Post-quantum cryptography using multivariate polynomial systems

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Multivariate public-key cryptography (MPKC) is one of the four most common branches of post-quantum cryptography, describing cryptosystems based on solving systems of multivariate polynomials. An important step in the cryptanalysis of MPKC system is finding a Gröbner basis for the system. My research focusses on adapting generic Gröbner Basis algorithms to families of multivariate polynomial systems with specific structures. I am currently looking at multivariate linearised polynomials, which have not been studied in great detail. Additionally I am exploring applications of the HHL quantum algorithm for solving systems of multivariate polynomials, in particular Boolean systems.This project is linked to the EPSRC Cyber Security research theme