Modelling Threshold Secret Sharing Schemes in Ad Hoc Networks

A threshold secret sharing scheme divides a secret key into multiple shares. The secret key can be constructed based on a certain number of shares, if the number is bigger than the threshold. Threshold secret sharing schemes increase the availability of service in ad hoc networks and avoid the single point of failure. Consequently, many security mechanisms have been proposed based on threshold secret sharing. However, research about how to choose an appropriate threshold is still missing. In this paper, we use fork/join queueing theories to develop a general model to evaluate the performance of a threshold secret sharing scheme in ad hoc networks. Specifically, we focus on the response time a requesting node needs to wait before it receives enough responded shares. Our proposed model allows one to numerically calculate the response time based on the threshold. It also provides a tool for people to choose an appropriate threshold when deploying a threshold secret sharing scheme in ad hoc networks.