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Multivariate cryptography is a specialized category of books focused on public-key cryptosystems built from systems of multivariate polynomial equations over finite fields, a class of constructions whose security rests on the hardness of the MQ (multivariate quadratic) problem. Works in this category typically span the algebraic foundations (finite fields, polynomial algebra, Gröbner bases), scheme design and optimization (HFE, Oil-and-Vinegar, Rainbow and variants), cryptanalysis methods (algebraic attacks, linearization, differential and rank attacks), implementation and performance considerations (key/signature sizes, speed, side-channel issues), and the role of multivariate approaches in post-quantum cryptography and standardization efforts. Such books target researchers, graduate students, and engineers interested in both the theoretic complexity and practical deployment of alternatives to number-theory- based crypto in a quantum-threat landscape.

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