Practical Cryptanalysis of Bluetooth Encryption with Condition Masking

In this paper, we study the security of a general two-level E0-like encryption model and its instance, the real-world Bluetooth encryption scheme. Both unconditional and conditional correlation properties of the two-level model are investigated in theory and a key-recovery framework based on condition masking, that studies how to choose the condition to get better tradeoffs on the time/memory/data complexity curve, is refined. A novel design criterion to resist the attack is proposed and analyzed. Inspired by these cryptanalytic principles, we describe more threatening and real time attacks on two-level E0. It is shown that only the latest four inputs going into the FSM play the most important role in determining the magnitude of the conditional correlation and the data complexity analysis of the previous practical attacks on two-level E0 are inaccuracy. A new decoding method to improve the data complexity is provided. In the known-IV scenario, if the first 24 bits of $$2^{24}$$224 frames are available, the secret key can be reliably found with $$2^{25}$$225 on-line computations, $$2^{21.1}$$221.1 off-line computations and 4 MB memory. Then, we convert the attack into a ciphertext-only attack, which needs the first 24 bits of $$2^{26}$$226 frames and all the complexities are under $$2^{26}$$226. This is the first practical ciphertext-only attack on the real Bluetooth encryption scheme so far. A countermeasure is suggested to strengthen the security of Bluetooth encryption in practical applications.