Knapsack cryptosystems and unreliable reliance on density

With the possible advent of quantum computers, the most famous public key cryptosystem for network applications - RSA, is facing critical challenges in the near future. A replacement might be knapsack cryptosystems, which do not yield any benefits to quantum computation. Before making knapsack cryptosystems suitable for applications, it is necessary to guarantee their security. At present, the most significant challenge towards knapsack cryptosystems is lattice attacks. Public key density has historically been used to measure the security of the knapsack cryptosystems against these lattice attacks. However, an acceptably dense knapsack cryptosystem was broken using lattice attack implementation in our research. In order to study the security of knapsack cryptosystems against lattice attacks, we design a series of experiments to analyze these factors. We conclude it is not appropriate to assess knapsack cryptosystem security by simply considering density. From our results, we provide suggested directions for knapsack cryptosystem developers.