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Public-key cryptosystems, a revolutionary breakthrough in cryptography, are indispensable for our modern communication network. The Internet, as well as other communication systems, rely principally on public-key cryptosystems that depend for security on the difficulty of certain number-theoretic problems such as integer factorization or the "discrete log problem." However, it is now known that a quantum computer could efficiently solve these problems, thus rendering all public-key cryptosystems based on such assumptions impotent if a large-scale quantum computer can be built. To address this issue, technologies resistant to such quantum attack are becoming a central topic in information security; this new science bears the moniker "post-quantum cryptography." One of the four main families of post-quantum cryptosystems under development is known as multivariate public-key cryptosystems (MPKCs). This research project is devoted to an in-depth study of multivariate public-key cryptosystems, with the goal of facilitating the analysis of several multivariate candidates that have great potential for cyber security. Results of the project are expected to produce secure and efficient alternatives for the post-quantum computer world, with application both to addressing the threat that quantum computers pose to existing cryptosystems and to the growing security needs for small devices with limited computing resources. The project includes a diverse group of undergraduate and graduate students who will receive training through involvement in the research.
The focus of the project is on developing more efficient and more secure MPKCs and their fast implementations, as well as exploring provable security for MPKCs and analyzing the security of specific MPKCs. The approach is a combination of new mathematical ideas and computer experiments, relying primarily on mathematical tools from algebraic geometry and the theory of symmetry. Since the systems under study cannot be analyzed by hand, the investigator will use computer experiments to build intuitive understanding and will use theoretical methods to study the mathematical structures hidden within the MPKC constructions. The results are expected to lead to a better understanding of the fundamentals of the MPKCs and of how to design secure and efficient MPKCs. Furthermore, the project should make a significant contribution in developing the next generation of standards for post-quantum cryptography.
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SaTC: CORE: Small: Multivariate Public Key Cryptosystems - Candidates for the Next Generation Post-Quantum Standards