Cryptanalysis of a Public-key Cryptosystem Using Lattice Basis Reduction Algorithm

In this paper, we proposed a new attack against Hwang et al.’s cryptosystem. This cryptosystem uses a super-increasing sequence as private key and the authors investigate a new algorithm called permutation combination algorithm to enhance density of knapsack to avoid the low-density attack. Sattar J. Aboud [Aboud j. Sattar, “An improved knapsack public key cryptography system”, International Journal of Internet Technology and Secured Transactions, Vol.3 (3), pp.310-319, 2011] used Shamir’s attack on the basic Merkle-Hellman cryptosystem to break this cryptosystem. Due to use of Lenstera’s integer programming, Lagarias showed that Shamir’s attack is inefficient in practice; So, Aboud’s attack is impractical too. In this paper, we introduce a direct attack against Hwang et al.’s cryptosystem based on Lattice basis reduction algorithms. By computing complexity of propose attack, we show that unlike Aboud’s cryptanalysis, our cryptanalysis is more efficient and practicable.