Professor Kathy Horadam

Position	Professor
School / Work Unit	Math & Geospatial Sciences
Contact Details	+(61 3) 9925 2752 kathy.horadam@rmit.edu.au
Location	Building: 8 Level: 9 Room: 11 City Campus
College/Portfolio	Science, Engineering & Health

Professor Kathryn Horadam

Qualifications

Doctor of Philosophy, Pure Mathematics, Australian National University, 1977
Bachelor of Science (Honours 1st class), Pure Mathematics, Australian National University, 1972

Responsibilities

Honours Advanced Topics in Discrete Mathematics
Professor of Mathematics

Teaching Activities

Areas of expertise

Abstract algebra, combinatorial design theory, coding theory and information security, biometrics and complex networks.

Postgraduate Programs in Information Security and Assurance

Credentials

Fellow, Australian Mathematical Society, 2001
Life Member, Combinatorial Mathematics Society of Australasia, 1993
Fellow, Institute of Combinatorics and its Applications, 1991

Research Activities

Application of finite group cohomology to combinatorial design theory and to reliable and secure digital communications. I am an originator of the theory of cocyclic Hadamard matrices and the originator of the theory of cocyclic error-correcting codes.
Information Security, specialising in nonlinearity of data and digital sequences used for cryptographic purposes, and authentication and identification problems, particularly biometrics.
Complex spatial and information networks.
Author of over 70 research publications; keynote speaker and session chair at numerous national and international conferences.
Senior or sole supervisor of 9 Postdoctoral Research Fellows (6 completed) and of 12 Postgraduate Research Students (8 PhD and 3 MSc completed) and second supervisor of 3 PhD students (all completed).
Supervisor of 8 Honours student theses (8 completed).
Leader, Information Security – Informatics Research Group

Accomplishments

Program Leader, Security and Safety Program, RMIT Platform Technologies Research Institute
Director and Lead Researcher of national competitive and internal research projects awarded more than AUD 2.5M in funding, including 2 ARC Large Grants and 1 ARC Linkage Grant.

Research information

Platform Technologies Research Institute

Selected publications

Books

HORADAM, K. J., Hadamard Matrices and Their Applications, Princeton University Press, Princeton, NJ, 2007. (commissioned)

Refereed Journal Articles since 2003

HORADAM, K. J. and EAST, R., Partitioning CCZ classes into EA classes, Advances Math. Comm. (2012) to appear.
HORADAM, K. J., Equivalence classes of functions between finite groups, J. Algebraic Combin. (2012) to appear.
XU, Z., WU, H. R., YU, X., HORADAM, K. J. and QIU, B., Robust shape-feature-vector-based face recognition system, IEEE Trans. Instrument. & Meas. 60 (12): 3781-3791 (2011).
ARAKALA, A., HORADAM K. J., JEFFERS, J. and BOZTAS S., Protection of minutiae-based templates using biocryptographic constructs in the set difference metric, Security Comm. Networks, 4: 563-576 (2011).
FARMER, D.G. and HORADAM, K. J., Equivalence classes of multiplicative central (p^n, p^n, p^n, 1)-relative difference sets, Cryptogr.Commun., 3: 17-28 (2011).
HORADAM, K. J., Hadamard matrices and their applications: Progress 2007—2010 Cryptogr. Commun., 2: 129-154 (2010).
BAYLY, D. CASTRO, M. ARAKALA, A. JEFFERS, J. and HORADAM, K. J., Fractional biometrics: Safeguarding privacy in biometric applications, Int. J. Information Security, 9: 69-82 (2010).
HORADAM, K. J., Relative difference sets, graphs and inequivalence of functions between groups, J. Combin. Designs, 18: 260-273 (2010).
LeBEL, A. FLANNERY, D. and HORADAM, K. J., Group algebra series and coboundary modules, J. Pure Appl. Algebra, 214: 1291-1300 (2010).
FARMER, D. G., and HORADAM, K. J., A polynomial approach to cocycles over elementary abelian groups, J. Austral. Math. Soc., 85: 177-190 (2008).
HORADAM, K. J. and FARMER, D. G., Bundles, presemifields and nonlinear functions, Des., Codes and Cryptogr., 49: 79–94 (2008).
LeBEL, A. and HORADAM, K. J., Direct sums of balanced functions, perfect nonlinear functions and orthogonal cocycles, J. Combin. Designs, 16: 173–181 (2008).
LUO, H. and HORADAM, K. J., Simulation and measurement of large-scale complex networks, Fund. Inf. 84: 61-79(2008).
CHEN, Y-Q., HORADAM, K. J., LIU, W-H., Relative difference sets fixed by inversion (III) — cocycle theoretical approach, Discrete Math. 13: 2764–2775 (2008).
LIU, W-H., CHEN, Y-Q., HORADAM, K. J., Relative difference sets fixed by inversion (II) — character theoretical approach, J. Combin. Theory A, 111: 175–189 (2005).
HORADAM, K. J., The shift action on 2–cocycles, J. Pure Appl. Algebra 188: 127–143 (2004).
HORADAM, K. J., UDAYA, P., A new class of ternary cocyclic Hadamard codes, Appl. Algebra Engrg. Comm. Comput. 14: 65–73 (2003).

