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A Hopfield neural network exhibits the phenomenon of stochastic error in convergence. Based on this non-determinism, Guo-Cheng-Cheng proposed a symmetric block cipher. Cryptanalysis of this cryptosystem led to an interesting mathematical problem - given two matrices that are conjugate of each other by a permutation matrix, find such permutation matrix. The authors present cryptanalysis of the proposed block cipher, as well as a practical method for solving the mentioned problem in some instances. The key space and, therefore, the security of the block cipher is significantly reduced, when the proposed method can be effectively employed.
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