Abstract: 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, we investigate a
new Permutation Combination Algorithm. By exploiting this
algorithm, we shall propose a novel knapsack public-key cryptosystem.
Our proposed scheme can enjoy a high density to avoid the
low-density attack. The density d can also exceed 0.9408 to avoid
the low-density attack.