Refereed LNCS Publications and Conference Proceedings Since 2003

JEFFERS, J., DAVIS, S. A. and HORADAM, K. J., Estimating Individuality in Feature Point Based Retina Templates, Proc. ICB 2012, New Delhi April 2012, IEEE, to appear (2012).
HORADAM K. J., DAVIS, S. A., ARAKALA, A. and JEFFERS, J., Fingerprints as spatial graphs: nodes and edges, Proc. DICTA 2011, Noosa, December 2011, to appear (2011).
ARAKALA, A., HORADAM K. J. and DAVIS, S. A., Retina features based on vessel graph substructures, Proc. Int. Joint Conf. Biometrics, Washington October 2011, IEEE, to appear (2011)
JEFFERS, J., ARAKALA, A., and HORADAM, K. J., Entropy of Feature Point-Based Retina Templates, Proc. International Conference on Pattern Recognition, Istanbul, Turkey, Aug 2010, IEEE Computer Society, 213-216 (2010).
ARAKALA, A., CULPEPPER, S., JEFFERS, J., TURPIN, A., BOZTAS, S., HORADAM, K. J. and McKENDRICK, A., Entropy of the retinal template, Proc. 3rd IAPR/IEEE International Conference on Biometrics (ICB 2009), Massimo Tistarelli and Mark Nixon (ed.), Springer, 1250-1259 (2009).
HORADAM, K. J., EA and CCZ equivalence of functions over GF (2^n), LNCS 5130, Springer, 134-143 (2008).
ARAKALA, A. HORADAM, K. J. and BOZTAS, S., Practical considerations for secure minutiae based templates, 2008 Biometrics Symposium, L. Hornak, A. Jain, J. Kittler, T. Tan (ed.), IEEE, United States 53-58 (2008).
FARMER, D. and HORADAM, K. J., Presemifield bundles over GF(p^3), Proc. IEEE International Symposium on Information Theory, Ralf Koetter, Gerhard Kramon, Helmut Bofeskei (ed.), IEEE, United States, 2613-2616 (2008)
ARAKALA, A., JEFFERS, J., and HORADAM, K. J., Fuzzy extractors for minutiae-based fingerprint authentication, Advances in Biometrics, LNCS 4642, Springer: 760–769 (2007).
HORADAM, K. J. and FARMER, D. G., Bundles, presemifields and nonlinear functions, Workshop on Coding and Cryptography 2007, INRIA April 2007: 197–206 (2007).
LUO, H. and HORADAM, K. J., Simulation and measurement of a two-stage complex network model, Complexity and nonlinear dynamics, Adelaide, December 2006, Proc. SPIE 6417: 64170B (2007).
HORADAM, K. J., A theory of highly nonlinear functions, LNCS 3857, Springer: 87–100 (2006).
HORADAM, K. J. and RAO, A., Fourier Transforms from a weighted trace map, Proc. 2006 IEEE ISIT, Seattle, July 2006: 1080–1084 (2006).
LUO, H. and HORADAM, K. J., Simulation and measurement of large-scale complex networks, Proc. AWOCA, Ballarat, Australia, September 2005: 173–184 (2005).
HORADAM, K. J., A generalised Hadamard transform, Proc. 2005 IEEE ISIT, Adelaide, Australia, September 2005: 1006–1008 (2005).
HORADAM, K. J., Differential uniformity for arrays, Cryptography and Coding, LNCS 2898, Springer: 115–124 (2003).
HORADAM, K. J., Differentially 2-uniform cocycles - the binary case, LNCS 2643, Springer: 150–157 (2003).
HORADAM, K. J., Differentially 2-uniform cocycles - the binary case, Proc. AAECC- Toulouse: 2pp, (2003).

Current externally funded research projects

2011-2014: A fast and effective automated insider threat detection and prediction system (ARC Linkage Project, $255,000, Chief Investigators S. Boztas, A. Rao, K. J. Horadam)
2012-2014: Novel dissimilarity techniques for characterising noisy spatial networks (ARC Discovery Project, $285,000, Chief Investigators K. J. Horadam, S. A. Davis)
2011-2012: Happy Feet: A study of the infant footprint biometric to improve childhood vaccination programmes in the developing world (Bill & Melinda Gates Foundation, Grand Challenges Exploration Phase I, $100,000 USD, Chief Investigators S. A. Davis, K. J. Horadam, J. McVernon)
2010-2013: Fusion of networked data from multivariate sources in the presence of uncertainty (Department of Defence, $180,000, Chief Investigators K. J. Horadam, S. Boztas, A. Rao)