Interactions among Cryptography, Quantum Computation, Artificial Intelligence and Applied Algebra

I will give an overview about my current research program and will pose some questions for potential collaborations within the department of computer science.

I began my scientific career as a pure mathematician specialising in algebra. I soon became interested in the deep connections between algebra and cryptography. Although the mathematical field of number theory has long been applied to cryptography, algebra's fundamental connection to cryptography is not nearly as well understood or explored. Algebraic cryptosystems have been shown to have some advantages over number theoretic cryptosystems.

 

For instance, number theoretic cryptosystems are not resistant against quantum computers, but cryptosystems based on combinatorial algebra appear to be stronger platforms against quantum computer attacks. My research in algebra-based cryptography has focused on solving real-world computer security problems. The real-world problems that I am focused on have economic, health, and national security significance. They include secure computation and data mining with medical data, and secure processing of data by artificial intelligence systems.

New cryptographic tools I am developing, not only have influence in theoretical cryptography but to also find real-world applications. My research is mainly focused on post-quantum cryptography, secure delegation of computation, fully homomorphic encryption for secure processing of sensitive data by artificial intelligence systems. All of these areas play important roles in modern technological solutions including secure communication, cloud computing, and healthcare. These applications have become indispensable in the real-world, and enhancing their efficiency and security will have a positive impact on the economy, healthcare, and government.

I am currently the Chair of Cyber Security at the University of York, a position I have held since November 2018. While at York, I founded and am the director of the York Interdisciplinary Centre for Cyber Security. Before coming to York, I was Full Professor at the City University of New York (CUNY) in New York City. I was at CUNY for 12 years, among other duties, I supervised 7 PhD computer science and mathematics students. In addition to my position at York, I am also an Adjunct Professor of Computer Science at the Centre for Cyber Security at New York University (NYU). I have been an adjunct at NYU since 2016. I was a lecturer in Pure Mathematics at the University of St Andrews before New York.

I am an associate editor of the Advances of Mathematics of Communication, published by the American Institute of Mathematical Sciences, the chief editor of the International Journal of Computer Mathematics: Computer Systems Theory, Taylor & Francis, and an associate editor of SIAM Journal on Applied Algebra and Geometry, The Society for Industrial and Applied Mathematics. I also have entrepreneurial experience as President and Co-founder of Infoshield, Inc., a computer security company.

My main research area is Post-Quantum Algebraic Cryptography, Information Security, Data Science and Applied Algebra. My research has been supported by grants from the US military: US Office of Naval Research, Canadian New Frontiers in Research Fund Exploration, American Association of Advancement in Sciences, National Science Foundation, National Security Agency, Maastricht-York Investment Fund, Research Foundation of CUNY, London Mathematical Society, the Edinburgh Mathematical Society, Swiss National Foundation, Institute Henri Poincare, and the Association for Women in Mathematics. I have 70 publications in prestigious journals and conference proceedings and several US patents. I have given about 240 invited talks at conferences and seminars around the world.

A long term career objective of mine is to further develop the York Interdisciplinary Centre for Cyber Security to address and solve the main cyber security questions relevant to industry, health and government; collaborating with industry and businesses around the UK for commercialising academic research to help the economy; making links between the research centres and sectors (such as healthcare) with private/sensitive data to enable research centres to access and perform data analysis over sensitive data to solve real life problems such as cancer.