Reducing file size and time complexity in secret sharing based document protection

Recently, Tu and Hsu proposed a secret sharing based document protecting scheme. In their scheme, a document is encrypted into $n$ shares using Shamir's $(k, n)$ secret sharing, where the $n$ shares are tied in with a cover document. The document reconstruction can be accomplished by acknowledgement of any $k$ shares and the cover document. In this work, we construct a new document protecting scheme which is extended from Tu-Hsu's work. In Tu-Hsu's approach, each inner code of secret document takes one byte length, and shares are generated from all inner codes with the computation in $GF(257)$, where $257$ is a Fermat Prime that satisfies $257 = 2^{2^{3}}+1$. However, the share size expands when it equals to $255$ or $256$. In our scheme, each two inner codes of document is combined into one double-bytes inner code, and shares are generated from these combined inner codes with the computation in $GF(65537)$ instead, where $65537$ is also a Fermat Prime that satisfies $65537 = 2^{2^{4}}+1$. Using this approach, the share size in our scheme can be reduced from Tu-Hsu's scheme. In addition, since the number of combined inner codes is half of the inner codes number in Tu-Hsu's scheme, our scheme is capable of saving almost half running time for share generation and document reconstruction from Tu-Hsu's scheme.