A knapsack public-key cryptosystem using two random sequences

In 2012, the present authors proposed a knapsack public-key cryptosystem using a random sequence as a secret key, which will be referred to as MHK scheme. MHK scheme has a remarkable feature that the public sequence is indistinguishable from uniformly distributed random sequence. However, in CSS2013, Nagao and Morii discovered that the plaintext of MHK scheme can be disclosed by computing an alternative solution, which is not equal to the genuine solution, with the conventional low-density attack. This attack will be referred to as NM attack. In this paper, we shall propose a new knapsack scheme using two random sequences, which is secure against NM attack.