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
Symmetrical graphs, generalized polygons and expanders. This project proposes to study a class of highly symmetrical graphs -- locally s-arc-transitive graphs. Studying the class of graphs has been one of the central topics in algebraic graph theory for over 50 years. This class of graphs has been effectively used in computer science, communication network, group theory, geometry, and other areas. This project will develop new methods to solve several fundamental problems regarding locally s-arc ....Symmetrical graphs, generalized polygons and expanders. This project proposes to study a class of highly symmetrical graphs -- locally s-arc-transitive graphs. Studying the class of graphs has been one of the central topics in algebraic graph theory for over 50 years. This class of graphs has been effectively used in computer science, communication network, group theory, geometry, and other areas. This project will develop new methods to solve several fundamental problems regarding locally s-arc-transitive graphs, and apply the outcomes to solve important problems in communication networks, graph theory, group theory, and geometry.Read moreRead less
Enhancing Privacy for Digital Communication. Protecting one's privacy in cyber world is a challenging task. Every contact to a Web server leaves a digital footprint that can be linked with other publicly available information to compile a profile of one's activities. Anonymous communication is a powerful tool for enhancing individuals' privacy and providing services such as electronic election where a person's vote must be unlinkable to him/her. However, anonymity may be misused by criminals to ....Enhancing Privacy for Digital Communication. Protecting one's privacy in cyber world is a challenging task. Every contact to a Web server leaves a digital footprint that can be linked with other publicly available information to compile a profile of one's activities. Anonymous communication is a powerful tool for enhancing individuals' privacy and providing services such as electronic election where a person's vote must be unlinkable to him/her. However, anonymity may be misused by criminals to hide their identities and engage in illegal activities. The aim of this project is to design and analyse privacy enhancing communication systems that balance individuals' privacy and accountability, and develop criteria and metrics to compare performance of these systems.Read moreRead less
Mathematics of Cryptography. The Australian economy and society requires fast, reliable, and secure communication. Current 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 an important and urgent tasks. In addition, t ....Mathematics of Cryptography. The Australian economy and society requires fast, reliable, and secure communication. Current 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 an important and urgent tasks. In addition, 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
Approximate authentication systems for digital information. Assurance about the origin and integrity of digital content is crucial not only in high security applications but also in everyday life scenarios such as providing proof that an X-ray image presented as part of an insurance claim is authentic, or a news clip is not tampered with. The outcomes of this project will significantly enhance trustworthiness of multimedia information systems which are increasingly used in areas such as surveil ....Approximate authentication systems for digital information. Assurance about the origin and integrity of digital content is crucial not only in high security applications but also in everyday life scenarios such as providing proof that an X-ray image presented as part of an insurance claim is authentic, or a news clip is not tampered with. The outcomes of this project will significantly enhance trustworthiness of multimedia information systems which are increasingly used in areas such as surveillance (traffic control), health, digital content production and distribution, tourism and journalism. It will also result in the development of secure biometric authentication systems which are critical in securing cyber space.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
Geometric representation of small-rank totally disconnected groups. Mathematics research creates and develops new concepts for understanding the world. Group theory is a branch of mathematics based on our innate sense of of symmetry. It was invented 200 hundred years ago and has grown into a language for analysing and classifying things ranging from wallpaper patterns to crystals, the fundamental particles of physics and Rubik's cube. The chief investigators have significant breakthroughs in the ....Geometric representation of small-rank totally disconnected groups. Mathematics research creates and develops new concepts for understanding the world. Group theory is a branch of mathematics based on our innate sense of of symmetry. It was invented 200 hundred years ago and has grown into a language for analysing and classifying things ranging from wallpaper patterns to crystals, the fundamental particles of physics and Rubik's cube. The chief investigators have significant breakthroughs in the study of symmetry groups of networks, giving Australia an international lead in this research. The project will develop the insights gained to make Australia a centre of expertise on these symmetry groups, which have applications to information and communication technology, among many others.Read moreRead less
Credential Systems and Their Applications in Securing Electronic Health Records. The expected result of this project will be frontier technologies that are essential in applications and services, whose acceptance and take-up will depend on users' assurance of their security in the cyber world. In particular, a service such as the EHR system, which is known to be a complex system, requires the use of new and innovative credential-based systems. The result will also contribute to maintaining Austr ....Credential Systems and Their Applications in Securing Electronic Health Records. The expected result of this project will be frontier technologies that are essential in applications and services, whose acceptance and take-up will depend on users' assurance of their security in the cyber world. In particular, a service such as the EHR system, which is known to be a complex system, requires the use of new and innovative credential-based systems. The result will also contribute to maintaining Australia's leading position in the telecommunication and information technology industries, which has been recognised by increased government funding levels. The resulting applications of this project will place Australia as the first country able to design and implement a secure EHR system.Read moreRead less
Reflection groups. The study of symmetry in geometrical and abstract contexts is a central issue in such diverse areas as mathematical physics, singularity theory, algebraic geometry, quantum groups and the study of knots and braids. Group theory provides the mathematical framework for the analysis of symmetry. Reflection groups, simple examples of which are the symmetry groups of the five platonic solids, play a key role in all of the areas mentioned above. Thus an improved understanding of ref ....Reflection groups. The study of symmetry in geometrical and abstract contexts is a central issue in such diverse areas as mathematical physics, singularity theory, algebraic geometry, quantum groups and the study of knots and braids. Group theory provides the mathematical framework for the analysis of symmetry. Reflection groups, simple examples of which are the symmetry groups of the five platonic solids, play a key role in all of the areas mentioned above. Thus an improved understanding of reflection groups will significantly enhance the development of several important theories.
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Analysis of the structure of latin squares. The benefits to Australia of fundamental research in core disciplines such as mathematics are well documented. Discrete mathematics and combinatorics are boom disciplines of the computer age and this project seeks new knowledge concerning basic building blocks of combinatorial mathematics. The outcomes will be of interest to theoretical discrete mathematicians around the world, enhancing Australia's already high research profile in this important area ....Analysis of the structure of latin squares. The benefits to Australia of fundamental research in core disciplines such as mathematics are well documented. Discrete mathematics and combinatorics are boom disciplines of the computer age and this project seeks new knowledge concerning basic building blocks of combinatorial mathematics. The outcomes will be of interest to theoretical discrete mathematicians around the world, enhancing Australia's already high research profile in this important area of pure mathematical research. Importantly, the problems under investigation offer substantial opportunity for excellent postgraduate training, critical for the future of Australian research. Read moreRead less