An algebraic attack to the Bluetooth stream cipher E0

In this paper we study the security of Bluetooth stream cipher E0 from viewpoint it is a “difference cipher”, that is, defined by system explicit difference equations over finite field GF(2). This approach highlights some issues encryption such as invertibility its state transition map, special set 14 bits 132-bit which when guessed implies linear among other and finally small number spurious keys, with 83 bits, are compatible keystream about 60 bits. Exploiting these issues, implement an algebraic attack using Gröbner bases, SAT solvers Binary Decision Diagrams. Testing activities suggest version based on bases best one able to in 279 seconds Intel i9 CPU. To our knowledge, work improves any previous short keystream, hence fitting specifications.