Security of Knapsack PKC with Plaintext Encoding against Low-Density Attack

Merkle and Hellman proposed the first knapsack cryptosystem. However, it was broken because the density is not sufficiently high. The knapsack scheme is expected to be one of the post quantum cryptosystems. In this paper, we describe the high-density knapsack PKCs with plaintext encoding over GF(2). We discuss the influence of the number of non-zero elements of the generator matrix on the security against the low-density attack. As the result, the scheme with plaintext encoding is secure against the low-density attack when the Hamming weight of the generator matrix is sufficiently large.