Coulter, Ed Dawson, Eiji Okamoto
- ACISP
- 2002

The development of Public Key Infrastructures (PKIs) is highly desirable to support secure digital transactions and communications throughout existing networks. It is important to adopt a particular trust structure or PKI model at an early stage as this forms a basis for the PKI's development. Many PKI models have been proposed but use only natural language… (More)

- Chuchang Liu, Maris A. Ozols, Marie Henderson, Anthony Cant
- Public Key Cryptography
- 2000

- Maris A. Ozols, Marie Henderson, Chuchang Liu, Anthony Cant
- ACISP
- 2000

- Robert S. Coulter, Marie Henderson
- Discrete Mathematics
- 1999

We give an alternative proof of the fact that a planar function cannot exist on groups of even order. The argument involved leads us to define a class of functions which we call semi-planar. Through the introduction of an incidence structure we construct semi-biplanes using semi-planar functions. The method involved represents a new approach to constructing… (More)

We report on a recent implementation of Giesbrecht's algorithm for factoring poly-nomials in a skew-polynomial ring. We also discuss the equivalence between factor-ing polynomials in a skew-polynomial ring and decomposing p s-polynomials over a finite field, and how Giesbrecht's algorithm is outlined in some detail by Ore in the 1930's. We end with some… (More)

- M H Henderson
- Medical teacher
- 2000

The main features of a learning programme for medical students that addresses attitudinal issues, using as an example attitudes to homosexuality, are described. Essential and useful features and strategies of the exercise are outlined, together with potential problems.

- Robert S. Coulter, Marie Henderson
- Finite Fields and Their Applications
- 2013

Note: This is a personal preprint; for correct page numbering and references please see the original paper, the proper citation for which is: Abstract In a recent paper, Kyureghyan and¨Ozbudak proved that u ∈ {1, 2} was a sufficient condition for the polynomial X(X q 2 + X q + (1 − u)X) to be planar over F q 3 , and conjectured the condition was also… (More)