Quantitative Analysis on Coin Flipping Protocol

Coin tossing protocol allows two mutually trustful parties to generate relative fair random numbers. The performance and security of this protocol is of great importance where random numbers are used. This paper focuses on the analysis of the performance and security of the coin tossing protocol from quantitative perspective. Data for this study is collected using probabilistic model checking technique. The behavior of a single dice can be modeled as a discrete time Markov chain. The combination of two dice can be described as a Markov decision process since the cooperation of them will generate non-deterministic choices. This paper verifies the properties such as the generation of random results and the expected number of coin tossing. Experimental results show that the protocol can work well in normal situation. The expected number of coin tossing is 4 for a single dice, and 8 for the combination of two dice. As for the security, this paper assumes that one party has been seized by a malicious adversary, the behavior of the dice combination does have been greatly affected. The probability that the expected number of coin tossing within 8 steps cannot even exceed 0.11.