Hilbert series for systems of UOV polynomials

Multivariate public key cryptosystems (MPKC) are constructed based on the problem of solving multivariate quadratic equations (MQ problem). Among various schemes, UOV is an important signature scheme since it underlying some schemes such as MAYO, QR-UOV, and Rainbow which was a finalist NIST PQC standardization project. To analyze security scheme, necessary to first fall degree or for system polynomial used in specific attacks. It known that often relates Hilbert series ideal generated by system. In this paper, we study more specifically, ideals polynomials central map UOV. particular, derive prediction formula using experimental results. Moreover, apply analysis reconciliation attack MAYO.