Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended wor ....Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Computer Security and E-Commerce.Read moreRead less
Information security and digital watermarking with Latin squares. The importance of digital information is increasing constantly. Audio, video, and still image data dominate our daily lives. Such information has commercial and strategic importance. It is invaluable in crime prevention: for example, video from security cameras. The protection of commercially valuable material against piracy and sensitive information against security breaches is vital to our economy and our safety. This project ad ....Information security and digital watermarking with Latin squares. The importance of digital information is increasing constantly. Audio, video, and still image data dominate our daily lives. Such information has commercial and strategic importance. It is invaluable in crime prevention: for example, video from security cameras. The protection of commercially valuable material against piracy and sensitive information against security breaches is vital to our economy and our safety. This project addresses these issues, by developing new, secure watermarks and fingerprints to protect digital information. Such watermarks can also protect radio communication channels, which is important due to the rising demand for wireless connectivity.Read moreRead less
Exploring the Frontiers of Feasible Computation. The project aims to delineate the boundary between feasible and infeasible computational problems. A problem is considered feasible if there is an algorithm to solve it in worst-case time bounded by a polynomial in the input size. This is probably impossible for the important class of NP-complete problems. However, typical examples of NP-complete problems can often be solved in polynomial time, because worst-case problems are rare. The project is ....Exploring the Frontiers of Feasible Computation. The project aims to delineate the boundary between feasible and infeasible computational problems. A problem is considered feasible if there is an algorithm to solve it in worst-case time bounded by a polynomial in the input size. This is probably impossible for the important class of NP-complete problems. However, typical examples of NP-complete problems can often be solved in polynomial time, because worst-case problems are rare. The project is relevant to public-key cryptography, where breaking an encryption scheme should be infeasible, and to many real-life situations where NP-complete problems need to be solved, either exactly or approximately.Read moreRead less
Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, ....Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Cryptography, Computer Security and E-Commerce.Read moreRead less
A mathematical model relating neural activity to cerebral blood flow. An ageing population is increasingly prone to neurodegenerative disease and the associated mental impairment can severely disrupt the lives of both the sufferers and the carers. Non-invasive brain imaging techniques are used to both diagnose and supervise treatment of such disease, but at present a lack of understanding of the underlying physiology leaves these methods open to criticism. The construction of a detailed quanti ....A mathematical model relating neural activity to cerebral blood flow. An ageing population is increasingly prone to neurodegenerative disease and the associated mental impairment can severely disrupt the lives of both the sufferers and the carers. Non-invasive brain imaging techniques are used to both diagnose and supervise treatment of such disease, but at present a lack of understanding of the underlying physiology leaves these methods open to criticism. The construction of a detailed quantitative model of the basic processes underlying this imaging will enable precise interpretation of such brain scans and increase their usefulness both as a research and as a therapeutic tool.Read moreRead less
A new theory for retinotectal map formation. How brains become wired up during development is a question of
importance to both biology and computing. In this project we adopt a
novel computational approach to understanding the development of
topographic maps, a wiring pattern that is ubiquitous in biological
nervous systems. This project will build capacity for research in
computational neuroscience in Australia. It may also lead to
technological benefits such as new ideas for the design o ....A new theory for retinotectal map formation. How brains become wired up during development is a question of
importance to both biology and computing. In this project we adopt a
novel computational approach to understanding the development of
topographic maps, a wiring pattern that is ubiquitous in biological
nervous systems. This project will build capacity for research in
computational neuroscience in Australia. It may also lead to
technological benefits such as new ideas for the design of self-wiring
computing devices, and new insights into
the causes of wiring defects both during normal development and
rewiring after injury.
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Security Applications of Combinatorial Puzzles. This project provides a basis for improving the implementation and maintenance of key management systems. The application of discrete mathematics to information security will help safeguard Australia, will provide opportunities for Australians to take a leading role in an important area and will develop a research network, bridging both theoretical and practical aspects of mathematics and computer science. The project will enhance Australia's inter ....Security Applications of Combinatorial Puzzles. This project provides a basis for improving the implementation and maintenance of key management systems. The application of discrete mathematics to information security will help safeguard Australia, will provide opportunities for Australians to take a leading role in an important area and will develop a research network, bridging both theoretical and practical aspects of mathematics and computer science. The project will enhance Australia's international reputation by establishing collaborations with well-respected international mathematicians and computer scientists. The proposal contains topics suitable for the training of new graduates, allowing them to make high quality original research contributions in a novel and important area. Read moreRead less
Timed Commitment Schemes to Smooth Internet Bottlenecks, Defend against Denial of Service Attacks, and Bypass Some Legal Problems of Enccryption. Bottlenecks on the Internet and Denial of Service attacks on a server are both caused by excessive demands made on a system. This proposal is to reduce the ill-effects of either by building on our previous theoretical work on strongboxes of combinatorial designs. In the case of bottlenecks, the demands are legitimate but badly timed, and our approach ....Timed Commitment Schemes to Smooth Internet Bottlenecks, Defend against Denial of Service Attacks, and Bypass Some Legal Problems of Enccryption. Bottlenecks on the Internet and Denial of Service attacks on a server are both caused by excessive demands made on a system. This proposal is to reduce the ill-effects of either by building on our previous theoretical work on strongboxes of combinatorial designs. In the case of bottlenecks, the demands are legitimate but badly timed, and our approach will redistribute the demands more evenly. In the case of Denial of Service attacks, the demands are malicious, and our approach will respond in such a way as to deplete the resources of the attacker.Read moreRead less
Mathematical modelling in developmental biology. Modern observational techniques in biology and medicine generate a wealth of genetic and molecular detail. Mathematical modelling integrates and synthesises this information to provide insight into how complex biological processes are coupled to produce experimentally observed behaviour. Mathematical modelling generates experimentally testable predictions that can be used to verify the validity of the models. This program is dedicated to exciting ....Mathematical modelling in developmental biology. Modern observational techniques in biology and medicine generate a wealth of genetic and molecular detail. Mathematical modelling integrates and synthesises this information to provide insight into how complex biological processes are coupled to produce experimentally observed behaviour. Mathematical modelling generates experimentally testable predictions that can be used to verify the validity of the models. This program is dedicated to exciting opportunities for advancing our knowledge of normal and abnormal developmental processes, especially in embryonic growth. Understanding these processes will lead to prediction and treatment of congenital disorders and contribute to a healthy start to life. Read moreRead less
Motor Unit Numbers Estimation (MUNE) using Bayesian statistical methodology for monitoring of progression of neuromuscular diseases. A means of objectively measuring the pathology of a neuromuscular disease involving motor unit loss, such as motor neuron disease, is much needed. This will be achieved by using newly developed electrophysiological techniques and developing new Bayesian statistical methodology to determine the number of motor units that supply a muscle. Our innovations will reliabl ....Motor Unit Numbers Estimation (MUNE) using Bayesian statistical methodology for monitoring of progression of neuromuscular diseases. A means of objectively measuring the pathology of a neuromuscular disease involving motor unit loss, such as motor neuron disease, is much needed. This will be achieved by using newly developed electrophysiological techniques and developing new Bayesian statistical methodology to determine the number of motor units that supply a muscle. Our innovations will reliably determine the number of motor units that supply a muscle in both normal subjects and in diseased patients with loss of motor nerves. This will enable the monitoring of disease progression. An outcome will be a software package that can be used with standard electrophysiology machines.Read moreRead less