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This paper aims to propose a general framework for fair exchanges of valuable information through digital signatures and cryptographic keys over networks, which are essential for e-commerce (electronic commerce) applications to prevent fraudulent or unfair on-line activities. This new framework incorporates a set of signature schemes as primitives, offers three generalised functions for the generation, verification and recovery of verifiably encrypted signatures and keys using these signature schemes, and provides a generic protocol built on these thee functions to accomplish various fair exchange scenarios of valuable information. The security analysis of the framework is also presented to confirm its assurance of fairness in exchange. Moreover, a comparison with related work is carried out to demonstrate the novel features of the framework, which can be highlighted by a good blend of generality, flexibility, efficiency and simplicity offered by the framework.