Optimization of rainbow tables for practically cracking GSM A5/1 based on validated success rate modeling

Abstract

GSM (Global System for Mobile Communications) communication is a ubiquitous technology developed by European Telecommunications Standards Institute for cellular network. To ensure the confidentiality of the user communication, it is protected against eavesdroppers by the A5/1 cryptographic algorithm. Various time-memory trade-off (TMTO) techniques have been proposed to crack A5/1. These techniques map the keystreams to the initial states of the algorithm at a reasonable success rate. Among TMTO techniques, rainbow table is an efficient method that allows a good trade-off between run-time and storage. The link between rainbow table parameters and the success rate is not well established yet. In view of this, a statistical success rate model is proposed in this paper, which takes various parameters of a given TMTO structure into consideration. The developed success rate model can be used to optimize the TMTO parameters for the best performance. Comprehensive experiments show that A5/1 can be broken with 43% success rate in 9 s using 1.29 TB rainbow tables, which is consistent with the theoretically predicted success rate. When using 3.84 TB rainbow tables, the extrapolated success rate is 81%.