Revisiting the Security of VDOO

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VDOO is a multivariate signature scheme submitted to the Next-generation Commercial Cryptographic Algorithms Program (NGCC). We study the security of its submitted parameter sets. In this paper, VDOO is described as a multilayer Rainbow construction. By retaining only its last oil space, we obtain a generalized UOV instance and apply existing wedge attacks. For the parameter set targeting 512-bit security, we estimate costs of $2^{432}$ and $2^{379}$ gates for the reconciliation and intersect