Key Recovery Attacks on Multivariate Public Key Cryptosystems Derived from Quadratic Forms over an Extension Field

One of major ideas to design a multivariate public key cryptosystem (MPKC) is to generate its quadratic forms by a polynomial map over an extension field. In fact, Matsumoto-Imai's scheme (1988), HFE (Patarin, 1996), MFE (Wang et al., 2006) and multi-HFE (Chen et al., 2008) are constructed in t...

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