Formal Analysis of Fairness for Optimistic Multiparty Contract Signing Protocol

Algorithm 3

Modeling of four-party GM abort and recovery subprotocols.

T_process()=

Modeling of the four-party GM abort subprotocol

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//(1)T agrees with the abort requirement from P₂

[][!T_Respond2 && P₂_Abort_Send && !T_Validated && ( T_S4 ∣∣ T_S3)]TabortP₂1{T_S2=true; T_Abort_Send_P₂=true;

T_Respond2=true;}->P₂H_process()

//(2)T refuses the abort requirement from P₂

[][!T_Respond2 && P₂_Abort_Send && T_Validated ]TabortP₂2{T_S2=true; T_Recovery_Send_P₂=true; T_Respond2=true;}-

>P₂H_process()

Modeling of the four-party GM recovery subprotocol

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//(3)T agrees with the recovery requirement from P₃

[] [P₃_Recovery_1_3_3 && !T_Respond4 && !T_Respond3 && !T_Respond2 && !T_Respond1]TreocveryP₃1

{T_Recovery_Send_P₃=true; T_Respond3=true; T_Validated=true;}->P₃_process()

//(4)T refuses the recovery requirement from P₃

[] [P₃_Recovery_1_3_3 && !T_Respond3 && (!T_Respond4 ∣∣ !T_Respond3 ∣∣ !T_Respond2 ∣∣ !T_Respond1)&&

!T_Validated && T_S4]TreocveryP₃12{T_F1=true;T_F2=true;T_S3=true;T_Abort_Send_P₃=true;

T_Respond3=true}->P₃_process()