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 = 2²+ 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+ 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.