Professor Kathy Horadam
Math & Geospatial Sciences
+61 3 9925 2752
Science, Engineering & Health
Doctor of Philosophy, Pure Mathematics, Australian National University, 1977
Bachelor of Science (Honours 1st class), Pure Mathematics, Australian National University, 1972
- Honours Advanced Topics in Discrete Mathematics
- Professor of Mathematics
Areas of expertise
Abstract algebra, combinatorial design theory, coding theory and information security, biometrics and complex networks.
Postgraduate Programs in Information Security and Assurance
- Fellow, Australian Mathematical Society, 2001
- Life Member, Combinatorial Mathematics Society of Australasia, 1993
- Fellow, Institute of Combinatorics and its Applications, 1991
- 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
- 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.
- 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)