A Rational Threshold Signature Model and Protocol Based on Different Permissions

Table 1

Several models comparison.

Model	Verifiable	Bit Commitment	Resists conspiracy attack	Forward security	Permission	Convergence time	Range of parameters
Halpern and Teague	No	No	No	No	Different	𝑂5𝛼^3(0<𝛼<1)	𝛼^2𝛼^2+(1−𝛼)^2𝑈^+(𝜎𝑖,𝜎−𝑖)+(1−𝛼)^2𝛼^2+(1−𝛼)^2𝑈^−(𝜎𝑖,𝜎−𝑖)>𝑈(𝜎^∗𝑖,𝜎−𝑖)
Gordon and Katz	No	No	No	No	Different	𝑂1𝛽(0<𝛽<1)	𝛽≤𝑈(𝜎^∗𝑖,𝜎−𝑖)−𝑈^−(𝜎𝑖,𝜎−𝑖)𝑈^+(𝜎𝑖,𝜎−𝑖)−𝑈^−(𝜎𝑖,𝜎−𝑖)
Computable complete and perfect information dynamic game	Yes	Yes	Yes	Yes	Different	𝑂(𝜆)(𝜆>0)	𝑈𝜆<^(𝑟∗,𝑖)−𝜀𝑈^++(0,𝑖)(1−𝜀)∗𝑈(𝑟∗,𝑖)