Randomness analysis of end-to-end delay in random forwarding networks

Random forwarding networks play a significant role in solving security and load balancing problems. As a random quantity easily obtained by both sender and receiver, the end-to-end delay of random forwarding networks can be utilized as an effective random source for cryptography-related applications. In this paper, we propose a mathematical model of Random forwarding networks and give the calculation method of end-to-end delay distribution. In exploring the upper limit of the randomness of end-to-end delay, we find that the end-to-end delay collision of different forwarding routes is the main reason for the decrease of end-to-end delay randomness. Some of these collisions can be optimized by better network deployment, while others are caused by some interesting network topology, which is unavoidable. For further analysis, we propose an algorithm to calculate the inevitable collision in random forwarding networks skillfully by using Symbol Matrix, and we give the optimal node forwarding strategy with the maximum randomness of the end-to-end delay for a given number of middle forwarding nodes and forwarding times. Finally, we introduce a specific application of generating symmetric keys by using the randomness of the end-to-end delay. Copyright 2022 Wang et al.