Discrete Markov Chain Modeling for Efficient Key Processing in Anonymous Networks

Anonymous networks are designed for confidentiality, while simultaneously keeping the sender’s identity hidden from all nodes except the designated receiver. The decryption process requires the actual receiver to try out all possible keys stored in memory, thereby making computation very time-consuming, especially in noisy conditions where errors and hash collisions occur. This paper proposes a probabilistic algorithm to reduce the number of keys that must be processed, without compromising accuracy. The algorithm models the decryption process as a discrete Markov chain the Bernoulli formula in all its facets to calculate the probability of correct key detection and thereby determine an optimal stopping condition. Simulation results with 15 sources and an error probability of 0.15 exhibited up to a 14% reduction in the number of key trials required compared to brute-force search, with expected higher efficiencies for larger network sizes. This research contribution introduces a lightweight, scalable model that reduces computational cost, saves energy, and extends node lifetime. These findings stress the importance of providing a practical means for enhancing the performance of anonymous communication systems, especially while working under a resource-constrained environment such as the IoT and decentralized networks.