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A new secure knapsack cryptosystem based on the Merkle-Hellman public key cryptosystem will be proposed in this paper. Although it is common sense that when the density is low, the knapsack cryptosystem turns vulnerable to the low-density attack. The density d of a secure knapsack cryptosystem must be larger than 0.9408 to avoid low-density attack. In this paper, the authors investigate a new Permutation Combination Algorithm. By exploiting this algorithm, the authors shall propose a novel knapsack public-key cryptosystem. They proposed scheme can enjoy a high density to avoid the low-density attack.
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