An algebraic attack to the Bluetooth stream cipher E0
This work improves attacks on Bluetooth encryption, addressing a specific security problem for wireless communication protocols, though it is incremental as it builds on prior algebraic methods.
The paper tackles the security of the Bluetooth stream cipher E0 by identifying vulnerabilities such as invertibility issues and linear dependencies, leading to an algebraic attack using Gröbner bases that breaks E0 in about 2^79 seconds on an Intel i9 CPU.
In this paper we study the security of the Bluetooth stream cipher E0 from the viewpoint it is a "difference stream cipher", that is, it is defined by a system of explicit difference equations over the finite field GF(2). This approach highlights some issues of the Bluetooth encryption such as the invertibility of its state transition map, a special set of 14 bits of its 132-bit state which when guessed implies linear equations among the other bits and finally a small number of spurious keys, with 83 guessed bits, which are compatible with a keystream of about 60 bits. Exploiting these issues, we implement an algebraic attack using Gröbner bases, SAT solvers and Binary Decision Diagrams. Testing activities suggest that the version based on Gröbner bases is the best one and it is able to attack E0 in about 2^79 seconds on an Intel i9 CPU. To the best of our knowledge, this work improves any previous attack based on a short keystream, hence fitting with Bluetooth specifications.