Correlation Properties of the Bluetooth Combiner

Abstract

In its intended usage the lengths of the key stream sequences produced by the Bluetooth stream cipher E ₀ are strictly limited. In this paper the importance of this limitation is proved by showing that the Bluetooth stream cipher with 128 bit key can be broken in $\mathcal{O}(2^{64})$ steps given an output key stream segment of length $\mathcal{O}(2^{64})$. We also show how the correlation properties of the E ₀ combiner can be improved by making a small modification in the memory update function.