Formal Analysis of Fairness for Optimistic Multiparty Contract Signing Protocol

Algorithm 2

Modeling of four-party GM main subprotocol.

Modeling the behaviors of honest 𝐏_𝟏 in the four-party GM main subprotocol

P₁H_process()=

⋯ ⋯

//(1) honest P₁ sends 1-level promises to P₂

[][!P₁_stop && !P₁_contacted_T && P_r_1_4_L==0 && P_r_1_3_L==0 && P_r_1_2_L==0 && P_r_2_1_L==1 && P_r_3_1_L==1 &&

P_r_4_1_L==1]P₁sendsp₂1{P_r_1_2_L=1;}->P₁H_process()

//(2) honest P₁ sends recovery requirement to T

[] [!P₁_stop && !P₁_contacted_T && P_r_1_4_L==0 && P_r_1_3_L==0 && P_r_1_2_L==1 && P_r_2_1_L==1 && P_r_4_1_L==1 &&

P_r_3_1_L==1]p₁recovery111{P₁_contacted_T=true; P₁_Recovery_1_1_1=true;}->T_process()

Modeling the behaviors of dishonest 𝐏_𝟐 in the four-party GM main subprotocol

P₂_process()=

⋯ ⋯

//(3)dishonest P₂ sends 1-level promise to P₁

[] [!P₂_stop && P_r_2_1_L<1] P₂sendP₃2 {P_r_2_1_L=1;}->P₂_process()

//(4)dishonest P₂ sends recovery requirement to T

[] [!P₂_stop && P_r_4_2_L==1 && P_r_3_2_L==1 && P_r_1_2_L==1]P₂recovery111{P₂_Recovery_1_1_1=true;}

->T_process()

System definition

sys1H∣=P₁H_process() ∣∣∣ P₂_process() ∣∣∣ P₃_process() ∣∣∣P₄_process();