Generalized Access Structure Congestion System

The k-out-of-n secret sharing schemes are effective, reliable, and secure methods to prevent a secret or secrets from being lost, stolen, or corrupted. The circular sequential k-out-of-n congestion (CSknC) system , based upon this type of secret sharing scheme, is presented for reconstructing secret(s) from any k servers among n servers in circular, sequential order. When a server is connected successfully, it will not be reconnected in later rounds until the CSknC system has k distinct, successfully connected servers. An optimal server arrangement in a CSknC system is determined in where n servers have known network connection probabilities for two states, i.e., congested, and successful. In this paper, we present: i) a generalized access structure congestion (GGammaC) system that is based upon the generalized secret sharing scheme, and ii) an efficient connection procedure for the GGammaC system in terms of the minimal number of server connection attempts. The k-out-of-n secret sharing schemes are considered as simple cases of the generalized secret sharing schemes. It implies that the GGammaC system is a more general system than the CSknC system. We established an iterative connection procedure for the new system. Simulation results are used to demonstrate that the iterative connection procedure is more efficient in terms of minimizing the number of connection attempts