Analysis of the improved knapsack cipher

Computational complexity of order 256n to solve the knapsack cipher 0/255 (or improved knapsack cipher) recently suggested by Pham is optimistic result. In this paper, we systematically analyze the improved knapsack cipher in relation to the complexity claims. During the analysis of the improved knapsack cipher, we examined that the public key size must be large to satisfy the constraint of complexity. Though we chose keys of large sizes, the improved knapsack cipher is not safe and its security is compromised by lattice-based attacks. Furthermore, the cipher lost its practicality, since the use of large size public keys. Hence, we identify a construction of practical knapsack cipher 0/f, characterize its requirements and demonstrate asymptotically, that the computational complexity of the knapsack cipher 0/f and knapsack cipher 0/1 (basic or sum-of-subset cipher) is equal. It is worth pointing out that the proposed knapsack cipher 0/f is a compact and viable option to use as a building block for security purpose in resource-constrained devices such as RFID tags, smart cards and the like.