Cryptanalysis of 2-Layer Nonlinear Piece in Hand Method

Piece in Hand method is a security enhancement method for Multivariate Public Key Cryptosystems (MPKCs). Since 2004, many types of this method have been proposed. In this paper, we consider the 2-layer nonlinear Piece in Hand method as proposed by Tsuji et al. in 2009. The key point of this method is to introduce an invertible quadratic polynomial map on the plaintext variables to construct perturbation of the original MPKC. Through our analysis, we find that the security of the enhanced scheme is mainly relying on the quadratic polynomials of this auxiliary map. The two examples proposed by Tsuji et al. for this map can not resist the Linearization Equation attack. Given a valid ciphertext, we can easily get a public key which is equivalent to the original MPKC. If there is an algorithm that can recover the plaintext corresponding to a valid ciphertext of the original MPKC, we can construct an algorithm that can recover the plaintext corresponding to a valid ciphertext of the enhanced MPKC.