Formal Analysis of Fairness for Optimistic Multiparty Contract Signing Protocol

Table 2

System variables.

𝑃𝑟_𝑖_𝑗	𝑃𝑟_𝑖_𝑗=𝑘, if 𝑃𝑖 has successfully sent the 𝑘 level promise to 𝑃𝑗
𝑃𝑖_𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦_𝑗; 𝑃𝑖_𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦_𝑗_𝑡; 𝑃𝑖_𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦_𝑗_𝑡_𝑚	𝑃𝑖 sends recovery requirement message to TTP, 𝑗 is the max level of message 𝑃𝑗 has sent to 𝑃𝑖, 𝑡 is the max level of message 𝑃𝑡 has sent to 𝑃𝑖, and m is the max level of message 𝑃𝑡 has sent to 𝑃𝑖, and so on
𝑃𝑖_𝑠𝑡𝑜𝑝	𝑃𝑖 quits the protocol
𝑃𝑖_𝑐𝑜𝑛𝑡𝑎𝑐𝑡𝑒𝑑_𝑇	𝑃𝑖 has sent recovery or abort requirement messages to TTP
𝑃𝑖_𝑆𝑗	𝑃𝑖 has successfully received the 𝑃𝑗 signed contract
𝑃𝑖_𝐴𝑏𝑜𝑟𝑡𝑇𝑎𝑘𝑒𝑛	𝑃𝑖 sends abort requirement message to TTP
𝑇_𝑅𝑒𝑠𝑝𝑜𝑛𝑑𝑖	TTP has responded to the requirement of 𝑃𝑖
𝑇_𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦_𝑠𝑒𝑛𝑑_𝑃𝑖	TTP sends recovery message to 𝑃𝑖
𝑇_𝐴𝑏𝑜𝑟𝑡_𝑠𝑒𝑛𝑑_𝑃𝑖	TTP sends abort message to 𝑃𝑖
𝑇_𝐹𝑖	𝑃𝑖 has not sent abort message and TTP will force him/her to abort in certain situation
𝑇_𝑆𝑖	𝑃𝑖 has sent abort message
𝑇_ℎ𝑖	The highest level 𝑃𝑖 has sent to higher signer before it contacts TTP
𝑇_𝑙𝑖	The lowest level 𝑃𝑖 has sent to lower signer before it contacts TTP
𝑇_𝑘𝑖	The highest level 𝑃𝑖 has received from 𝑃𝑗 𝑖<𝑗; The highest level 𝑃𝑖 has received from all signers 𝑚, 𝑚,𝑗<𝑖