How to sign multiple versions of digital documents

In some applications, it is useful to record multiple versions of digital documents, so that we can trace the history and changes applied to the documents. The creators of the documents are often required to sign the documents to protect the origin and integrity of the documents. A typical implementation of the signature method is by using a standard signature scheme (i.e. RSA) and storing the signature along with the document. The version numbers of the documents are appended to the documents before signing. The problem is, when we need to sign many versions of the documents, the signer should create the signature of each version, which is not efficient in term of the storage. In this paper, we propose a more efficient method to sign multiple version of digital document and show the security argument of the signature scheme.