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Cryptanalysis of two knapsack-type public-key cryptosystems

In this paper, we cryptanalyze two knapsack-type cryptosystems. The first one is proposed by Hwang et al [4], which is based on a new permutation algorithm named Permutation Combination Algorithm. We show that this permutation algorithm is useless to the security of the cryptosystem. Because of the special super increasing structure, we can break this cryptosystem use a variant of the method provided by Shamir at Crypto'82. The second one is provided by Su et al [16], which is based on the elliptic curve discrete logarithm and knapsack problem. We show that one can recover the plaintext as long as he solve a knapsack problem. Unfounately, this knapsack problem can be solved by Shamir's method or the low density attack. Finally, we give a improved version of Su's cryptosystem to avoid these attacks.