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Abstract: Many traditional applications can be refined thanks to the development of Blockchain technologies. One of these services is non-repudiation in which participants in a communications process cannot deny their involvement. Due to the vulnerabilities of the non-repudiation protocols, one of the parties involved in communication can often avoid the non-repudiation rules and obtain the expected information to the detriment of the interests of the other party, resulting in adverse effects. This paper studies the fairness guarantee quantitatively through probabilistic model checking. E-fairness is measured by modeling the protocol in probabilistic timed automata and verifying the appropriate property specified in Probabilistic Computation Tree Logic (PCTL). Furthermore, our analysis proposes insight for choosing suitable values for different parameters associated with the protocol so that a certain degree of fairness can be obtained, and therefore answers the reverse question: For a certain degree of fairness, ε, how can the protocol parameters be specified to ensure fairness?