Adapt Crossbred to RMQ

Determine whether the Crossbred algorithm for solving multivariate polynomial systems can be effectively adapted to the Regular Multivariate Quadratic (RMQ) problem over finite fields, and rigorously quantify its asymptotic and practical efficiency relative to fast exhaustive search and hybrid Gröbner-basis-based solvers on RMQ instances at cryptographic parameter sizes.

Background

The paper introduces the Regular Multivariate Quadratic (RMQ) problem and analyzes several algebraic and probabilistic methods for solving RMQ instances, concluding that hybrid algebraic cryptanalysis appears most efficient asymptotically and for practical parameters.

The authors note that, unlike in classic MQ, probabilistic methods have not shown practical superiority for cryptographic parameters. They highlight the Crossbred algorithm as the unique method that defeats fast exhaustive search for practical parameters in related contexts, and pose the adaptation and evaluation of Crossbred for RMQ as an explicit open problem.