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The authors aim to present a protocol for fair document exchange between two parties, that incorporates a signature scheme based method for the recovery of a document decryption key. The principal idea for such key recovery is based on a verifiable and recoverable encryption of a key. This means that any party can verify the correctness of the key encrypted without actually viewing the key, and the party can be assured that a designated party can decrypt the encrypted key to recover the original key. A DSA (digital signature algorithm) is applied as an example to demonstrate how to implement such key encryption based on an off-line semi-trusted third party. The third party is off-line as they do not participate in an exchange in normal situations, and semi-trusted in the sense that they may misbehave but do not conspire with any party involved in the exchange. The main contribution of the paper is that it presents a fair document exchange protocol which is more efficient, simpler and easier to implement in comparison with related work.