Unsafe Mechanisms of Bluetooth, \(E_0\) Stream Cipher Cryptanalysis with Quantum Annealing

Due to Shor’s and Grover’s algorithms, quantum computing has become one of the fastest-evolving areas in computational science. Nowadays, one of the most interesting branches of quantum computing is quantum annealing. This paper presents the efficient method of transforming stream cipher E0 to the QUBO problem and then retrieving the Encryption Key of this cipher using quantum annealing. Comparably to other asymmetric and symmetric cryptographic algorithms, the presented transformation is efficient, requiring only 2,728 (2,751) logical variables for attack with 128 (129) consecutive keystream bits. According to our knowledge, it is the most efficient algorithm transformation with a 128-bit key. Moreover, we show that using current quantum annealers, one can embed the attack for E0 for 58 consecutive bits of keystream, from 128 (129), which are necessary for the attack’s first stage (second stage). Therefore, it is likely that it will be possible to embed E0 on available quantum annealers in the next few years.